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	<title>parachute - User contributions [en]</title>
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	<updated>2026-05-21T01:37:25Z</updated>
	<subtitle>User contributions</subtitle>
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	<entry>
		<id>https://mediawiki.aerodecelerator.org/index.php?title=File:Knacke_Fig4-1.jpg.jpg&amp;diff=457</id>
		<title>File:Knacke Fig4-1.jpg.jpg</title>
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		<updated>2024-06-10T18:52:08Z</updated>

		<summary type="html">&lt;p&gt;TuanHTruong: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;Illustration of streamlines&lt;/div&gt;</summary>
		<author><name>TuanHTruong</name></author>
	</entry>
	<entry>
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		<title>File:Knacke Fig4-1.png</title>
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		<updated>2024-06-10T18:47:22Z</updated>

		<summary type="html">&lt;p&gt;TuanHTruong: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;Diagram of flow streamlines to illustrate continuity law.&lt;/div&gt;</summary>
		<author><name>TuanHTruong</name></author>
	</entry>
	<entry>
		<id>https://mediawiki.aerodecelerator.org/index.php?title=Recovery_System_Design&amp;diff=42</id>
		<title>Recovery System Design</title>
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		<updated>2024-05-08T15:26:46Z</updated>

		<summary type="html">&lt;p&gt;TuanHTruong: /* 7.2.1 Landing Analysis */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;= DESIGN OF A PARACHUTE RECOVERY AND LANDING SYSTEM =&lt;br /&gt;
This chapter deals with the design of a parachute recovery and landing attenuation system for a military reconnaissance drone. The prime emphasis in the design of this system is on undamaged recovery of the drone from the total flight performance envelope during the development and test phase, on undamaged recovery after a completed mission during military operations, and on multiple use of the recovery system. An engineering team conducts performance and system analyses and chooses what recovery concept to use, what types of parachutes to select for high-speed deceleration and for final recovery, and what impact-attenuation system is best for the particular application. This chapter covers the selection process for concepts and components. Different engineers may make different selections based on experiences with particular types of parachutes or deployment concepts; experience is always a viable reason for selecting a particular approach. However, using the selection criteria shown in Figure 2-6. the designer must put reliability of operation, undamaged recovery, reusability of the landing system, and minimum weight and volume at the top of the list of requirements. &lt;br /&gt;
&lt;br /&gt;
== 7.1 REQUIREMENTS ==&lt;br /&gt;
=== 7.1.1 System Requirements ===&lt;br /&gt;
&lt;br /&gt;
An unmanned air vehicle used for military reconnaissance must be recovered after a completed mission in rough terrain, undamaged and ready for multiple reuse. The recovery system must be able to &lt;br /&gt;
&lt;br /&gt;
# Recover the air vehicle after the completed mission when the vehicle has landed in rough terrain at altitudes from sea level to 5000 feet.&lt;br /&gt;
# Recover the drone during the engineering test phase from all controlled and uncontrolled flight conditions.&lt;br /&gt;
# Serve as a range-safety device to prevent the air vehicle from leaving the boundaries of the test range.&lt;br /&gt;
&lt;br /&gt;
The air vehicle has a takeoff weight of 7200 pounds and a landing weight, after the i completed mission, of 4800 pounds. Undamaged landing shall be possible in rough terrain with rocks up to 8 inches in diameter. Replacement parts and refurbishment cost shall be kept to a minimum.  &lt;br /&gt;
&lt;br /&gt;
=== 7.1.2 Requirements for Normal Operation ===&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|Drone weight at recovery after completed mission&lt;br /&gt;
|W&amp;lt;sub&amp;gt;d&amp;lt;/sub&amp;gt; = 4800 lb&lt;br /&gt;
|-&lt;br /&gt;
|Recovery velocity&lt;br /&gt;
|v&amp;lt;sub&amp;gt;o&amp;lt;/sub&amp;gt; = 150 to 200 KEAS&lt;br /&gt;
|-&lt;br /&gt;
|Minimum recovery altitude&lt;br /&gt;
|H&amp;lt;sub&amp;gt;o&amp;lt;/sub&amp;gt; = 2000 ft above ground level (AGL)&lt;br /&gt;
|-&lt;br /&gt;
|Maximum ground level&lt;br /&gt;
|H = 5000 ft&lt;br /&gt;
|-&lt;br /&gt;
|Maximum allowable total parachute force&lt;br /&gt;
|F&amp;lt;sub&amp;gt;o&amp;lt;/sub&amp;gt; = 16,000 lb&lt;br /&gt;
|-&lt;br /&gt;
|Maximum allowable impact deceleration at landing&lt;br /&gt;
|a = 9.0 ''g''&amp;lt;nowiki/&amp;gt;'s&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
=== 7.1.3 Requirements for Emergency Operation ===&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|Drone weight at takeoff &lt;br /&gt;
|W&amp;lt;sub&amp;gt;dma&amp;lt;/sub&amp;gt; = 7200 lb&lt;br /&gt;
|-&lt;br /&gt;
|&lt;br /&gt;
|&lt;br /&gt;
|-&lt;br /&gt;
|&lt;br /&gt;
|&lt;br /&gt;
|} &lt;br /&gt;
&lt;br /&gt;
Emergency operation includes recovery during the test phase from takeoff to landing and also includes recovery for range-safety reasons. &lt;br /&gt;
&lt;br /&gt;
Drone weight at takeoff .................................. Wdma = 7200 lb &lt;br /&gt;
&lt;br /&gt;
Maximum recovery velocity at mean sea level (MSL) ................................... vo = 490 KEAS &lt;br /&gt;
&lt;br /&gt;
Maximum recovery velocity at 38,000 to 50,000 ft altitude ........................................ vo = 1.5 Mach &lt;br /&gt;
&lt;br /&gt;
Maximum dynamic pressure .............................. qmm = 812 lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; &lt;br /&gt;
&lt;br /&gt;
Maximum allowable parachute force ........................ F0 = 22,000 lb  &lt;br /&gt;
&lt;br /&gt;
=== 7.1.4 Requirements Analysis ===&lt;br /&gt;
Three primary requirements pace the design of the recovery system: &lt;br /&gt;
&lt;br /&gt;
1. The drone must be able to land in rocky but level terrain without damage. &lt;br /&gt;
&lt;br /&gt;
2. Refurbishment cost and time shall be kept to a minimum. &lt;br /&gt;
&lt;br /&gt;
3. Recovery must be possible from all flight conditions during the flight test phase, including cases where the out-of-control drone flies off the range.  &lt;br /&gt;
&lt;br /&gt;
== 7.2 LANDING ANALYSIS AND IMPACT-ATTENUATION SYSTEM ==&lt;br /&gt;
&lt;br /&gt;
=== 7.2.1 Landing Analysis ===&lt;br /&gt;
Three known recovery concepts prevent damage during landing in rocky terrain: &lt;br /&gt;
&lt;br /&gt;
1. Midair retrieval.&lt;br /&gt;
&lt;br /&gt;
2. Dual air bags or dual frangibles.&lt;br /&gt;
&lt;br /&gt;
3. Retrorockets combined with small, nondeflatable air bags.&lt;br /&gt;
&lt;br /&gt;
The need for retrieval helicopters or retrieval aircraft makes Method 1, midair retrieval, impractical. The other two methods are affected by the deceleration distance required to meet the 9-g limit. &lt;br /&gt;
&lt;br /&gt;
In section 6.8 of this manual, the required deceleration distance(s) is determined to be&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;s=\frac{{V_{e_1}}^2-{V_{e_2}}^2}{2g(n\eta-1)}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;{V_{e_1}}&amp;lt;/math&amp;gt; = velocity of the drone descending on the parachute (rate of descent), ft/s&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;V_{e_2}&amp;lt;/math&amp;gt; = permissible impact velocity, ft/s&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;g&amp;lt;/math&amp;gt; = acceleration of gravity, ft/s2&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\eta&amp;lt;/math&amp;gt; = effectiveness of the impact attenuation system used, dimensionless&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;n&amp;lt;/math&amp;gt; = allowable impact deceleration, ratio &amp;lt;math&amp;gt;n=\frac{a}{g}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Figure 6-68 of Chapter 6 shows the range of various impact attenuation systems as a function of rate of descent and allowable ground impact deceleration. The information indicates that air bags may be the most practical concept for this application. A cursory analysis indicates that a rate of descent of 25 ft/s at 5000 fee: altitude will result in a close to optimum weight ratio of the combined parachute air bag system (see Figure 6-83). Properly designed air bags will have an effectiveness of 65% as shown in the stroke-pressure diagram in Figure 6-78 and allow ground contact or final velocity of close to 0 ft/s.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
With these assumptions, the required effective air bag deceleration stroke is obtained&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;s=\frac{25^2-00}{(2\cdot 32.174)(9.0\cdot 0.65-1)} = 2.0\ ft\ or\ 24\ in.&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
This deceleration distance is too short for a parachute retrorocket system because of the required timing accuracy and rocket burning time. Retrorocket systems are most practical for deceleration distances greater than 4 or 5 feet. Crushable and frangible impact attenuators are suitable for deceleration distances of less than 15 inches. Air bag systems work best for deceleration distances of 24 to 48 inches. The original assumption that an air bag concept maybe the most practical approach for this air vehicle is therefore confirmed.&lt;br /&gt;
&lt;br /&gt;
=== 7.2.2 Impact Attenuator System ===&lt;br /&gt;
The design of impact attenuator systems is discussed in section 6.8 of this manual. Figure 7-1 shows the reconnaissance drone and the air-bag attenuator systems that consist of two deflatable, two-compartment wing-bag bags (A); a single-compartment, deflatable nose bag (B); and a nondeflatable nose-buffer bag (C). The wing bags, the primary energy absorbers, need the already calculated 24-inch effective-deceleration stroke. For design reasons, 33 inches must be added to the bag height, 19 inches for the distance from the wing underside to the underside of the jet ,i rlucts, 10 inches for ground clearance, and 4 inches for bag bottom curvature. These additions result in a total bag height of 57 inches. To ensure landing stability, an air bag height-to-diameter ratio of 1.25 is selected for the two wing bags, resulting in a bag diameter of 48 inches. The cross-hatched lower part of the two wing bags (see Figure 7-1) deflates at impact, but the upper part stays inflated and keeps the drone off the ground. The nose bag, B, helps to absorb the impact and deflates, and the nose of the drone comes to rest on the nondeflatable buffer bag, C. All air bags are inflated from 3000 psi nitrogen containers using aspirators for a 50/50 nitrogen air mixture. The air bags are prepressurized to 2 psi for full bag inflation prior to landing. Multiple blowout valves consisting of staggered blowout rubber disks around the circumference of the air bags control the bag deflation to stay within the 9-g deceleration limit.&lt;br /&gt;
&lt;br /&gt;
The weight of the impact-attenuation system-air bags, nitrogen containers, plumbing, and A/C containers-is estimated from section 6.7 to be 2.2% of the total drone weight, or 105.6 pounds. The air bags should be stored in containers that can be easily removed from the drone for repacking. Air bags must be deployed after the main parachutes are fully open to prevent air-bag damage caused by high dynamic pressure. Air-bag deployment begins with simultaneous pyroejecting of the removable air-bag-container covers and opening of the nitrogen-container valves. The wing bags, the primary nose bag, and the nose-buffer bag inflate. At ground contact, the bags compress, increasing the pressure inside the bags. At a preselected pressure level, the blowout valves (rubber disks, metal disks, or rubber-type sleeves) open and limit the maximum drone deceleration to the preselected level.&lt;br /&gt;
&lt;br /&gt;
== 7.3 MAIN PARACHUTE SYSTEM ==&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.3.1 Main Parachute System Requirements&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Section 2.4 defines the criteria for parachute type selection. Requirements for low weight and volume rule out the low-drag slotted parachutes (ribbon, ringslot, and ringsail) as well as guide-surface and cross parachutes (see Tables 5.2 and 5.3). Parachute deployment past the vertical stabilizer rules out a single parachute in favor of a cluster of two parachutes deployed independently left and right of the vertical stabilizer. No cluster experience is available with annular or cross parachutes, and no reefing experience is available with annular parachutes. Cross parachutes cannot be reefed to the low reefing ratios required for this application. Extended-skirt and polyconical parachutes have been used successfully in clusters of large, reefed parachutes.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7-6&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
A cluster of two conical full extended skirt parachutes is most suitable for this system. In&lt;br /&gt;
&lt;br /&gt;
section 5.2, Figures 5.24 and 5-25 show that properly designed extended-skirt parachutes have&lt;br /&gt;
&lt;br /&gt;
drag coefficients equal to 0.8 to 0.9 in the 20- to 25-ft/s rate of descent range. Available data&lt;br /&gt;
&lt;br /&gt;
(Reference 5.23) indicate that a cluster of two extended-skirt parachutes is sufficiently stable&lt;br /&gt;
&lt;br /&gt;
for use with air bags. Extended-skirt parachutes have a low opening-force coefficient of 1.4,&lt;br /&gt;
&lt;br /&gt;
compared to an opening-force coefficient of 1.8 for conical and triconical parachutes.&lt;br /&gt;
&lt;br /&gt;
Extended-skirt parachutes can also be reefed to low reefing ratios, a requirement for final&lt;br /&gt;
&lt;br /&gt;
descent parachutes (see Chapter 5, Figure 5-72).&lt;br /&gt;
&lt;br /&gt;
73.3 Parachute Diameter&lt;br /&gt;
&lt;br /&gt;
The rate of descent at 5000 feet altitude was selected to 25 ft/s (see section 7.3.1). The&lt;br /&gt;
&lt;br /&gt;
equivalent rate of descent at sea level is&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The drag coefficient, CDo, for a conical full extended skirt parachute with a 23.2-ft/s rate of&lt;br /&gt;
&lt;br /&gt;
descent and a suspension-line ratio, [.e/Do, of 1.0 is obtained from Figure 5-25&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
A suspension-line ratio of 1.15 is selected. This is the longest practical length for extended skirt&lt;br /&gt;
&lt;br /&gt;
parachutes (see Figure 5-20).&lt;br /&gt;
&lt;br /&gt;
The length of the riser, Lr, depends on its installation in the drone; the riser should be long&lt;br /&gt;
&lt;br /&gt;
enough to extend beyond the fuselage and vertical stabilizer of the drone (see Figure 7-2),&lt;br /&gt;
&lt;br /&gt;
which gives the final configuration of the parachute cluster, including risers and parachutes.&lt;br /&gt;
&lt;br /&gt;
7.3.4 Parachute Deployment System&lt;br /&gt;
&lt;br /&gt;
A cluster of two main parachutes is selected and deployed left and right of the vertical&lt;br /&gt;
&lt;br /&gt;
stabilizer to avoid hang-up or damage of a single parachute by the vertical stabilizer. Each&lt;br /&gt;
&lt;br /&gt;
parachute needs its own extraction and deployment system to properly deploy past the&lt;br /&gt;
&lt;br /&gt;
stabilizer and to avoid interference with the other main parachute during deployment and&lt;br /&gt;
&lt;br /&gt;
inflation.&lt;br /&gt;
&lt;br /&gt;
TWo fast-opening extraction parachutes are used on each main parachute. Stable&lt;br /&gt;
&lt;br /&gt;
parachutes will minimize interferenc, during deployment. Experience with past recovery&lt;br /&gt;
&lt;br /&gt;
systems has shown that the most positive deployment is obtained by forced ejection of the&lt;br /&gt;
&lt;br /&gt;
extractiou or pilot chutes into good airflow past the vertical stabilizer by either mortar or&lt;br /&gt;
&lt;br /&gt;
drogue gun ejection. A mortar can eject large, heavy parachutes but creates large leaction&lt;br /&gt;
&lt;br /&gt;
forces and needs considerable space for installation. Drogue gun ejection is effective, but is&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
limited to the deployment of small, lightweight parachutes such as pilot chutes. Drogue gun ejected pilot chutes are selected for initiating main parachute deployment. To ensure proper&lt;br /&gt;
&lt;br /&gt;
clearance of the vertical stabilizer, the pilot chutes are ejeLted 45 degrees upward, backward&lt;br /&gt;
&lt;br /&gt;
and outward past the vertical stabilizer. The parachute installation in the drone fuselage&lt;br /&gt;
&lt;br /&gt;
requires cross-wind deployment and therefore forced ejection of the main parachute&lt;br /&gt;
&lt;br /&gt;
deployment bags. Four different methods have been used successfully to accomplish forced&lt;br /&gt;
&lt;br /&gt;
ejection: (1) using ejector springs enclosed in a textile cylinder. (2) gas-inflating nonporous&lt;br /&gt;
&lt;br /&gt;
ejector bags, (3) catapulting the bag out of the compartment, or (4) using a lift-web&lt;br /&gt;
&lt;br /&gt;
arrangement as discussed in section 6.1.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The deployment system selected consists of a drogue gun deployed pilot chute, an&lt;br /&gt;
&lt;br /&gt;
extraction parachute, and a main parachute deployment bag lifted from the parachute&lt;br /&gt;
&lt;br /&gt;
compartment by lift webs. When the hinged compartment doors open, two drogue gun slugs&lt;br /&gt;
&lt;br /&gt;
are fired 45 degrees upward and aft; each slug deploys a pilot chute sufficiently behind the&lt;br /&gt;
&lt;br /&gt;
drone into good airflow. These pilot chutes in turn extract two extraction chutes stowed on top of the main parachute deployment bags. The extraction chutes extract and deploy the two main 0&lt;br /&gt;
&lt;br /&gt;
parachutes left and right of the vertical stabilizers. Lift webs and unsymmetrical bag handles&lt;br /&gt;
&lt;br /&gt;
lift the main parachute bags out of the drone compartment and extract the main parachute&lt;br /&gt;
&lt;br /&gt;
past the vertical stabilizer (see Figure 7-3)&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.3.5 Extraction Parachute Assembly&lt;br /&gt;
&lt;br /&gt;
The two extraction parachutes must properly deploy the two main parachutes. The size of&lt;br /&gt;
&lt;br /&gt;
the extraction parachutes and their location in the wake of the drone is determined as follows:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
A stable, 7.4-foot-diameter ringslot parachute is selected. &lt;br /&gt;
&lt;br /&gt;
The weight of the ringslot extraction parachute can be estimated from section 6.7 to 2.5 pounds, and the weight of the extraction parachute assembly including riser and deployment bag to 1.5 . 2.5 pounds = 3.75 pounds. The weight of a single 72.7-foot-diameter main parachute, as determined from section 6.7, is 54 pounds. This weight estimate assumes an efficiently designed main canopy that has a combination of tape and radial seams to carry the radial loads and has other, similar weight-saving design features. The arrangement of the extraction parachute in relation to the drone is shown in Figure 7-5. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.3.6 Pilot Parachute Assembly &lt;br /&gt;
&lt;br /&gt;
The extraction parachute assembly weight of 3.75 pounds is too heavy to be deployed by a drogue-gun slug; therefore, a small pilot chute is selected for initial deployment by the drogue-gun slug. This pilot chute, in turn, will deploy the extraction parachute.&lt;br /&gt;
&lt;br /&gt;
Evaluation of past good and poor deployments has led to the rule that the extraction force of the pilot chute should be greater than or equal to four times the weight of the unit to be extracted; in this case, the extraction parachute assembly. So that the pilot chute has enough force, a pilot chute is selected that will produce, at the minimum deployment speed of 150 KEAS, an extraction force equal to five times the weight of the extraction parachute assembly: 5. 3.75 pounds - 18.75 pounds. The minimum dynamic pressure at 150 KEAS is&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.3.7 Main Parachute Forces&lt;br /&gt;
&lt;br /&gt;
7.3.7.1 Requirements &lt;br /&gt;
&lt;br /&gt;
Drone weight ............................................. W D = 4800 lb&lt;br /&gt;
&lt;br /&gt;
Maximum deployment speed .............................. vo = 200 KEAS &lt;br /&gt;
&lt;br /&gt;
Minimum deployment speed ........................ Vo minimum = 150 KEAS &lt;br /&gt;
&lt;br /&gt;
Maximum allowable total parachute force (two main parachutes) ................................... FT = 16,000 lb &lt;br /&gt;
&lt;br /&gt;
Deployment altitude .................................. H = 2000 to 7000 ft &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.3.7.2 Velocity-Altitude Profile &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Section 5.5 states that the maximum opening force of the main parachute occurs at maximum deployment altitude. Figure 7-8 shows a velocity-altitude-versus-time profile for a typical vehicle recovery system. &lt;br /&gt;
&lt;br /&gt;
The maximum dynamic pressure, qo, occurs at the 200-KEAS deployment velocity &lt;br /&gt;
&lt;br /&gt;
2. The Pflanz method is quite accurate for all conditions including high altitude, but neglects the effect of gravity. Parachutes opened in vertical descent will have a 1-g (one weight unit) higher force than calculated. It is necessary to calculate the canopy filling times for the various reefed stages (see section 5.4.3) and to determine the drag-area-versus-time profile for the specific parachute (see section 5.4.4). This method permits the investigation of variations in filling times and drag-area-versus-time profiles. &lt;br /&gt;
&lt;br /&gt;
3. The force-trajectory-time computer method includes the effects of altitude, gravity, and changing trajectory angle. This method requires determination of a drag-area-versus-time profile for the entire parachute opening sequence (see Figure 5-52). Computers permit multiple runs with changes in times, drag-area-versus-time profiles, starting velocities, and altitudes.&lt;br /&gt;
&lt;br /&gt;
7.3.7.4 Reefed Opening Forces&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
To  save trajectory time, the reef-d pardchute is disreefed at a dynamic pressure 10 to 20% higher than the terminal reefed dynamic pressure. Therefore,&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Results of changing the canopy inflation time, tf, and the drag-area-versus-time profile, n, are shown in Thble 7-2. Reference 5-76, the Pflanz report, provides a more detailed study of the effect of canopy fill time and drag-area-increase-versus-time profile on the magnitude of the parachute force&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Force-Trajectory-Time Computer Method &lt;br /&gt;
&lt;br /&gt;
The program established oy NWC determines as a function of time the parachute forces, the vehicle deceleration, and the space-positioning (trajectory) data in a two-axis system. The method requires a drag-area-versus-time profile for the individual parachutes and the total vehicle system (Figure 7-9). This profile was previously shown in Figure 5-52. Figure 7-9 includes the change in air-vehicle drag caused by the change in vehicle attitude during the parachute opening process&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.3.7.6 Comments on Calculated Opening Forces 1. The reefed opening force for the single parachute is higher than thie contractor-requested maximum allowable force per parachute of 8000 pounds&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
2. The average disreef force is approximately 1500 pounds lower than the reefed force. Therefore, it appears logical to lower the reefed force and increase the disreef force. Although this adjustment probably cannot be made within the 8000-pound limit, 8500 pounds appears to be an obtainable goal. &lt;br /&gt;
&lt;br /&gt;
3. To meet the contractor requirement of an 8000-pound maximum force limit per parachute, two-stage reefing is required. &lt;br /&gt;
&lt;br /&gt;
4. It appears practical to determine in drop tests if a 2.0 to 2.1% reefed drag area can be obtained. This drag area would decrease the reefed opening force and somewhat increase the disreef force. However, reaching an average maximum force of less than 8000 pounds appears doubtful. &lt;br /&gt;
&lt;br /&gt;
5. In the calculations, both parachutes are assumed to have equal opening forces. In reality, opening forces of the two parachutes can differ because of variations in filling time. lead-ann-lag chute behavior caused by blanketing, and resultant nonuniform canopy inflation. 7-22 NWC TP 6575 &lt;br /&gt;
&lt;br /&gt;
The fast-opening Apollo ringsail-type main parachutes had a load distribution among the three parachutes of 40-40-20. The individual parachutes, therefore, had to be overdesigned in a 40/33 ratio. However, the total parachute force load taken by the vehicle hard points did not exceed the calculated average load because of the high-low variation of the individual parachutes. &lt;br /&gt;
&lt;br /&gt;
The two slower-opening extended-skirt parachutes used for this application are more uniform in their load distribution. A cursory analysis of available test data indicates that a 55/45 load distribution between the two parachutes and a no-overload condition for the vehicle hard points should be an acceptable load distribution. &lt;br /&gt;
&lt;br /&gt;
A contractor-subcontractor agreement is required to determine whether the individual parachutes should be designed for the 55/45 load variation or whether this overload can be accommodated by the 1.5 safety factor and the additional safety provided by the normal overstrength of textile specification materials.&lt;br /&gt;
&lt;br /&gt;
7.3.7.7 Snatch Forces &lt;br /&gt;
&lt;br /&gt;
The snatch force is caused by the acceleration of the mass of the parachute assembly to the velocity of the forebody (drone). A canopy, partially inflated at line stretch, increases the mass of the parachute by the mass of the air included in the canopy; this can increase the snatch force (mass shock) considerably.  &lt;br /&gt;
&lt;br /&gt;
Two  principal rules should be followed to keep the snatch force within allowable limits.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
1. Keep the parachute canopy closed until line (canopy) stretch occurs by use of a deployment bag o! %kirt restrictor.&lt;br /&gt;
&lt;br /&gt;
2. Accelerate I!: mass of the parachute assembly in incremental steps. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Known means of accomplishing these goals are discussed in Chapter 6.1. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The difference between a poor deployment and a deployment that accomplishes the first rule and partially accomplishes ' second is illustrated in Figure 5-54, which shows snatch and opening forces for the C-9 p. tchute with and without the quarter deployment bag. The deployment method outlined in ! tilon 7.3.4 should hold snatch forces at a level below the parachute opening forces. &lt;br /&gt;
&lt;br /&gt;
A method for calculating ,tch forces is described in Reference 2.2, the 1963 edition of the USAF parachute handbook. : nreferred method for calculating parachute deployment. including the snatch force, is cont.iiiici in J. W Purvis's AIAA paper, &amp;quot;Improved Prediction of Parachute Line Sail During I incs-First Deployment&amp;quot; (Reference 5.86)&lt;br /&gt;
&lt;br /&gt;
7.3.8 Parachute Stress Analysis &lt;br /&gt;
&lt;br /&gt;
7.3.8.1 Parachute Design Data&lt;br /&gt;
&lt;br /&gt;
A total parachute assembly is shown in Figure 7-10.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.3.8.2 Parachute Forces &lt;br /&gt;
&lt;br /&gt;
The maximum reefed opening force, FR, is 9255 pounds. The maximum disreef opening force, F., is 7404 pounds. The maximum design force for stressing the parachute assembly, FI, is 9255 pounds.&lt;br /&gt;
&lt;br /&gt;
The forces obtained in computer runs are selected as the most accurate forces for stressing the parachute assembly and its components. Based on multiple computer runs, a diligent choice must be made for the most likable forces.&lt;br /&gt;
&lt;br /&gt;
7.3.83 Main-Parachute Safety and Design Factors &lt;br /&gt;
&lt;br /&gt;
Section 6.4 is used as a guide for selecting the safety, load, loss, and design factors in Table 7.4&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
1. Connection of suspension lines to riser legs and drone hardpoints is made easier if the number of suspension lines are a multiple of 4 or 8. &lt;br /&gt;
&lt;br /&gt;
2. The gore at the skirt should not be wider than 3.5 feet for packing reasons. &lt;br /&gt;
&lt;br /&gt;
3. The canopy should have no fewer than 12 gores to avoid gore distortion during inflation. &lt;br /&gt;
&lt;br /&gt;
4. Radial ribbons or radial seams should not overlap at the vent; overlapping causes bunching of material and associated sewing problems. &lt;br /&gt;
&lt;br /&gt;
5. The strengths of available suspension-line types may affect the gore selection. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Table 7-5 shows the required suspension line strength and the resultant gore width as functions of the number of gore/suspension lines used. &lt;br /&gt;
&lt;br /&gt;
7-25 NWC TP 6575&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The width of the goie of the skirt on conical, full-extended-skirt (CFES) parachutes is about 85% of the maximum gore width, Eo. Sixty-four suspension lines are selected in accordance with MIL-C-7515, TIpe XI, with 300-pound tensile strength. This selection provides a margin of safety (MS) of&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The suspension line will be attached to the canopy skirt in a loop connection. &lt;br /&gt;
&lt;br /&gt;
7.3.8.5 Canopy Stress&lt;br /&gt;
&lt;br /&gt;
No precise method has been d.-veloped for calculating the stress in a circular, solid-material, bias-construction canopy.&lt;br /&gt;
&lt;br /&gt;
Section 6.4 describes a semi-empirical method for determining the required fabric strength of a solid material canopy in pounds per unit width using the stress in a pressure vessel as an analogy. The stress in a cylindrical vessel, expressed as force per unit length, is&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
where p is the pressure in the cylindrical vessel and r is the vessel radius. Using this analogy and considering the canopy gore as part of a pressure vessel, the required material strength of the canopy per unit width is obtained&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The maximum stress actually occurs during reefed inflation because of the smaller inflated diameter:&lt;br /&gt;
&lt;br /&gt;
7.3.8.6 Canopy Reinforcing Tapes &lt;br /&gt;
&lt;br /&gt;
1. Skirt Tape. The skirt tape should Iv. equal or greater in strength than the individual suspension lines but not less than 1000 pounds, and 1-inch-wide tape should be used for parachutes larger than 20 feet in diameter. &lt;br /&gt;
&lt;br /&gt;
The nylon tape selected is 1-inch-wide MIL-T-5038, Type IV, with 1000-pound strength. Proper connection of the skirt tape to the radial seam (tape) and the suspension line must be ensured.&lt;br /&gt;
&lt;br /&gt;
2. Vent Tape. From the geometric design of the parachute vent (Figure 7-11). the force in the vent tape, FVT, is calculated&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
A 1-inch-wide, 4000-pound webbing (MIL-W-5625) or 7/8-inch-wide, 3100-pound webbing (MIL-W-5625) is selected. &lt;br /&gt;
&lt;br /&gt;
3. Vent Lines. The strength of the vent line- should be equal to or greater than 60% of the strength of the radials&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.3.8.7 Design of Radials &lt;br /&gt;
&lt;br /&gt;
The following four types of radial designs are in use: &lt;br /&gt;
&lt;br /&gt;
1. Radial seams with suspension lines running in channels over the canopy and attached at the vent and the skirt as on the canopy of the C-9 personnel parachute. &lt;br /&gt;
&lt;br /&gt;
2. Suspension lines running on top of the radials over the canopy and sewn at full length to the canopy as on many heavy-duty ribtx'n parachutes. &lt;br /&gt;
&lt;br /&gt;
3. Radial tapes sewn on top of or inside the radial seams, and suspension lines attached to the radial tapes by sewing or by skirt loops (NB-7 and T-10 canopies). &lt;br /&gt;
&lt;br /&gt;
4. Radial ribbons on ribbon parachutes designed to take the total radial load with suspension lines sewn onto d e radials or connected by a skirt loop. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The following are some comments on the design of radials: &lt;br /&gt;
&lt;br /&gt;
1. Making the strength of the radials 1:qtlal to 80% of the strength of the suspension lines has been satisfactory on thousands of ribbon parachutes. &lt;br /&gt;
&lt;br /&gt;
2. When tapes or suspension lines are sewn at full length to the radials, care must be taken that fullness in the radials ensures that the radial tapes or the suspension lines are the primary load carrying members. For an explanation of fullness, see section 6.6.4. &lt;br /&gt;
&lt;br /&gt;
3. Uniform material distribution is of utmost importance when sewn tapes or lines are used for radial reinforcemetnt. &lt;br /&gt;
&lt;br /&gt;
For the radial design of the main parachute, we use a tape with 80% strength of the suspension lint (0.8. 300 lb - 240 Ib) sewn on top of the radial scam. A 250-pound strength, 'A-inch-wide tape is selected in accordance with MIL-T-5038, 7ýpe III. Thpe and radial seams are marked every 24 inches for proper material distribution&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.3.8.8 Check for Proper Gore Fullness &lt;br /&gt;
&lt;br /&gt;
When the first parachute of a new design has been completed in the manufacturing shop, a gore fullness check in accordance with Figure 7-12 should be conducted. A slight amount of slack should be noticeable in the canopy fabric in both directions when all four corners of a gore are pulled radially outward. Slack indicates that the main loads are carried by the radials and reinforcing tapes and not by the canopy fabric. Stress folds in the canopy indicate faults in the design or manufacture of the parachute&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
’&lt;br /&gt;
&lt;br /&gt;
This is a large vent opening for a reefed parachute. Several criteria may be used to determine the size of the canopy vent as follows: &lt;br /&gt;
&lt;br /&gt;
1. Unreefed parachutes with vents up to 1% of the canopy surface area, So, have been operated successfully.&lt;br /&gt;
&lt;br /&gt;
2. Reefed parachutes require a vent diameter, DV, smaller than the reefing line circle, diameter DR, of the parachute; Dv is smaller than DR (see section 5.6, Figure 5-66). &lt;br /&gt;
&lt;br /&gt;
3. The radials at the vent should not overlap. A 1-inch free space between radials is desirable (see Figure 7-14)&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Stress in the canopy gore area can be relieved by making the gore at the vent 10% wider than the calculated gore dimension, ev. Therefore, ev* - 1.1 . ev - 1.1(1.6) = 1.76 inches. The vent tape is sewn to the vent at the original ev dimension, thereby gathering the vent 10% and creating a stress-relieving arcing in the gore fabric next to the vent. See Figure 7-15 for an example of final gore dimensions.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.3.10 Pocket Bands The pocket bands used on every gore make canopy inflation more uniform and eliminates long and short filling times. A narrow tape is used as the pocket band, which will :ot affect the average length of the canopy filling time. Data on the dimensioning of pocket bands are given in section 6.4. As shown in Figure 7-16, the pocket band dimensions are&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The diameter of the reefing line circle, DR, is larger than the 3.64-foot vent diameter of the canopy, Dv. This difference in diameters is an important design requirement (see section 7.3.9).&lt;br /&gt;
&lt;br /&gt;
7.3.11.2 Strength of the Reefing Line&lt;br /&gt;
&lt;br /&gt;
The force in the reefing line is determined according to information in section 5.6.8. Test items 22 and 23 in Figure 5-76 closely resemble the main parachute used here. A reefing-lineforce-to-reefed-parachute-force ratio of 2.5% is selected for this assembly. Therefore, the force in the reefing line is&lt;br /&gt;
&lt;br /&gt;
(0.025)FR = 0.025(9255 Ib) = 231.4 lb&lt;br /&gt;
&lt;br /&gt;
The design factor, DF, for the reefing system was determined in section 7.3.8, Table 7-4, to be 2.74.&lt;br /&gt;
&lt;br /&gt;
== 7.4 HIGH-SPEED DROGUE CHUTE ASSEMBLY ==&lt;br /&gt;
7.4.1 Requirements &lt;br /&gt;
&lt;br /&gt;
The following operational requirements govern the design of the first-stage drogue chute:&lt;br /&gt;
&lt;br /&gt;
1. The drone must be recoverable from any conceivable flight condition during the engineering test phase. &lt;br /&gt;
&lt;br /&gt;
2. An out-of-control drone or a drone that loses radio contact with the controller must be prevented from flying off the range. Recovery is initiated by an independent range signal. This type of recovery requires a high-speed deceleration parachute that can be deployed and operated when the drone is moving at maximum speed, or is in a spin, or during any other abnormal flight condition. &lt;br /&gt;
&lt;br /&gt;
This type of recovery established the following requirements for the type and size of the drogue chute:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
1. The drogue chute must have reliable operation in the velocity range from 200 knots at sea level to Mach 1.5 at 50,000 feet.&lt;br /&gt;
&lt;br /&gt;
2. Stability must be better than :: 3 degrees. &lt;br /&gt;
&lt;br /&gt;
3. Minimum weight and volume is mandatory. &lt;br /&gt;
&lt;br /&gt;
4. The drogue chute must be able to decelerate the drone to the permissible opening speed of the main parachute assemblies.&lt;br /&gt;
&lt;br /&gt;
5. The drogue chute must be suitable for the operational environment. Figure 7-17 shows the altitude-velocity flight envelope of the drone.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.2 Drogue Chute Selection &lt;br /&gt;
&lt;br /&gt;
Tables 5-1 through 5-5 in Chapter 5 list commonly used parachute types. Table 7-6 evaluates possible drogue chute candidates. Of the parachute candidates, only the conical ribbon and the hemisflo ribbon have been used successfully for similar applications.&lt;br /&gt;
&lt;br /&gt;
A 25-degree conical ribbon parachute is selected for this application. The conical ribbon parachute meets all requirements and has a higher subsonic drag coefficient than the equally&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.3 Required Drogue Chute Diameter &lt;br /&gt;
&lt;br /&gt;
The size of the fully open drogue chute is determined by the requirement that it must decelerate the 7200-pound drone to the allowable opening speed of the main parachute, which is governed by the requirement that the opening force of the two main parachutes must stay within the 9350-pound-per-chute limit established for the 200-knot opening speed of the 4800-pound drone. &lt;br /&gt;
&lt;br /&gt;
A preliminary calculation shows that a terminal velocity of about 175 KEAS is required to limit the opening load of the reefed main parachutes to 9350 pounds. A 13- to 14-footdiameter drogue chute is needed to meet this requirement. &lt;br /&gt;
&lt;br /&gt;
To reach 175 KEAS at main parachute line stretch, the drogue chute will be disconnected by an aneroid sensor at about 7000 feet mean sea level (MSL) while descending vertically from high altitude. The drone will free-fall for 0.8 second until main parachute line stretch occurs; the free-fall causes a 10-knot increase in velocity. In addition, the changing density, p, results in&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
NWC TP 6575 &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The gain in drag caused by the longer suspension lines and the 5% loss in drag caused by forebody wake (Figure 5-21) result in a final drag coefficient, CDo, for the drogue chute of &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
CDo = 0.55. 1.085 . 0.95 = 0.57&lt;br /&gt;
&lt;br /&gt;
and a corrected drogue chute diameter &lt;br /&gt;
&lt;br /&gt;
Do - 13.61 ft&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.4 Computer Analysis of Drogue Chute Performance &lt;br /&gt;
&lt;br /&gt;
At this point, a computer program should be established to determine the following performance conditions: &lt;br /&gt;
&lt;br /&gt;
1. Balance reefed and disreef parachute forces and filling times. Start at Mach 1.5 at 34,000 feet (see point () on Figure 7-17). Check final selection for a 10,000-foot-altitude condition. &lt;br /&gt;
&lt;br /&gt;
2. Determine required opening altitude for high-speed, low-altitude deployment. This requires trajectory runs with both the drogue and main parachutes. &lt;br /&gt;
&lt;br /&gt;
3. Determine maximum horizontal range, including prevailing wind conditions. &lt;br /&gt;
&lt;br /&gt;
4. Verify that the selected main parachute opening speed of 175 KEAS is reached for all important flight conditions and that, for an opening velocity of 175 KEAS, the main parachute forces stay within the allowable force limit of 9255 pounds. &lt;br /&gt;
&lt;br /&gt;
5. Include opening of the air bags with a 6.0-second inflation time in some of the trajectories. Inflation starts after main parachute opening. &lt;br /&gt;
&lt;br /&gt;
The prime contractor should point out any special flight conditions that may require parachute recovery. The prime contractor will probably also perform recovery computer runs to determine for which flight conditions and from what altitudes recovery can be accomplished. &lt;br /&gt;
&lt;br /&gt;
7.4.5 Flight Emergency Recovery Conditions &lt;br /&gt;
&lt;br /&gt;
Certain flight conditions other than recovery command from the flight controller or the range safety officer may result in automatic on-board recovery command. These conditions include &lt;br /&gt;
&lt;br /&gt;
1. Loss of RF link. &lt;br /&gt;
&lt;br /&gt;
2. Loss of engine power (glide on internal power). &lt;br /&gt;
&lt;br /&gt;
3. High accelerations in x, y, and z caused by out-of-control flight conditions or in-flightafflicted damage on target drones. &lt;br /&gt;
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&lt;br /&gt;
7-38&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
NWC TP 6575 &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.6 Drogue Chute Opening Forces &lt;br /&gt;
&lt;br /&gt;
Parachute opening forces should be obtained from the computer program. However, a hand calculation is required for defining the force range before setting up the computer program. Furthermore, canopy filling times and force coefficient, C,. must be determined before computer runs (see section 5.4). &lt;br /&gt;
&lt;br /&gt;
Determining the drogue chute opening forces with the W/CDS method is normally sufficiently accurate for high-canopy-loading drogue chutes. If no computer backup is available, the Pflanz method (see section 5.4.6) will provide good force data.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.6.1 Drogue Chute Reefed Opening Forces When the W/CDS method is used, the reefed opening force, FR, is calculated to&lt;br /&gt;
&lt;br /&gt;
and the maximum allowable drogue chute drag area with a 2Z000 force limit is calculated to&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
where &lt;br /&gt;
&lt;br /&gt;
FR, the maximum allowable force, is 22,000 lb &lt;br /&gt;
&lt;br /&gt;
q, the maximum dynamic pressure, is 813.9 lb/ft2 &lt;br /&gt;
&lt;br /&gt;
For supersonic application, Figure 5-50 in section 5.4 shows CK = C' . X1 for the supersonic deployment of conical ribbon parachutes. Most applicable are the data for the Mercury and the Cook conical ribbon parachutes, which were deployed at velocities up to Mach 1.6. CK factors of 1.3 to 1.75 have been measured in supersonic deployment of conical ribbon parachutes. Forebody wake and poor deployment greatly affect the force coefficient. Mortar deployment often produces bag strip-off before canopy stretch, causing premature partial canopy inflation and a high X1 factor. Rocket extraction or drogue gun/pilot chute deployment, both resulting in canopy stretch before skirt inflation, generally avoid this problem. A force coefficient C, = 1.25 is selected.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The canopy loading of the reefed drogue chute is&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The required reefing-line length for obtaining this drag area can be determined from Figure 5-73, section 5.6.6, using the method of section 7.3.11.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.6.2 Drogue Chute Disreef Opening Force &lt;br /&gt;
&lt;br /&gt;
An important factor to determine is reefing time. A long time is required to reach close to terminal velocity before disreef. A practical approach, based on experience, is to select the 1.1-times-terminal-velocity point for disreef. If this time is too long, then a shorter reefing time is required, resulting in a higher disreef velocity and forces&lt;br /&gt;
&lt;br /&gt;
The terminal velocity of the reefed parachute is&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
and disreef force, Fo, is calculated&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Both forces FR and Fo are close to the allowable force limit of 22,000 pounds. Because loads vary 5 to 10%, slight overloads may occur. However, the 7200-pound drone weight is the take-off weight. Off-range recovery and conceivable emergencies will occur at lighter drone weights, resulting in lower parachute forces.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.7 Drogue Chute Stress Analysis and Design &lt;br /&gt;
&lt;br /&gt;
Dimensioning of the various components of the parachute assembly involves three primary tasks (1) establishing design and safety factors, (2) determining the loads and stresses in the assembly components, and (3) dimensioning all assembly members. The methods used for these tasks are described in section 6.4. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.7.1 Drogue Chute Safety, Load, Loss, and Design Factors &lt;br /&gt;
&lt;br /&gt;
The method used is similar to the one developed in section 6.4. Table 7-7 shows safety, load, and loss factors in relation to design factor.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.7.2 Number of Gores and Suspension-Line Strength &lt;br /&gt;
&lt;br /&gt;
The drogue chute will be designed for a maximumn force, Fo, of 22,000 pounds in the reefed and full-open stages. The suspension-line arrangement was selected in accordance with Table 7-8.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.7.2 Number of Gores and Suspension-Line Strength &lt;br /&gt;
&lt;br /&gt;
The drogue chute will be designed for a maximumn force, Fo, of 22,000 pounds in the reefed and full-open stages. The suspension-line arrangement was selected in accordance with Table 7-8.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
A canopy with 24 gores and 3000-pound-individual-strength suspension lines is selected primarily for gore width and vent diameter. The relatively large vent must be covered with wide vent lines held in place by proper connections. &lt;br /&gt;
&lt;br /&gt;
The method described in section 6.4 is used for preliminary dimensioning of the horizontal ribbons. In this method, the expression Fo/(CDS)p is an indication of the pressure in the parachute canopy; the gore width, es, is an indication of the gore radius. A smaller gore width and resultant gore radius causes lower stress in the individual horizontal ribbons for a given internal pressure. Figure 6-41 shows boundary curves for the required horizontal ribbon strength. These data, based on analysis of many tested ribbon parachutes, were first presented in Reference 5.39 and subsequently updated by the author. &lt;br /&gt;
&lt;br /&gt;
For the reefed parachute,&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The gore width of the reefed parachute is obtained from the following consideration. The reefed drag area is equivalent to the drag area of a parachute with the following nominal diameter (DRJ):&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The equivalent nominal diameter for the reefed parachute is&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Two-inch-wide ribbon with 460-pound strength, MIL-T-5608, Trype DII, is selected for the upper canopy part, and 2-inch-wide ribbon with 300-pound strength, MIL-T-5608, Type CV, is used for the lower part of the canopy. This drogue parachute will be subjected to high-frequency ribbon flutter during its high-speed descent from altitude, which may include a descent on the drogue chute from 50,000 to 7000 feet. Disintegration of horizontal and vertical ribbon and the stitching connecting the ribbons has occurred in the past during long-duration, high-speed applications of reefed and unreefed ribbon chutes. This high-frequency flutter is especially pronounced on the uninflated part of reefed ribbon parachutes. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Experience has shown that the following design features will counteract this problem: &lt;br /&gt;
&lt;br /&gt;
1. Tight spacing of vertical ribbons. &lt;br /&gt;
&lt;br /&gt;
2. wo vertical ribbons, one on each side of horizontal ribbon. &lt;br /&gt;
&lt;br /&gt;
3. Three rows of stitching with F-F thread in the vertical ribbon. All three features are used in this canopy design. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.7.3 Design of Radials, Vent and Skirt Tape, and Vent Lines &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Radials.Based on experience, radials are designed to have 80% of the strength of the suspension lines; 0.8 3000 = 2400 pounds. Three 2-inch-wide tapes of MIL-T-5608 form each radial; two 1000-pound Class Eli tapes and one 460-pound Class DII tape give each radial a combined strength of 2460 pounds. It may be possible to use only two 1000-pound strength tapes that have 80% of the actual load of 2548 pounds. &lt;br /&gt;
&lt;br /&gt;
Skirt and Vent Tape. In accordance with the discussion in section 7.6.6, the selected skirt tape is equal in strength to the suspension line but is 2 inches wide. Nylon tape (MIL-T-5608, Class E, lype V) with 3000-pound strength meets this requirement.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The required strength of the vent tape is&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Because some of this load will be taken by the vent lines, a double 4000-pound webbing is chosen in accordance with MIL-W-2756, lype IL. &lt;br /&gt;
&lt;br /&gt;
Special attention is required to obtain a design that achieves proper connection between radial tape, vent tape, and vent lines. &lt;br /&gt;
&lt;br /&gt;
Vent lines. The vent lines should have 60% of the strength of the radial tapes and be 5% shorter than the finished vent diameter. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.7.4 Drogue Chute Riser Design &lt;br /&gt;
&lt;br /&gt;
The drogue chute riser is formed of bundled suspension lines. This design eliminates the 20% connection loss, u, on the parachute side and permits a highly efficient connection on the drone side. The individual lines must be secured against each other to prevent flutter abrasion. Each line runs from a loop on the canopy radial, down the riser, around the drone connection point, and up the riser to an opposite radial-tape loop. Tests should be made to determine the strength of the radial-tape and suspension-line-loop connection and the individual loop around the drone hard point. A wrap-around keeper is used on the riser suspension line transfer point.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.8.1 Canopy Porosity &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The porosity of a ribbon canopy is defined as the percentage ratio of openings in the canopy plus the material porosity divided by the total canopy surface area. Canopy porosity affects parachute stability, drag, and opening process. A canopy with high porosity provides for good parachute stability, and uniform, low force inflation, but also lower drag than a canopy with lower porosity. Too high a canopy porosity may result in no or only partial canopy inflation.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The operational porosity limit decreases with decreasing parachute diameter from about 35% total porosity for a stable 3-foot-diameter parachute to about 12% porosity for a 100-foot-diameter parachute (see Figure 6-23 (a) and Table 6-3). Section 6.2.4 discusses the effect of canopy porosity on the design and performance of ribbon parachutes. &lt;br /&gt;
&lt;br /&gt;
Properly designed conical ribbon parachutes with the correct porosity have an oscillation equal to or less than 2 to 3 degrees; a drag coefficient, CDo, of 0.55; and an opening-force coefficient, C., of 1.05 to 1.07 for subsonic applications with low forebody drag, such as experienced in wind-tunnel tests. &lt;br /&gt;
&lt;br /&gt;
The vertical ribbon spacing discussed in section 7.4.8.2 is of utmost importance for supersonic application. A canopy porosity of 25 to 26% in accordance with Figure 6-23, Curve III, and Thble 6-3 is recommended for this application. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.8.2 Vertical Ribbon Spacing &lt;br /&gt;
&lt;br /&gt;
Ribbon parachutes in the past were designed with individual gores, and the gores were connected with radial ribbons and several rows of stitching. This arrangement created the &amp;quot;venetian blind effect&amp;quot; shown in Figure 7-19. The venetian blind effect increases the effective canopy porosity discussed in section 6.2.4. &lt;br /&gt;
&lt;br /&gt;
More recently, ribbon canopies have been designed with continuous horizontal ribbons, a design that offers savings in weight and cost. This design is described in detail in section 7.4.10. &lt;br /&gt;
&lt;br /&gt;
Figure 7-20 shows the basic arrangement of a canopy gore and ribbon grid consisting of horizontal and vertical ribbons.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Section 6.2.4 explains the relationship of canopy loading, W/(CDS)p; effective porosity, Ne; and vertical ribbon spacing, a. Ribbon parachutes used as final descent parachutes use a vertical ribbon spacing to horizontal ribbon width a/B of 2.5 to 4.0. This spacing allows advantage to be taken of the change in effective porosity. High-canopy-loading ribbon parachutes, such as first-stage drogue chutes, use a vertical ribbon spacingof I to 2 to avoid the negative effects of the change in effective porosity. A narrow vertical ribbon spacing of 1.25 times the width of the horizontal ribbon width will be used for the drogue chute.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
All previous gore dimensions and the dimensions shown in Figure 7-21 are preliminary. The horizontal ribbon spacing, b, is controlled by the required porosity, k. Required changes in horizontal ribbon spacing may result in slight changez in gore and canopy dimensions.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.9.2 Preliminary Gore-Porosity Check &lt;br /&gt;
&lt;br /&gt;
Two methods of calculating gore porosity are in use. The older method, described in Reference 5.39, has been updated in this chapter. This method allows calculation of the porosity for preliminary design purposes when no final gore drawings are available. Reference 2.2 shows how to calculate canopy porosity if a drawing is available based on the ratio of open spaces to total canopy area. Both methods include an estimation of the ribbon (material) porosity&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The porosity of a ribbon grid with variations in the distance of the horizontal ribbons is now calculated. The total porosity is estimated, and the most likable horizontal ribbon distance is selected for the first gore-porosity check (Thble 7-9). The widths of the vertical ribbon, A, and the horizontal ribbon, B, are fixed values. The ratio of vertical ribbon spacing, to horizontal ribbon width, a/B, was previously selected to 1.25, which is equal to 2.5 inches. A horizontal ribbon distance, b, of 1.1 inches is selected as first approach based on data in Thble 7-9.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
To avoid a decrease in parachute diameter, 26 horizontal ribbons are selected, changing the gore dimensions from those shown in Figure 7-21 to those shown in Figure 7-22.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.9.S General Comments on Gore Design and Porosity Selection &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The canopy gore design-total canopy porosity, XT; spacing of vertical ribbon; size of vent; and pocket-band arrangement-are the primary design features that determine the aerodynamic performance of the parachute. The most important characteristics of parachute performance are stability, smooth opening, drag, and opening-force coefficients. Determining porosity under a no-load condition is rather unrealistic, because most of the important aerodynamic characteristics occur under high-load conditions (opening shock) or medium-load conditions (descent). However, since the beginning of parachute development, aerodynamic parachute characteristics obtained in wind-tunnel and free-flight tests have been related to fixed design dimensions such as diameter and porosity. &lt;br /&gt;
&lt;br /&gt;
Determining the effective porosity caused by the changing load during the opening process and by the venetian-blind effect of the ribbon grid design is practically impossible. Furthermore, the change in effective porosity is similar on all ribbon parachutes because of the similarities of the ribbon grid designs, load factors, and related changes in material elongation that cause deformation of the ribbon grids and the parachute canopies. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.9.6 Computer Programs for Determining Gore Design and Porosity Calculation &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Both gore design and porosity calculations can be determined by computer programs. Organizations involved in frequent design of ribbon parachutes should establish these programs. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.10 Ribbon Parachute Canopies with Continuous Horizontal Ribbons &lt;br /&gt;
&lt;br /&gt;
Ribbon parachute canopies are frequently designed and manufactured with continuous horizontal ribbons either in single or two-section canopies. The continuous ribbon Jesign decreases weight and volume, increases the strength of the horizontal ribbon-radial connection, and simplifies manufacturing. Continuous horizontal ribbons change the porosity characteristics of the canopy. &lt;br /&gt;
&lt;br /&gt;
Figure 7-19 shows how the individual horizontal ribbons orient themselves in a canopy manufactured from individual triangular gores. In the inflated canopy, the horizontal ribbons in the canopy crown area orient parallel to the canopy design. However, in the skirt area, the canopy design line is almost parallel to the airflow. This design, usually called the &amp;quot;venetian blind effect,&amp;quot; causes ti:e longer leading edge of each horizoatal ribbon to bulge out and position the ribbon with a positive angle of attack to the airflow. The result is an increase in effective porosity under high dynamic pressure conditions. The venetian blind effect is discussed in section 6.2.4, and the influence of canopy loading on the change in effective porosity is shown in Figure 6-24.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Designing canopies with continuous horizontal ribbons changes the venetian blind effect. Returning to Figure 7.19, it is obvious that continuous horizontal ribbons in the canopy skirt area do not bulge out since leading and trailing ribbon edges have the same length and do not position themselves with an angle of attack to the airflow. However, in the crown area of the canopy where each gore forms a triangle, the equal length of the leading and trailing ribbon edges now gives each ribbon a negative angle of attack thereby increasing the effective porosity in the canopy crown area. The effect is minimized by large number of gores arid by the use of a center vertical ribbon, or a miniradial, as Sandia engineers call it. &lt;br /&gt;
&lt;br /&gt;
Discussion with Sandia and industry personnel indicates that no measurable difference has been found in the aerodynamic characteristics of ribbon parachute canopies designed with individual gores or with continuous horizontal ribbons so long as the canopies contain a large number of gores and a center vertical ribbon. However, a slight delay in initial inflation seems to occur on small parachutes with a small number of gores. Closer spacing of vertical ribbons in the canopy crown area should counteract this delay. Another method of counteracting the delay is by gathering the trailing edges of horizontal ribbons with several rows of stitching and using a lower porosity in the crown area. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.11 Use of Kevlar Fabrics &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Many modern ribbon parachutes use Kevlar suspension lines, risers, and canopy skirt, lateral, and vent tapes, which results in a decrease in weight and volume. Section 6.5.5 discusses all aspects of working with Kevlar in the design of parachute assemblies. This includes physical characteristics of Kevlar fibers and fabrics, available Kevlar fabrics, and experience ;il designing in Kevlar. Section 6.6.5 should be studied before designing in Kevlar.&lt;/div&gt;</summary>
		<author><name>TuanHTruong</name></author>
	</entry>
	<entry>
		<id>https://mediawiki.aerodecelerator.org/index.php?title=Recovery_System_Design&amp;diff=41</id>
		<title>Recovery System Design</title>
		<link rel="alternate" type="text/html" href="https://mediawiki.aerodecelerator.org/index.php?title=Recovery_System_Design&amp;diff=41"/>
		<updated>2024-05-08T15:23:24Z</updated>

		<summary type="html">&lt;p&gt;TuanHTruong: /* 7.1.3 Requirements for Emergency Operation */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;= DESIGN OF A PARACHUTE RECOVERY AND LANDING SYSTEM =&lt;br /&gt;
This chapter deals with the design of a parachute recovery and landing attenuation system for a military reconnaissance drone. The prime emphasis in the design of this system is on undamaged recovery of the drone from the total flight performance envelope during the development and test phase, on undamaged recovery after a completed mission during military operations, and on multiple use of the recovery system. An engineering team conducts performance and system analyses and chooses what recovery concept to use, what types of parachutes to select for high-speed deceleration and for final recovery, and what impact-attenuation system is best for the particular application. This chapter covers the selection process for concepts and components. Different engineers may make different selections based on experiences with particular types of parachutes or deployment concepts; experience is always a viable reason for selecting a particular approach. However, using the selection criteria shown in Figure 2-6. the designer must put reliability of operation, undamaged recovery, reusability of the landing system, and minimum weight and volume at the top of the list of requirements. &lt;br /&gt;
&lt;br /&gt;
== 7.1 REQUIREMENTS ==&lt;br /&gt;
=== 7.1.1 System Requirements ===&lt;br /&gt;
&lt;br /&gt;
An unmanned air vehicle used for military reconnaissance must be recovered after a completed mission in rough terrain, undamaged and ready for multiple reuse. The recovery system must be able to &lt;br /&gt;
&lt;br /&gt;
# Recover the air vehicle after the completed mission when the vehicle has landed in rough terrain at altitudes from sea level to 5000 feet.&lt;br /&gt;
# Recover the drone during the engineering test phase from all controlled and uncontrolled flight conditions.&lt;br /&gt;
# Serve as a range-safety device to prevent the air vehicle from leaving the boundaries of the test range.&lt;br /&gt;
&lt;br /&gt;
The air vehicle has a takeoff weight of 7200 pounds and a landing weight, after the i completed mission, of 4800 pounds. Undamaged landing shall be possible in rough terrain with rocks up to 8 inches in diameter. Replacement parts and refurbishment cost shall be kept to a minimum.  &lt;br /&gt;
&lt;br /&gt;
=== 7.1.2 Requirements for Normal Operation ===&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|Drone weight at recovery after completed mission&lt;br /&gt;
|W&amp;lt;sub&amp;gt;d&amp;lt;/sub&amp;gt; = 4800 lb&lt;br /&gt;
|-&lt;br /&gt;
|Recovery velocity&lt;br /&gt;
|v&amp;lt;sub&amp;gt;o&amp;lt;/sub&amp;gt; = 150 to 200 KEAS&lt;br /&gt;
|-&lt;br /&gt;
|Minimum recovery altitude&lt;br /&gt;
|H&amp;lt;sub&amp;gt;o&amp;lt;/sub&amp;gt; = 2000 ft above ground level (AGL)&lt;br /&gt;
|-&lt;br /&gt;
|Maximum ground level&lt;br /&gt;
|H = 5000 ft&lt;br /&gt;
|-&lt;br /&gt;
|Maximum allowable total parachute force&lt;br /&gt;
|F&amp;lt;sub&amp;gt;o&amp;lt;/sub&amp;gt; = 16,000 lb&lt;br /&gt;
|-&lt;br /&gt;
|Maximum allowable impact deceleration at landing&lt;br /&gt;
|a = 9.0 ''g''&amp;lt;nowiki/&amp;gt;'s&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
=== 7.1.3 Requirements for Emergency Operation ===&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|Drone weight at takeoff &lt;br /&gt;
|W&amp;lt;sub&amp;gt;dma&amp;lt;/sub&amp;gt; = 7200 lb&lt;br /&gt;
|-&lt;br /&gt;
|&lt;br /&gt;
|&lt;br /&gt;
|-&lt;br /&gt;
|&lt;br /&gt;
|&lt;br /&gt;
|} &lt;br /&gt;
&lt;br /&gt;
Emergency operation includes recovery during the test phase from takeoff to landing and also includes recovery for range-safety reasons. &lt;br /&gt;
&lt;br /&gt;
Drone weight at takeoff .................................. Wdma = 7200 lb &lt;br /&gt;
&lt;br /&gt;
Maximum recovery velocity at mean sea level (MSL) ................................... vo = 490 KEAS &lt;br /&gt;
&lt;br /&gt;
Maximum recovery velocity at 38,000 to 50,000 ft altitude ........................................ vo = 1.5 Mach &lt;br /&gt;
&lt;br /&gt;
Maximum dynamic pressure .............................. qmm = 812 lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; &lt;br /&gt;
&lt;br /&gt;
Maximum allowable parachute force ........................ F0 = 22,000 lb  &lt;br /&gt;
&lt;br /&gt;
=== 7.1.4 Requirements Analysis ===&lt;br /&gt;
Three primary requirements pace the design of the recovery system: &lt;br /&gt;
&lt;br /&gt;
1. The drone must be able to land in rocky but level terrain without damage. &lt;br /&gt;
&lt;br /&gt;
2. Refurbishment cost and time shall be kept to a minimum. &lt;br /&gt;
&lt;br /&gt;
3. Recovery must be possible from all flight conditions during the flight test phase, including cases where the out-of-control drone flies off the range.  &lt;br /&gt;
&lt;br /&gt;
== 7.2 LANDING ANALYSIS AND IMPACT-ATTENUATION SYSTEM ==&lt;br /&gt;
&lt;br /&gt;
=== 7.2.1 Landing Analysis ===&lt;br /&gt;
Three known recovery concepts prevent damage during landing in rocky terrain: &lt;br /&gt;
&lt;br /&gt;
1. Midair retrieval.&lt;br /&gt;
&lt;br /&gt;
2. Dual air bags or dual frangibles.&lt;br /&gt;
&lt;br /&gt;
3. Retrorockets combined with small, nondeflatable air bags.&lt;br /&gt;
&lt;br /&gt;
The need for retrieval helicopters or retrieval aircraft makes Method 1, midair retrieval, impractical. The other two methods are affected by the deceleration distance required to meet the 9-g limit. &lt;br /&gt;
&lt;br /&gt;
In section 6.8 of this manual, the required deceleration distance(s) is determined to be&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;s=\frac{{V_{e_1}}^2-{V_{e_2}}^2}{2g(n\eta-1)}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;{V_{e_1}}&amp;lt;/math&amp;gt; = velocity of the drone descending on the parachute (rate of descent), ft/s&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;V_{e_2}&amp;lt;/math&amp;gt; = permissible impact velocity, ft/s&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;g&amp;lt;/math&amp;gt; = acceleration of gravity, ft/s2&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\eta&amp;lt;/math&amp;gt; = effectiveness of the impact attenuation system used, dimensionless&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;n&amp;lt;/math&amp;gt; = allowable impact deceleration, ratio &amp;lt;math&amp;gt;n=\frac{a}{g}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Figure 6-68 of Chapter 6 shows the range of various impact attenuation systems as a&lt;br /&gt;
&lt;br /&gt;
function of rate of descent and allowable ground impact deceleration. The information&lt;br /&gt;
&lt;br /&gt;
indicates that air bags may be the most practical concept for this application. A cursory&lt;br /&gt;
&lt;br /&gt;
analysis indicates that a rate of descent of 25 ft/s at 5000 fee: altitude will result in a close to&lt;br /&gt;
&lt;br /&gt;
optimum weight ratio of the combined parachute air bag system (see Figure 6-83). Properly&lt;br /&gt;
&lt;br /&gt;
designed air bags will have an effectiveness of 65% as shown in the stroke-pressure diagram in&lt;br /&gt;
&lt;br /&gt;
Figure 6-78 and allow ground contact or final velocity of close to 0 ft/s.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
With these assumptions, the required effective air bag deceleration stroke is obtained&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;s=\frac{25^2-00}{(2\cdot 32.174)(9.0\cdot 0.65-1)} = 2.0\ ft\ or\ 24\ in.&amp;lt;/math&amp;gt;This deceleration distance is too short for a parachute retrorocket system because of the required timing accuracy and rocket burning time. Retrorocket systems are most practical for deceleration distances greater than 4 or 5 feet. Crushable and frangible impact attenuators are suitable for deceleration distances of less than 15 inches. Air bag systems work best for deceleration distances of 24 to 48 inches. The original assumption that an air bag concept maybe the most practical approach for this air vehicle is therefore confirmed.&lt;br /&gt;
&lt;br /&gt;
=== 7.2.2 Impact Attenuator System ===&lt;br /&gt;
The design of impact attenuator systems is discussed in section 6.8 of this manual. Figure 7-1 shows the reconnaissance drone and the air-bag attenuator systems that consist of two deflatable, two-compartment wing-bag bags (A); a single-compartment, deflatable nose bag (B); and a nondeflatable nose-buffer bag (C). The wing bags, the primary energy absorbers, need the already calculated 24-inch effective-deceleration stroke. For design reasons, 33 inches must be added to the bag height, 19 inches for the distance from the wing underside to the underside of the jet ,i rlucts, 10 inches for ground clearance, and 4 inches for bag bottom curvature. These additions result in a total bag height of 57 inches. To ensure landing stability, an air bag height-to-diameter ratio of 1.25 is selected for the two wing bags, resulting in a bag diameter of 48 inches. The cross-hatched lower part of the two wing bags (see Figure 7-1) deflates at impact, but the upper part stays inflated and keeps the drone off the ground. The nose bag, B, helps to absorb the impact and deflates, and the nose of the drone comes to rest on the nondeflatable buffer bag, C. All air bags are inflated from 3000 psi nitrogen containers using aspirators for a 50/50 nitrogen air mixture. The air bags are prepressurized to 2 psi for full bag inflation prior to landing. Multiple blowout valves consisting of staggered blowout rubber disks around the circumference of the air bags control the bag deflation to stay within the 9-g deceleration limit.&lt;br /&gt;
&lt;br /&gt;
The weight of the impact-attenuation system-air bags, nitrogen containers, plumbing, and A/C containers-is estimated from section 6.7 to be 2.2% of the total drone weight, or 105.6 pounds. The air bags should be stored in containers that can be easily removed from the drone for repacking. Air bags must be deployed after the main parachutes are fully open to prevent air-bag damage caused by high dynamic pressure. Air-bag deployment begins with simultaneous pyroejecting of the removable air-bag-container covers and opening of the nitrogen-container valves. The wing bags, the primary nose bag, and the nose-buffer bag inflate. At ground contact, the bags compress, increasing the pressure inside the bags. At a preselected pressure level, the blowout valves (rubber disks, metal disks, or rubber-type sleeves) open and limit the maximum drone deceleration to the preselected level.&lt;br /&gt;
&lt;br /&gt;
== 7.3 MAIN PARACHUTE SYSTEM ==&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.3.1 Main Parachute System Requirements&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Section 2.4 defines the criteria for parachute type selection. Requirements for low weight and volume rule out the low-drag slotted parachutes (ribbon, ringslot, and ringsail) as well as guide-surface and cross parachutes (see Tables 5.2 and 5.3). Parachute deployment past the vertical stabilizer rules out a single parachute in favor of a cluster of two parachutes deployed independently left and right of the vertical stabilizer. No cluster experience is available with annular or cross parachutes, and no reefing experience is available with annular parachutes. Cross parachutes cannot be reefed to the low reefing ratios required for this application. Extended-skirt and polyconical parachutes have been used successfully in clusters of large, reefed parachutes.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7-6&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
A cluster of two conical full extended skirt parachutes is most suitable for this system. In&lt;br /&gt;
&lt;br /&gt;
section 5.2, Figures 5.24 and 5-25 show that properly designed extended-skirt parachutes have&lt;br /&gt;
&lt;br /&gt;
drag coefficients equal to 0.8 to 0.9 in the 20- to 25-ft/s rate of descent range. Available data&lt;br /&gt;
&lt;br /&gt;
(Reference 5.23) indicate that a cluster of two extended-skirt parachutes is sufficiently stable&lt;br /&gt;
&lt;br /&gt;
for use with air bags. Extended-skirt parachutes have a low opening-force coefficient of 1.4,&lt;br /&gt;
&lt;br /&gt;
compared to an opening-force coefficient of 1.8 for conical and triconical parachutes.&lt;br /&gt;
&lt;br /&gt;
Extended-skirt parachutes can also be reefed to low reefing ratios, a requirement for final&lt;br /&gt;
&lt;br /&gt;
descent parachutes (see Chapter 5, Figure 5-72).&lt;br /&gt;
&lt;br /&gt;
73.3 Parachute Diameter&lt;br /&gt;
&lt;br /&gt;
The rate of descent at 5000 feet altitude was selected to 25 ft/s (see section 7.3.1). The&lt;br /&gt;
&lt;br /&gt;
equivalent rate of descent at sea level is&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The drag coefficient, CDo, for a conical full extended skirt parachute with a 23.2-ft/s rate of&lt;br /&gt;
&lt;br /&gt;
descent and a suspension-line ratio, [.e/Do, of 1.0 is obtained from Figure 5-25&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
A suspension-line ratio of 1.15 is selected. This is the longest practical length for extended skirt&lt;br /&gt;
&lt;br /&gt;
parachutes (see Figure 5-20).&lt;br /&gt;
&lt;br /&gt;
The length of the riser, Lr, depends on its installation in the drone; the riser should be long&lt;br /&gt;
&lt;br /&gt;
enough to extend beyond the fuselage and vertical stabilizer of the drone (see Figure 7-2),&lt;br /&gt;
&lt;br /&gt;
which gives the final configuration of the parachute cluster, including risers and parachutes.&lt;br /&gt;
&lt;br /&gt;
7.3.4 Parachute Deployment System&lt;br /&gt;
&lt;br /&gt;
A cluster of two main parachutes is selected and deployed left and right of the vertical&lt;br /&gt;
&lt;br /&gt;
stabilizer to avoid hang-up or damage of a single parachute by the vertical stabilizer. Each&lt;br /&gt;
&lt;br /&gt;
parachute needs its own extraction and deployment system to properly deploy past the&lt;br /&gt;
&lt;br /&gt;
stabilizer and to avoid interference with the other main parachute during deployment and&lt;br /&gt;
&lt;br /&gt;
inflation.&lt;br /&gt;
&lt;br /&gt;
TWo fast-opening extraction parachutes are used on each main parachute. Stable&lt;br /&gt;
&lt;br /&gt;
parachutes will minimize interferenc, during deployment. Experience with past recovery&lt;br /&gt;
&lt;br /&gt;
systems has shown that the most positive deployment is obtained by forced ejection of the&lt;br /&gt;
&lt;br /&gt;
extractiou or pilot chutes into good airflow past the vertical stabilizer by either mortar or&lt;br /&gt;
&lt;br /&gt;
drogue gun ejection. A mortar can eject large, heavy parachutes but creates large leaction&lt;br /&gt;
&lt;br /&gt;
forces and needs considerable space for installation. Drogue gun ejection is effective, but is&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
limited to the deployment of small, lightweight parachutes such as pilot chutes. Drogue gun ejected pilot chutes are selected for initiating main parachute deployment. To ensure proper&lt;br /&gt;
&lt;br /&gt;
clearance of the vertical stabilizer, the pilot chutes are ejeLted 45 degrees upward, backward&lt;br /&gt;
&lt;br /&gt;
and outward past the vertical stabilizer. The parachute installation in the drone fuselage&lt;br /&gt;
&lt;br /&gt;
requires cross-wind deployment and therefore forced ejection of the main parachute&lt;br /&gt;
&lt;br /&gt;
deployment bags. Four different methods have been used successfully to accomplish forced&lt;br /&gt;
&lt;br /&gt;
ejection: (1) using ejector springs enclosed in a textile cylinder. (2) gas-inflating nonporous&lt;br /&gt;
&lt;br /&gt;
ejector bags, (3) catapulting the bag out of the compartment, or (4) using a lift-web&lt;br /&gt;
&lt;br /&gt;
arrangement as discussed in section 6.1.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The deployment system selected consists of a drogue gun deployed pilot chute, an&lt;br /&gt;
&lt;br /&gt;
extraction parachute, and a main parachute deployment bag lifted from the parachute&lt;br /&gt;
&lt;br /&gt;
compartment by lift webs. When the hinged compartment doors open, two drogue gun slugs&lt;br /&gt;
&lt;br /&gt;
are fired 45 degrees upward and aft; each slug deploys a pilot chute sufficiently behind the&lt;br /&gt;
&lt;br /&gt;
drone into good airflow. These pilot chutes in turn extract two extraction chutes stowed on top of the main parachute deployment bags. The extraction chutes extract and deploy the two main 0&lt;br /&gt;
&lt;br /&gt;
parachutes left and right of the vertical stabilizers. Lift webs and unsymmetrical bag handles&lt;br /&gt;
&lt;br /&gt;
lift the main parachute bags out of the drone compartment and extract the main parachute&lt;br /&gt;
&lt;br /&gt;
past the vertical stabilizer (see Figure 7-3)&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.3.5 Extraction Parachute Assembly&lt;br /&gt;
&lt;br /&gt;
The two extraction parachutes must properly deploy the two main parachutes. The size of&lt;br /&gt;
&lt;br /&gt;
the extraction parachutes and their location in the wake of the drone is determined as follows:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
A stable, 7.4-foot-diameter ringslot parachute is selected. &lt;br /&gt;
&lt;br /&gt;
The weight of the ringslot extraction parachute can be estimated from section 6.7 to 2.5 pounds, and the weight of the extraction parachute assembly including riser and deployment bag to 1.5 . 2.5 pounds = 3.75 pounds. The weight of a single 72.7-foot-diameter main parachute, as determined from section 6.7, is 54 pounds. This weight estimate assumes an efficiently designed main canopy that has a combination of tape and radial seams to carry the radial loads and has other, similar weight-saving design features. The arrangement of the extraction parachute in relation to the drone is shown in Figure 7-5. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.3.6 Pilot Parachute Assembly &lt;br /&gt;
&lt;br /&gt;
The extraction parachute assembly weight of 3.75 pounds is too heavy to be deployed by a drogue-gun slug; therefore, a small pilot chute is selected for initial deployment by the drogue-gun slug. This pilot chute, in turn, will deploy the extraction parachute.&lt;br /&gt;
&lt;br /&gt;
Evaluation of past good and poor deployments has led to the rule that the extraction force of the pilot chute should be greater than or equal to four times the weight of the unit to be extracted; in this case, the extraction parachute assembly. So that the pilot chute has enough force, a pilot chute is selected that will produce, at the minimum deployment speed of 150 KEAS, an extraction force equal to five times the weight of the extraction parachute assembly: 5. 3.75 pounds - 18.75 pounds. The minimum dynamic pressure at 150 KEAS is&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.3.7 Main Parachute Forces&lt;br /&gt;
&lt;br /&gt;
7.3.7.1 Requirements &lt;br /&gt;
&lt;br /&gt;
Drone weight ............................................. W D = 4800 lb&lt;br /&gt;
&lt;br /&gt;
Maximum deployment speed .............................. vo = 200 KEAS &lt;br /&gt;
&lt;br /&gt;
Minimum deployment speed ........................ Vo minimum = 150 KEAS &lt;br /&gt;
&lt;br /&gt;
Maximum allowable total parachute force (two main parachutes) ................................... FT = 16,000 lb &lt;br /&gt;
&lt;br /&gt;
Deployment altitude .................................. H = 2000 to 7000 ft &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.3.7.2 Velocity-Altitude Profile &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Section 5.5 states that the maximum opening force of the main parachute occurs at maximum deployment altitude. Figure 7-8 shows a velocity-altitude-versus-time profile for a typical vehicle recovery system. &lt;br /&gt;
&lt;br /&gt;
The maximum dynamic pressure, qo, occurs at the 200-KEAS deployment velocity &lt;br /&gt;
&lt;br /&gt;
2. The Pflanz method is quite accurate for all conditions including high altitude, but neglects the effect of gravity. Parachutes opened in vertical descent will have a 1-g (one weight unit) higher force than calculated. It is necessary to calculate the canopy filling times for the various reefed stages (see section 5.4.3) and to determine the drag-area-versus-time profile for the specific parachute (see section 5.4.4). This method permits the investigation of variations in filling times and drag-area-versus-time profiles. &lt;br /&gt;
&lt;br /&gt;
3. The force-trajectory-time computer method includes the effects of altitude, gravity, and changing trajectory angle. This method requires determination of a drag-area-versus-time profile for the entire parachute opening sequence (see Figure 5-52). Computers permit multiple runs with changes in times, drag-area-versus-time profiles, starting velocities, and altitudes.&lt;br /&gt;
&lt;br /&gt;
7.3.7.4 Reefed Opening Forces&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
To  save trajectory time, the reef-d pardchute is disreefed at a dynamic pressure 10 to 20% higher than the terminal reefed dynamic pressure. Therefore,&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Results of changing the canopy inflation time, tf, and the drag-area-versus-time profile, n, are shown in Thble 7-2. Reference 5-76, the Pflanz report, provides a more detailed study of the effect of canopy fill time and drag-area-increase-versus-time profile on the magnitude of the parachute force&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Force-Trajectory-Time Computer Method &lt;br /&gt;
&lt;br /&gt;
The program established oy NWC determines as a function of time the parachute forces, the vehicle deceleration, and the space-positioning (trajectory) data in a two-axis system. The method requires a drag-area-versus-time profile for the individual parachutes and the total vehicle system (Figure 7-9). This profile was previously shown in Figure 5-52. Figure 7-9 includes the change in air-vehicle drag caused by the change in vehicle attitude during the parachute opening process&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.3.7.6 Comments on Calculated Opening Forces 1. The reefed opening force for the single parachute is higher than thie contractor-requested maximum allowable force per parachute of 8000 pounds&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
2. The average disreef force is approximately 1500 pounds lower than the reefed force. Therefore, it appears logical to lower the reefed force and increase the disreef force. Although this adjustment probably cannot be made within the 8000-pound limit, 8500 pounds appears to be an obtainable goal. &lt;br /&gt;
&lt;br /&gt;
3. To meet the contractor requirement of an 8000-pound maximum force limit per parachute, two-stage reefing is required. &lt;br /&gt;
&lt;br /&gt;
4. It appears practical to determine in drop tests if a 2.0 to 2.1% reefed drag area can be obtained. This drag area would decrease the reefed opening force and somewhat increase the disreef force. However, reaching an average maximum force of less than 8000 pounds appears doubtful. &lt;br /&gt;
&lt;br /&gt;
5. In the calculations, both parachutes are assumed to have equal opening forces. In reality, opening forces of the two parachutes can differ because of variations in filling time. lead-ann-lag chute behavior caused by blanketing, and resultant nonuniform canopy inflation. 7-22 NWC TP 6575 &lt;br /&gt;
&lt;br /&gt;
The fast-opening Apollo ringsail-type main parachutes had a load distribution among the three parachutes of 40-40-20. The individual parachutes, therefore, had to be overdesigned in a 40/33 ratio. However, the total parachute force load taken by the vehicle hard points did not exceed the calculated average load because of the high-low variation of the individual parachutes. &lt;br /&gt;
&lt;br /&gt;
The two slower-opening extended-skirt parachutes used for this application are more uniform in their load distribution. A cursory analysis of available test data indicates that a 55/45 load distribution between the two parachutes and a no-overload condition for the vehicle hard points should be an acceptable load distribution. &lt;br /&gt;
&lt;br /&gt;
A contractor-subcontractor agreement is required to determine whether the individual parachutes should be designed for the 55/45 load variation or whether this overload can be accommodated by the 1.5 safety factor and the additional safety provided by the normal overstrength of textile specification materials.&lt;br /&gt;
&lt;br /&gt;
7.3.7.7 Snatch Forces &lt;br /&gt;
&lt;br /&gt;
The snatch force is caused by the acceleration of the mass of the parachute assembly to the velocity of the forebody (drone). A canopy, partially inflated at line stretch, increases the mass of the parachute by the mass of the air included in the canopy; this can increase the snatch force (mass shock) considerably.  &lt;br /&gt;
&lt;br /&gt;
Two  principal rules should be followed to keep the snatch force within allowable limits.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
1. Keep the parachute canopy closed until line (canopy) stretch occurs by use of a deployment bag o! %kirt restrictor.&lt;br /&gt;
&lt;br /&gt;
2. Accelerate I!: mass of the parachute assembly in incremental steps. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Known means of accomplishing these goals are discussed in Chapter 6.1. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The difference between a poor deployment and a deployment that accomplishes the first rule and partially accomplishes ' second is illustrated in Figure 5-54, which shows snatch and opening forces for the C-9 p. tchute with and without the quarter deployment bag. The deployment method outlined in ! tilon 7.3.4 should hold snatch forces at a level below the parachute opening forces. &lt;br /&gt;
&lt;br /&gt;
A method for calculating ,tch forces is described in Reference 2.2, the 1963 edition of the USAF parachute handbook. : nreferred method for calculating parachute deployment. including the snatch force, is cont.iiiici in J. W Purvis's AIAA paper, &amp;quot;Improved Prediction of Parachute Line Sail During I incs-First Deployment&amp;quot; (Reference 5.86)&lt;br /&gt;
&lt;br /&gt;
7.3.8 Parachute Stress Analysis &lt;br /&gt;
&lt;br /&gt;
7.3.8.1 Parachute Design Data&lt;br /&gt;
&lt;br /&gt;
A total parachute assembly is shown in Figure 7-10.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.3.8.2 Parachute Forces &lt;br /&gt;
&lt;br /&gt;
The maximum reefed opening force, FR, is 9255 pounds. The maximum disreef opening force, F., is 7404 pounds. The maximum design force for stressing the parachute assembly, FI, is 9255 pounds.&lt;br /&gt;
&lt;br /&gt;
The forces obtained in computer runs are selected as the most accurate forces for stressing the parachute assembly and its components. Based on multiple computer runs, a diligent choice must be made for the most likable forces.&lt;br /&gt;
&lt;br /&gt;
7.3.83 Main-Parachute Safety and Design Factors &lt;br /&gt;
&lt;br /&gt;
Section 6.4 is used as a guide for selecting the safety, load, loss, and design factors in Table 7.4&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
1. Connection of suspension lines to riser legs and drone hardpoints is made easier if the number of suspension lines are a multiple of 4 or 8. &lt;br /&gt;
&lt;br /&gt;
2. The gore at the skirt should not be wider than 3.5 feet for packing reasons. &lt;br /&gt;
&lt;br /&gt;
3. The canopy should have no fewer than 12 gores to avoid gore distortion during inflation. &lt;br /&gt;
&lt;br /&gt;
4. Radial ribbons or radial seams should not overlap at the vent; overlapping causes bunching of material and associated sewing problems. &lt;br /&gt;
&lt;br /&gt;
5. The strengths of available suspension-line types may affect the gore selection. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Table 7-5 shows the required suspension line strength and the resultant gore width as functions of the number of gore/suspension lines used. &lt;br /&gt;
&lt;br /&gt;
7-25 NWC TP 6575&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The width of the goie of the skirt on conical, full-extended-skirt (CFES) parachutes is about 85% of the maximum gore width, Eo. Sixty-four suspension lines are selected in accordance with MIL-C-7515, TIpe XI, with 300-pound tensile strength. This selection provides a margin of safety (MS) of&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The suspension line will be attached to the canopy skirt in a loop connection. &lt;br /&gt;
&lt;br /&gt;
7.3.8.5 Canopy Stress&lt;br /&gt;
&lt;br /&gt;
No precise method has been d.-veloped for calculating the stress in a circular, solid-material, bias-construction canopy.&lt;br /&gt;
&lt;br /&gt;
Section 6.4 describes a semi-empirical method for determining the required fabric strength of a solid material canopy in pounds per unit width using the stress in a pressure vessel as an analogy. The stress in a cylindrical vessel, expressed as force per unit length, is&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
where p is the pressure in the cylindrical vessel and r is the vessel radius. Using this analogy and considering the canopy gore as part of a pressure vessel, the required material strength of the canopy per unit width is obtained&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The maximum stress actually occurs during reefed inflation because of the smaller inflated diameter:&lt;br /&gt;
&lt;br /&gt;
7.3.8.6 Canopy Reinforcing Tapes &lt;br /&gt;
&lt;br /&gt;
1. Skirt Tape. The skirt tape should Iv. equal or greater in strength than the individual suspension lines but not less than 1000 pounds, and 1-inch-wide tape should be used for parachutes larger than 20 feet in diameter. &lt;br /&gt;
&lt;br /&gt;
The nylon tape selected is 1-inch-wide MIL-T-5038, Type IV, with 1000-pound strength. Proper connection of the skirt tape to the radial seam (tape) and the suspension line must be ensured.&lt;br /&gt;
&lt;br /&gt;
2. Vent Tape. From the geometric design of the parachute vent (Figure 7-11). the force in the vent tape, FVT, is calculated&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
A 1-inch-wide, 4000-pound webbing (MIL-W-5625) or 7/8-inch-wide, 3100-pound webbing (MIL-W-5625) is selected. &lt;br /&gt;
&lt;br /&gt;
3. Vent Lines. The strength of the vent line- should be equal to or greater than 60% of the strength of the radials&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.3.8.7 Design of Radials &lt;br /&gt;
&lt;br /&gt;
The following four types of radial designs are in use: &lt;br /&gt;
&lt;br /&gt;
1. Radial seams with suspension lines running in channels over the canopy and attached at the vent and the skirt as on the canopy of the C-9 personnel parachute. &lt;br /&gt;
&lt;br /&gt;
2. Suspension lines running on top of the radials over the canopy and sewn at full length to the canopy as on many heavy-duty ribtx'n parachutes. &lt;br /&gt;
&lt;br /&gt;
3. Radial tapes sewn on top of or inside the radial seams, and suspension lines attached to the radial tapes by sewing or by skirt loops (NB-7 and T-10 canopies). &lt;br /&gt;
&lt;br /&gt;
4. Radial ribbons on ribbon parachutes designed to take the total radial load with suspension lines sewn onto d e radials or connected by a skirt loop. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The following are some comments on the design of radials: &lt;br /&gt;
&lt;br /&gt;
1. Making the strength of the radials 1:qtlal to 80% of the strength of the suspension lines has been satisfactory on thousands of ribbon parachutes. &lt;br /&gt;
&lt;br /&gt;
2. When tapes or suspension lines are sewn at full length to the radials, care must be taken that fullness in the radials ensures that the radial tapes or the suspension lines are the primary load carrying members. For an explanation of fullness, see section 6.6.4. &lt;br /&gt;
&lt;br /&gt;
3. Uniform material distribution is of utmost importance when sewn tapes or lines are used for radial reinforcemetnt. &lt;br /&gt;
&lt;br /&gt;
For the radial design of the main parachute, we use a tape with 80% strength of the suspension lint (0.8. 300 lb - 240 Ib) sewn on top of the radial scam. A 250-pound strength, 'A-inch-wide tape is selected in accordance with MIL-T-5038, 7ýpe III. Thpe and radial seams are marked every 24 inches for proper material distribution&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.3.8.8 Check for Proper Gore Fullness &lt;br /&gt;
&lt;br /&gt;
When the first parachute of a new design has been completed in the manufacturing shop, a gore fullness check in accordance with Figure 7-12 should be conducted. A slight amount of slack should be noticeable in the canopy fabric in both directions when all four corners of a gore are pulled radially outward. Slack indicates that the main loads are carried by the radials and reinforcing tapes and not by the canopy fabric. Stress folds in the canopy indicate faults in the design or manufacture of the parachute&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
’&lt;br /&gt;
&lt;br /&gt;
This is a large vent opening for a reefed parachute. Several criteria may be used to determine the size of the canopy vent as follows: &lt;br /&gt;
&lt;br /&gt;
1. Unreefed parachutes with vents up to 1% of the canopy surface area, So, have been operated successfully.&lt;br /&gt;
&lt;br /&gt;
2. Reefed parachutes require a vent diameter, DV, smaller than the reefing line circle, diameter DR, of the parachute; Dv is smaller than DR (see section 5.6, Figure 5-66). &lt;br /&gt;
&lt;br /&gt;
3. The radials at the vent should not overlap. A 1-inch free space between radials is desirable (see Figure 7-14)&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Stress in the canopy gore area can be relieved by making the gore at the vent 10% wider than the calculated gore dimension, ev. Therefore, ev* - 1.1 . ev - 1.1(1.6) = 1.76 inches. The vent tape is sewn to the vent at the original ev dimension, thereby gathering the vent 10% and creating a stress-relieving arcing in the gore fabric next to the vent. See Figure 7-15 for an example of final gore dimensions.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.3.10 Pocket Bands The pocket bands used on every gore make canopy inflation more uniform and eliminates long and short filling times. A narrow tape is used as the pocket band, which will :ot affect the average length of the canopy filling time. Data on the dimensioning of pocket bands are given in section 6.4. As shown in Figure 7-16, the pocket band dimensions are&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The diameter of the reefing line circle, DR, is larger than the 3.64-foot vent diameter of the canopy, Dv. This difference in diameters is an important design requirement (see section 7.3.9).&lt;br /&gt;
&lt;br /&gt;
7.3.11.2 Strength of the Reefing Line&lt;br /&gt;
&lt;br /&gt;
The force in the reefing line is determined according to information in section 5.6.8. Test items 22 and 23 in Figure 5-76 closely resemble the main parachute used here. A reefing-lineforce-to-reefed-parachute-force ratio of 2.5% is selected for this assembly. Therefore, the force in the reefing line is&lt;br /&gt;
&lt;br /&gt;
(0.025)FR = 0.025(9255 Ib) = 231.4 lb&lt;br /&gt;
&lt;br /&gt;
The design factor, DF, for the reefing system was determined in section 7.3.8, Table 7-4, to be 2.74.&lt;br /&gt;
&lt;br /&gt;
== 7.4 HIGH-SPEED DROGUE CHUTE ASSEMBLY ==&lt;br /&gt;
7.4.1 Requirements &lt;br /&gt;
&lt;br /&gt;
The following operational requirements govern the design of the first-stage drogue chute:&lt;br /&gt;
&lt;br /&gt;
1. The drone must be recoverable from any conceivable flight condition during the engineering test phase. &lt;br /&gt;
&lt;br /&gt;
2. An out-of-control drone or a drone that loses radio contact with the controller must be prevented from flying off the range. Recovery is initiated by an independent range signal. This type of recovery requires a high-speed deceleration parachute that can be deployed and operated when the drone is moving at maximum speed, or is in a spin, or during any other abnormal flight condition. &lt;br /&gt;
&lt;br /&gt;
This type of recovery established the following requirements for the type and size of the drogue chute:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
1. The drogue chute must have reliable operation in the velocity range from 200 knots at sea level to Mach 1.5 at 50,000 feet.&lt;br /&gt;
&lt;br /&gt;
2. Stability must be better than :: 3 degrees. &lt;br /&gt;
&lt;br /&gt;
3. Minimum weight and volume is mandatory. &lt;br /&gt;
&lt;br /&gt;
4. The drogue chute must be able to decelerate the drone to the permissible opening speed of the main parachute assemblies.&lt;br /&gt;
&lt;br /&gt;
5. The drogue chute must be suitable for the operational environment. Figure 7-17 shows the altitude-velocity flight envelope of the drone.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.2 Drogue Chute Selection &lt;br /&gt;
&lt;br /&gt;
Tables 5-1 through 5-5 in Chapter 5 list commonly used parachute types. Table 7-6 evaluates possible drogue chute candidates. Of the parachute candidates, only the conical ribbon and the hemisflo ribbon have been used successfully for similar applications.&lt;br /&gt;
&lt;br /&gt;
A 25-degree conical ribbon parachute is selected for this application. The conical ribbon parachute meets all requirements and has a higher subsonic drag coefficient than the equally&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.3 Required Drogue Chute Diameter &lt;br /&gt;
&lt;br /&gt;
The size of the fully open drogue chute is determined by the requirement that it must decelerate the 7200-pound drone to the allowable opening speed of the main parachute, which is governed by the requirement that the opening force of the two main parachutes must stay within the 9350-pound-per-chute limit established for the 200-knot opening speed of the 4800-pound drone. &lt;br /&gt;
&lt;br /&gt;
A preliminary calculation shows that a terminal velocity of about 175 KEAS is required to limit the opening load of the reefed main parachutes to 9350 pounds. A 13- to 14-footdiameter drogue chute is needed to meet this requirement. &lt;br /&gt;
&lt;br /&gt;
To reach 175 KEAS at main parachute line stretch, the drogue chute will be disconnected by an aneroid sensor at about 7000 feet mean sea level (MSL) while descending vertically from high altitude. The drone will free-fall for 0.8 second until main parachute line stretch occurs; the free-fall causes a 10-knot increase in velocity. In addition, the changing density, p, results in&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
NWC TP 6575 &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The gain in drag caused by the longer suspension lines and the 5% loss in drag caused by forebody wake (Figure 5-21) result in a final drag coefficient, CDo, for the drogue chute of &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
CDo = 0.55. 1.085 . 0.95 = 0.57&lt;br /&gt;
&lt;br /&gt;
and a corrected drogue chute diameter &lt;br /&gt;
&lt;br /&gt;
Do - 13.61 ft&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.4 Computer Analysis of Drogue Chute Performance &lt;br /&gt;
&lt;br /&gt;
At this point, a computer program should be established to determine the following performance conditions: &lt;br /&gt;
&lt;br /&gt;
1. Balance reefed and disreef parachute forces and filling times. Start at Mach 1.5 at 34,000 feet (see point () on Figure 7-17). Check final selection for a 10,000-foot-altitude condition. &lt;br /&gt;
&lt;br /&gt;
2. Determine required opening altitude for high-speed, low-altitude deployment. This requires trajectory runs with both the drogue and main parachutes. &lt;br /&gt;
&lt;br /&gt;
3. Determine maximum horizontal range, including prevailing wind conditions. &lt;br /&gt;
&lt;br /&gt;
4. Verify that the selected main parachute opening speed of 175 KEAS is reached for all important flight conditions and that, for an opening velocity of 175 KEAS, the main parachute forces stay within the allowable force limit of 9255 pounds. &lt;br /&gt;
&lt;br /&gt;
5. Include opening of the air bags with a 6.0-second inflation time in some of the trajectories. Inflation starts after main parachute opening. &lt;br /&gt;
&lt;br /&gt;
The prime contractor should point out any special flight conditions that may require parachute recovery. The prime contractor will probably also perform recovery computer runs to determine for which flight conditions and from what altitudes recovery can be accomplished. &lt;br /&gt;
&lt;br /&gt;
7.4.5 Flight Emergency Recovery Conditions &lt;br /&gt;
&lt;br /&gt;
Certain flight conditions other than recovery command from the flight controller or the range safety officer may result in automatic on-board recovery command. These conditions include &lt;br /&gt;
&lt;br /&gt;
1. Loss of RF link. &lt;br /&gt;
&lt;br /&gt;
2. Loss of engine power (glide on internal power). &lt;br /&gt;
&lt;br /&gt;
3. High accelerations in x, y, and z caused by out-of-control flight conditions or in-flightafflicted damage on target drones. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7-38&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
NWC TP 6575 &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.6 Drogue Chute Opening Forces &lt;br /&gt;
&lt;br /&gt;
Parachute opening forces should be obtained from the computer program. However, a hand calculation is required for defining the force range before setting up the computer program. Furthermore, canopy filling times and force coefficient, C,. must be determined before computer runs (see section 5.4). &lt;br /&gt;
&lt;br /&gt;
Determining the drogue chute opening forces with the W/CDS method is normally sufficiently accurate for high-canopy-loading drogue chutes. If no computer backup is available, the Pflanz method (see section 5.4.6) will provide good force data.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.6.1 Drogue Chute Reefed Opening Forces When the W/CDS method is used, the reefed opening force, FR, is calculated to&lt;br /&gt;
&lt;br /&gt;
and the maximum allowable drogue chute drag area with a 2Z000 force limit is calculated to&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
where &lt;br /&gt;
&lt;br /&gt;
FR, the maximum allowable force, is 22,000 lb &lt;br /&gt;
&lt;br /&gt;
q, the maximum dynamic pressure, is 813.9 lb/ft2 &lt;br /&gt;
&lt;br /&gt;
For supersonic application, Figure 5-50 in section 5.4 shows CK = C' . X1 for the supersonic deployment of conical ribbon parachutes. Most applicable are the data for the Mercury and the Cook conical ribbon parachutes, which were deployed at velocities up to Mach 1.6. CK factors of 1.3 to 1.75 have been measured in supersonic deployment of conical ribbon parachutes. Forebody wake and poor deployment greatly affect the force coefficient. Mortar deployment often produces bag strip-off before canopy stretch, causing premature partial canopy inflation and a high X1 factor. Rocket extraction or drogue gun/pilot chute deployment, both resulting in canopy stretch before skirt inflation, generally avoid this problem. A force coefficient C, = 1.25 is selected.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The canopy loading of the reefed drogue chute is&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The required reefing-line length for obtaining this drag area can be determined from Figure 5-73, section 5.6.6, using the method of section 7.3.11.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.6.2 Drogue Chute Disreef Opening Force &lt;br /&gt;
&lt;br /&gt;
An important factor to determine is reefing time. A long time is required to reach close to terminal velocity before disreef. A practical approach, based on experience, is to select the 1.1-times-terminal-velocity point for disreef. If this time is too long, then a shorter reefing time is required, resulting in a higher disreef velocity and forces&lt;br /&gt;
&lt;br /&gt;
The terminal velocity of the reefed parachute is&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
and disreef force, Fo, is calculated&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Both forces FR and Fo are close to the allowable force limit of 22,000 pounds. Because loads vary 5 to 10%, slight overloads may occur. However, the 7200-pound drone weight is the take-off weight. Off-range recovery and conceivable emergencies will occur at lighter drone weights, resulting in lower parachute forces.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.7 Drogue Chute Stress Analysis and Design &lt;br /&gt;
&lt;br /&gt;
Dimensioning of the various components of the parachute assembly involves three primary tasks (1) establishing design and safety factors, (2) determining the loads and stresses in the assembly components, and (3) dimensioning all assembly members. The methods used for these tasks are described in section 6.4. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.7.1 Drogue Chute Safety, Load, Loss, and Design Factors &lt;br /&gt;
&lt;br /&gt;
The method used is similar to the one developed in section 6.4. Table 7-7 shows safety, load, and loss factors in relation to design factor.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.7.2 Number of Gores and Suspension-Line Strength &lt;br /&gt;
&lt;br /&gt;
The drogue chute will be designed for a maximumn force, Fo, of 22,000 pounds in the reefed and full-open stages. The suspension-line arrangement was selected in accordance with Table 7-8.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.7.2 Number of Gores and Suspension-Line Strength &lt;br /&gt;
&lt;br /&gt;
The drogue chute will be designed for a maximumn force, Fo, of 22,000 pounds in the reefed and full-open stages. The suspension-line arrangement was selected in accordance with Table 7-8.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
A canopy with 24 gores and 3000-pound-individual-strength suspension lines is selected primarily for gore width and vent diameter. The relatively large vent must be covered with wide vent lines held in place by proper connections. &lt;br /&gt;
&lt;br /&gt;
The method described in section 6.4 is used for preliminary dimensioning of the horizontal ribbons. In this method, the expression Fo/(CDS)p is an indication of the pressure in the parachute canopy; the gore width, es, is an indication of the gore radius. A smaller gore width and resultant gore radius causes lower stress in the individual horizontal ribbons for a given internal pressure. Figure 6-41 shows boundary curves for the required horizontal ribbon strength. These data, based on analysis of many tested ribbon parachutes, were first presented in Reference 5.39 and subsequently updated by the author. &lt;br /&gt;
&lt;br /&gt;
For the reefed parachute,&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The gore width of the reefed parachute is obtained from the following consideration. The reefed drag area is equivalent to the drag area of a parachute with the following nominal diameter (DRJ):&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The equivalent nominal diameter for the reefed parachute is&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Two-inch-wide ribbon with 460-pound strength, MIL-T-5608, Trype DII, is selected for the upper canopy part, and 2-inch-wide ribbon with 300-pound strength, MIL-T-5608, Type CV, is used for the lower part of the canopy. This drogue parachute will be subjected to high-frequency ribbon flutter during its high-speed descent from altitude, which may include a descent on the drogue chute from 50,000 to 7000 feet. Disintegration of horizontal and vertical ribbon and the stitching connecting the ribbons has occurred in the past during long-duration, high-speed applications of reefed and unreefed ribbon chutes. This high-frequency flutter is especially pronounced on the uninflated part of reefed ribbon parachutes. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Experience has shown that the following design features will counteract this problem: &lt;br /&gt;
&lt;br /&gt;
1. Tight spacing of vertical ribbons. &lt;br /&gt;
&lt;br /&gt;
2. wo vertical ribbons, one on each side of horizontal ribbon. &lt;br /&gt;
&lt;br /&gt;
3. Three rows of stitching with F-F thread in the vertical ribbon. All three features are used in this canopy design. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.7.3 Design of Radials, Vent and Skirt Tape, and Vent Lines &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Radials.Based on experience, radials are designed to have 80% of the strength of the suspension lines; 0.8 3000 = 2400 pounds. Three 2-inch-wide tapes of MIL-T-5608 form each radial; two 1000-pound Class Eli tapes and one 460-pound Class DII tape give each radial a combined strength of 2460 pounds. It may be possible to use only two 1000-pound strength tapes that have 80% of the actual load of 2548 pounds. &lt;br /&gt;
&lt;br /&gt;
Skirt and Vent Tape. In accordance with the discussion in section 7.6.6, the selected skirt tape is equal in strength to the suspension line but is 2 inches wide. Nylon tape (MIL-T-5608, Class E, lype V) with 3000-pound strength meets this requirement.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The required strength of the vent tape is&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Because some of this load will be taken by the vent lines, a double 4000-pound webbing is chosen in accordance with MIL-W-2756, lype IL. &lt;br /&gt;
&lt;br /&gt;
Special attention is required to obtain a design that achieves proper connection between radial tape, vent tape, and vent lines. &lt;br /&gt;
&lt;br /&gt;
Vent lines. The vent lines should have 60% of the strength of the radial tapes and be 5% shorter than the finished vent diameter. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.7.4 Drogue Chute Riser Design &lt;br /&gt;
&lt;br /&gt;
The drogue chute riser is formed of bundled suspension lines. This design eliminates the 20% connection loss, u, on the parachute side and permits a highly efficient connection on the drone side. The individual lines must be secured against each other to prevent flutter abrasion. Each line runs from a loop on the canopy radial, down the riser, around the drone connection point, and up the riser to an opposite radial-tape loop. Tests should be made to determine the strength of the radial-tape and suspension-line-loop connection and the individual loop around the drone hard point. A wrap-around keeper is used on the riser suspension line transfer point.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.8.1 Canopy Porosity &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The porosity of a ribbon canopy is defined as the percentage ratio of openings in the canopy plus the material porosity divided by the total canopy surface area. Canopy porosity affects parachute stability, drag, and opening process. A canopy with high porosity provides for good parachute stability, and uniform, low force inflation, but also lower drag than a canopy with lower porosity. Too high a canopy porosity may result in no or only partial canopy inflation.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The operational porosity limit decreases with decreasing parachute diameter from about 35% total porosity for a stable 3-foot-diameter parachute to about 12% porosity for a 100-foot-diameter parachute (see Figure 6-23 (a) and Table 6-3). Section 6.2.4 discusses the effect of canopy porosity on the design and performance of ribbon parachutes. &lt;br /&gt;
&lt;br /&gt;
Properly designed conical ribbon parachutes with the correct porosity have an oscillation equal to or less than 2 to 3 degrees; a drag coefficient, CDo, of 0.55; and an opening-force coefficient, C., of 1.05 to 1.07 for subsonic applications with low forebody drag, such as experienced in wind-tunnel tests. &lt;br /&gt;
&lt;br /&gt;
The vertical ribbon spacing discussed in section 7.4.8.2 is of utmost importance for supersonic application. A canopy porosity of 25 to 26% in accordance with Figure 6-23, Curve III, and Thble 6-3 is recommended for this application. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.8.2 Vertical Ribbon Spacing &lt;br /&gt;
&lt;br /&gt;
Ribbon parachutes in the past were designed with individual gores, and the gores were connected with radial ribbons and several rows of stitching. This arrangement created the &amp;quot;venetian blind effect&amp;quot; shown in Figure 7-19. The venetian blind effect increases the effective canopy porosity discussed in section 6.2.4. &lt;br /&gt;
&lt;br /&gt;
More recently, ribbon canopies have been designed with continuous horizontal ribbons, a design that offers savings in weight and cost. This design is described in detail in section 7.4.10. &lt;br /&gt;
&lt;br /&gt;
Figure 7-20 shows the basic arrangement of a canopy gore and ribbon grid consisting of horizontal and vertical ribbons.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Section 6.2.4 explains the relationship of canopy loading, W/(CDS)p; effective porosity, Ne; and vertical ribbon spacing, a. Ribbon parachutes used as final descent parachutes use a vertical ribbon spacing to horizontal ribbon width a/B of 2.5 to 4.0. This spacing allows advantage to be taken of the change in effective porosity. High-canopy-loading ribbon parachutes, such as first-stage drogue chutes, use a vertical ribbon spacingof I to 2 to avoid the negative effects of the change in effective porosity. A narrow vertical ribbon spacing of 1.25 times the width of the horizontal ribbon width will be used for the drogue chute.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
All previous gore dimensions and the dimensions shown in Figure 7-21 are preliminary. The horizontal ribbon spacing, b, is controlled by the required porosity, k. Required changes in horizontal ribbon spacing may result in slight changez in gore and canopy dimensions.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.9.2 Preliminary Gore-Porosity Check &lt;br /&gt;
&lt;br /&gt;
Two methods of calculating gore porosity are in use. The older method, described in Reference 5.39, has been updated in this chapter. This method allows calculation of the porosity for preliminary design purposes when no final gore drawings are available. Reference 2.2 shows how to calculate canopy porosity if a drawing is available based on the ratio of open spaces to total canopy area. Both methods include an estimation of the ribbon (material) porosity&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The porosity of a ribbon grid with variations in the distance of the horizontal ribbons is now calculated. The total porosity is estimated, and the most likable horizontal ribbon distance is selected for the first gore-porosity check (Thble 7-9). The widths of the vertical ribbon, A, and the horizontal ribbon, B, are fixed values. The ratio of vertical ribbon spacing, to horizontal ribbon width, a/B, was previously selected to 1.25, which is equal to 2.5 inches. A horizontal ribbon distance, b, of 1.1 inches is selected as first approach based on data in Thble 7-9.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
To avoid a decrease in parachute diameter, 26 horizontal ribbons are selected, changing the gore dimensions from those shown in Figure 7-21 to those shown in Figure 7-22.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.9.S General Comments on Gore Design and Porosity Selection &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The canopy gore design-total canopy porosity, XT; spacing of vertical ribbon; size of vent; and pocket-band arrangement-are the primary design features that determine the aerodynamic performance of the parachute. The most important characteristics of parachute performance are stability, smooth opening, drag, and opening-force coefficients. Determining porosity under a no-load condition is rather unrealistic, because most of the important aerodynamic characteristics occur under high-load conditions (opening shock) or medium-load conditions (descent). However, since the beginning of parachute development, aerodynamic parachute characteristics obtained in wind-tunnel and free-flight tests have been related to fixed design dimensions such as diameter and porosity. &lt;br /&gt;
&lt;br /&gt;
Determining the effective porosity caused by the changing load during the opening process and by the venetian-blind effect of the ribbon grid design is practically impossible. Furthermore, the change in effective porosity is similar on all ribbon parachutes because of the similarities of the ribbon grid designs, load factors, and related changes in material elongation that cause deformation of the ribbon grids and the parachute canopies. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.9.6 Computer Programs for Determining Gore Design and Porosity Calculation &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Both gore design and porosity calculations can be determined by computer programs. Organizations involved in frequent design of ribbon parachutes should establish these programs. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.10 Ribbon Parachute Canopies with Continuous Horizontal Ribbons &lt;br /&gt;
&lt;br /&gt;
Ribbon parachute canopies are frequently designed and manufactured with continuous horizontal ribbons either in single or two-section canopies. The continuous ribbon Jesign decreases weight and volume, increases the strength of the horizontal ribbon-radial connection, and simplifies manufacturing. Continuous horizontal ribbons change the porosity characteristics of the canopy. &lt;br /&gt;
&lt;br /&gt;
Figure 7-19 shows how the individual horizontal ribbons orient themselves in a canopy manufactured from individual triangular gores. In the inflated canopy, the horizontal ribbons in the canopy crown area orient parallel to the canopy design. However, in the skirt area, the canopy design line is almost parallel to the airflow. This design, usually called the &amp;quot;venetian blind effect,&amp;quot; causes ti:e longer leading edge of each horizoatal ribbon to bulge out and position the ribbon with a positive angle of attack to the airflow. The result is an increase in effective porosity under high dynamic pressure conditions. The venetian blind effect is discussed in section 6.2.4, and the influence of canopy loading on the change in effective porosity is shown in Figure 6-24.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Designing canopies with continuous horizontal ribbons changes the venetian blind effect. Returning to Figure 7.19, it is obvious that continuous horizontal ribbons in the canopy skirt area do not bulge out since leading and trailing ribbon edges have the same length and do not position themselves with an angle of attack to the airflow. However, in the crown area of the canopy where each gore forms a triangle, the equal length of the leading and trailing ribbon edges now gives each ribbon a negative angle of attack thereby increasing the effective porosity in the canopy crown area. The effect is minimized by large number of gores arid by the use of a center vertical ribbon, or a miniradial, as Sandia engineers call it. &lt;br /&gt;
&lt;br /&gt;
Discussion with Sandia and industry personnel indicates that no measurable difference has been found in the aerodynamic characteristics of ribbon parachute canopies designed with individual gores or with continuous horizontal ribbons so long as the canopies contain a large number of gores and a center vertical ribbon. However, a slight delay in initial inflation seems to occur on small parachutes with a small number of gores. Closer spacing of vertical ribbons in the canopy crown area should counteract this delay. Another method of counteracting the delay is by gathering the trailing edges of horizontal ribbons with several rows of stitching and using a lower porosity in the crown area. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.11 Use of Kevlar Fabrics &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Many modern ribbon parachutes use Kevlar suspension lines, risers, and canopy skirt, lateral, and vent tapes, which results in a decrease in weight and volume. Section 6.5.5 discusses all aspects of working with Kevlar in the design of parachute assemblies. This includes physical characteristics of Kevlar fibers and fabrics, available Kevlar fabrics, and experience ;il designing in Kevlar. Section 6.6.5 should be studied before designing in Kevlar.&lt;/div&gt;</summary>
		<author><name>TuanHTruong</name></author>
	</entry>
	<entry>
		<id>https://mediawiki.aerodecelerator.org/index.php?title=Recovery_System_Design&amp;diff=40</id>
		<title>Recovery System Design</title>
		<link rel="alternate" type="text/html" href="https://mediawiki.aerodecelerator.org/index.php?title=Recovery_System_Design&amp;diff=40"/>
		<updated>2024-05-08T15:01:16Z</updated>

		<summary type="html">&lt;p&gt;TuanHTruong: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;= DESIGN OF A PARACHUTE RECOVERY AND LANDING SYSTEM =&lt;br /&gt;
This chapter deals with the design of a parachute recovery and landing attenuation system for a military reconnaissance drone. The prime emphasis in the design of this system is on undamaged recovery of the drone from the total flight performance envelope during the development and test phase, on undamaged recovery after a completed mission during military operations, and on multiple use of the recovery system. An engineering team conducts performance and system analyses and chooses what recovery concept to use, what types of parachutes to select for high-speed deceleration and for final recovery, and what impact-attenuation system is best for the particular application. This chapter covers the selection process for concepts and components. Different engineers may make different selections based on experiences with particular types of parachutes or deployment concepts; experience is always a viable reason for selecting a particular approach. However, using the selection criteria shown in Figure 2-6. the designer must put reliability of operation, undamaged recovery, reusability of the landing system, and minimum weight and volume at the top of the list of requirements. &lt;br /&gt;
&lt;br /&gt;
== 7.1 REQUIREMENTS ==&lt;br /&gt;
=== 7.1.1 System Requirements ===&lt;br /&gt;
&lt;br /&gt;
An unmanned air vehicle used for military reconnaissance must be recovered after a completed mission in rough terrain, undamaged and ready for multiple reuse. The recovery system must be able to &lt;br /&gt;
1. Recover the air vehicle after the completed mission when the vehicle has landed in rough terrain at altitudes from sea level to 5000 feet.&lt;br /&gt;
2. Recover the drone during the engineering test phase from all controlled and uncontrolled flight conditions. &lt;br /&gt;
3. Serve as a range-safety device to prevent the air vehicle from leaving the boundaries of the test range. &lt;br /&gt;
&lt;br /&gt;
The air vehicle has a takeoff weight of 7200 pounds and a landing weight, after the i completed mission, of 4800 pounds. Undamaged landing shall be possible in rough terrain with rocks up to 8 inches in diameter. Replacement parts and refurbishment cost shall be kept to a minimum.  &lt;br /&gt;
&lt;br /&gt;
=== 7.1.2 Requirements for Normal Operation ===&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|Drone weight at recovery after completed mission&lt;br /&gt;
|W&amp;lt;sub&amp;gt;d&amp;lt;/sub&amp;gt; = 4800 lb&lt;br /&gt;
|-&lt;br /&gt;
|Recovery velocity&lt;br /&gt;
|v&amp;lt;sub&amp;gt;o&amp;lt;/sub&amp;gt; = 150 to 200 KEAS&lt;br /&gt;
|-&lt;br /&gt;
|Minimum recovery altitude&lt;br /&gt;
|H&amp;lt;sub&amp;gt;o&amp;lt;/sub&amp;gt; = 2000 ft above ground level (AGL)&lt;br /&gt;
|-&lt;br /&gt;
|Maximum ground level&lt;br /&gt;
|H = 5000 ft&lt;br /&gt;
|-&lt;br /&gt;
|Maximum allowable total parachute force&lt;br /&gt;
|F&amp;lt;sub&amp;gt;o&amp;lt;/sub&amp;gt; = 16,000 lb&lt;br /&gt;
|-&lt;br /&gt;
|Maximum allowable impact deceleration at landing&lt;br /&gt;
|a = 9.0 ''g''&amp;lt;nowiki/&amp;gt;'s&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
=== 7.1.3 Requirements for Emergency Operation ===&lt;br /&gt;
Emergency operation includes recovery during the test phase from takeoff to landing and also includes recovery for range-safety reasons. &lt;br /&gt;
&lt;br /&gt;
Drone weight at takeoff .................................. Wdma = 7200 lb &lt;br /&gt;
&lt;br /&gt;
Maximum recovery velocity at mean sea level (MSL) ................................... vo = 490 KEAS &lt;br /&gt;
&lt;br /&gt;
Maximum recovery velocity at 38,000 to 50,000 ft altitude ........................................ vo = 1.5 Mach &lt;br /&gt;
&lt;br /&gt;
Maximum dynamic pressure .............................. qmm = 812 lb/ft2 &lt;br /&gt;
&lt;br /&gt;
Maximum allowable parachute force ........................ F0 = 22,000 lb  &lt;br /&gt;
&lt;br /&gt;
7.1.4 Requirements Analysis &lt;br /&gt;
&lt;br /&gt;
Three primary requirements pace the design of the recovery system: &lt;br /&gt;
&lt;br /&gt;
1. The drone must be able to land in rocky but level terrain without damage. &lt;br /&gt;
&lt;br /&gt;
2. Refurbishment cost and time shall be kept to a minimum. &lt;br /&gt;
&lt;br /&gt;
3. Recovery must be possible from all flight conditions during the flight test phase, including cases where the out-of-control drone flies off the range.  &lt;br /&gt;
&lt;br /&gt;
== 7.2 LANDING ANALYSIS AND IMPACT-ATTENUATION SYSTEM ==&lt;br /&gt;
7.2.1 Landing Analysis &lt;br /&gt;
&lt;br /&gt;
Three known recovery concepts prevent damage during landing in rocky terrain: &lt;br /&gt;
&lt;br /&gt;
1. Midair retrieval.&lt;br /&gt;
&lt;br /&gt;
2. Dual air bags or dual frangibles.&lt;br /&gt;
&lt;br /&gt;
3. Retrorockets combined with small, nondeflatable air bags.&lt;br /&gt;
&lt;br /&gt;
The need for retrieval helicopters or retrieval aircraft makes Method 1, midair retrieval, impractical. The other two methods are affected by the deceleration distance required to meet the 9-g limit. &lt;br /&gt;
&lt;br /&gt;
In section 6.8 of this manual, the required deceleration distance(s) is determined to be&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;s=\frac{{V_{e_1}}^2-{V_{e_2}}^2}{2g(n\eta-1)}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;{V_{e_1}}&amp;lt;/math&amp;gt; = velocity of the drone descending on the parachute (rate of descent), ft/s&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;V_{e_2}&amp;lt;/math&amp;gt; = permissible impact velocity, ft/s&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;g&amp;lt;/math&amp;gt; = acceleration of gravity, ft/s2&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\eta&amp;lt;/math&amp;gt; = effectiveness of the impact attenuation system used, dimensionless&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;n&amp;lt;/math&amp;gt; = allowable impact deceleration, ratio &amp;lt;math&amp;gt;n=\frac{a}{g}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Figure 6-68 of Chapter 6 shows the range of various impact attenuation systems as a&lt;br /&gt;
&lt;br /&gt;
function of rate of descent and allowable ground impact deceleration. The information&lt;br /&gt;
&lt;br /&gt;
indicates that air bags may be the most practical concept for this application. A cursory&lt;br /&gt;
&lt;br /&gt;
analysis indicates that a rate of descent of 25 ft/s at 5000 fee: altitude will result in a close to&lt;br /&gt;
&lt;br /&gt;
optimum weight ratio of the combined parachute air bag system (see Figure 6-83). Properly&lt;br /&gt;
&lt;br /&gt;
designed air bags will have an effectiveness of 65% as shown in the stroke-pressure diagram in&lt;br /&gt;
&lt;br /&gt;
Figure 6-78 and allow ground contact or final velocity of close to 0 ft/s.&lt;br /&gt;
&lt;br /&gt;
0&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.3&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
With these assumptions, the required effective air bag deceleration stroke is obtained&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
This deceleration distance is too short for a parachute retrorocket system because of the&lt;br /&gt;
&lt;br /&gt;
required timing accuracy and rocket burning time. Retrorocket systems are most practical for deceleration distances greater than 4 or 5 feet. Crushable and frangible impact attenuators are suitable for deceleration distances of less than 15 inches. Air bag systems work best for deceleration distances of 24 to 48 inches. The original assumption that an air bag concept maybe the most practical approach for this air vehicle is therefore confirmed.&lt;br /&gt;
&lt;br /&gt;
7.2.2 Impact Attenuator System&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The design of impact attenuator systems is discussed in section 6.8 of this manual.&lt;br /&gt;
&lt;br /&gt;
Figure 7-1 shows the reconnaissance drone and the air-bag attenuator systems that consist of two deflatable, two-compartment wing-bag bags (A); a single-compartment, deflatable nose bag (B); and a nondeflatable nose-buffer bag (C). The wing bags, the primary energy absorbers, need the already calculated 24-inch effective-deceleration stroke. For design reasons, 33 inches must be added to the bag height, 19 inches for the distance from the wing underside to the underside of the jet ,i rlucts, 10 inches for ground clearance, and 4 inches for bag bottom curvature. These additio:;. result in a total bag lihight of 57 inches. To ensure landing stability, an air bag height-to-diameter ratio of 1.25 is selected for the two wing bags, resulting in a bag diameter of 48 inches. The cross-hatched lower part of the two wing bags (see Figure 7-1) deflates at impact, but the upper part stays inflated and keeps the drone off the ground. The nose bag, B, helps to absorb the impact and deflates, and the nose of the drone&lt;br /&gt;
&lt;br /&gt;
comes to rest on the nondeflatable buffer bag, C. All air bags are inflated from 3000 psi nitrogen containers using aspirators for a 50/50 nitrogen air mixture. The air bags are prepressurized to 2 psi for full bag inflation prior to landing. Multiple blowout valves consisting of staggered blowout rubber disks around the circumference of the air bags control the bag deflation to stay within the 9-g deceleration limit.&lt;br /&gt;
&lt;br /&gt;
The weight of the impact-attenuation system-air bags, nitrogen containers, plumbing, and A/C containers-is estimated from section 6.7 to be 2.2% of the total drone weight, or 105.6 pounds. The air bags should be stored in containers that can be easily removed from the drone for repacking. Air bags must be deployed after the main parachutes are fully open to prevent air-bag damage caused by high dynamic pressure. Air-bag deployment begins with simultaneous pyroejecting of the removable air-bag-container covers and opening of the nitrogen-container valves. The wing bags, the primary nose bag, and the nose-buffer bag inflate. At ground contact, the bags compress, increasing the pressure inside the bags. At a preselected pressure level, the blowout valves (rubber disks, metal disks, or rubber-type sleeves) open and limit the maximum drone deceleration to the preselected level.&lt;br /&gt;
&lt;br /&gt;
7-4&lt;br /&gt;
&lt;br /&gt;
== 7.3 MAIN PARACHUTE SYSTEM ==&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.3.1 Main Parachute System Requirements&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Section 2.4 defines the criteria for parachute type selection. Requirements for low weight and volume rule out the low-drag slotted parachutes (ribbon, ringslot, and ringsail) as well as guide-surface and cross parachutes (see Tables 5.2 and 5.3). Parachute deployment past the vertical stabilizer rules out a single parachute in favor of a cluster of two parachutes deployed independently left and right of the vertical stabilizer. No cluster experience is available with annular or cross parachutes, and no reefing experience is available with annular parachutes. Cross parachutes cannot be reefed to the low reefing ratios required for this application. Extended-skirt and polyconical parachutes have been used successfully in clusters of large, reefed parachutes.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7-6&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
A cluster of two conical full extended skirt parachutes is most suitable for this system. In&lt;br /&gt;
&lt;br /&gt;
section 5.2, Figures 5.24 and 5-25 show that properly designed extended-skirt parachutes have&lt;br /&gt;
&lt;br /&gt;
drag coefficients equal to 0.8 to 0.9 in the 20- to 25-ft/s rate of descent range. Available data&lt;br /&gt;
&lt;br /&gt;
(Reference 5.23) indicate that a cluster of two extended-skirt parachutes is sufficiently stable&lt;br /&gt;
&lt;br /&gt;
for use with air bags. Extended-skirt parachutes have a low opening-force coefficient of 1.4,&lt;br /&gt;
&lt;br /&gt;
compared to an opening-force coefficient of 1.8 for conical and triconical parachutes.&lt;br /&gt;
&lt;br /&gt;
Extended-skirt parachutes can also be reefed to low reefing ratios, a requirement for final&lt;br /&gt;
&lt;br /&gt;
descent parachutes (see Chapter 5, Figure 5-72).&lt;br /&gt;
&lt;br /&gt;
73.3 Parachute Diameter&lt;br /&gt;
&lt;br /&gt;
The rate of descent at 5000 feet altitude was selected to 25 ft/s (see section 7.3.1). The&lt;br /&gt;
&lt;br /&gt;
equivalent rate of descent at sea level is&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The drag coefficient, CDo, for a conical full extended skirt parachute with a 23.2-ft/s rate of&lt;br /&gt;
&lt;br /&gt;
descent and a suspension-line ratio, [.e/Do, of 1.0 is obtained from Figure 5-25&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
A suspension-line ratio of 1.15 is selected. This is the longest practical length for extended skirt&lt;br /&gt;
&lt;br /&gt;
parachutes (see Figure 5-20).&lt;br /&gt;
&lt;br /&gt;
The length of the riser, Lr, depends on its installation in the drone; the riser should be long&lt;br /&gt;
&lt;br /&gt;
enough to extend beyond the fuselage and vertical stabilizer of the drone (see Figure 7-2),&lt;br /&gt;
&lt;br /&gt;
which gives the final configuration of the parachute cluster, including risers and parachutes.&lt;br /&gt;
&lt;br /&gt;
7.3.4 Parachute Deployment System&lt;br /&gt;
&lt;br /&gt;
A cluster of two main parachutes is selected and deployed left and right of the vertical&lt;br /&gt;
&lt;br /&gt;
stabilizer to avoid hang-up or damage of a single parachute by the vertical stabilizer. Each&lt;br /&gt;
&lt;br /&gt;
parachute needs its own extraction and deployment system to properly deploy past the&lt;br /&gt;
&lt;br /&gt;
stabilizer and to avoid interference with the other main parachute during deployment and&lt;br /&gt;
&lt;br /&gt;
inflation.&lt;br /&gt;
&lt;br /&gt;
TWo fast-opening extraction parachutes are used on each main parachute. Stable&lt;br /&gt;
&lt;br /&gt;
parachutes will minimize interferenc, during deployment. Experience with past recovery&lt;br /&gt;
&lt;br /&gt;
systems has shown that the most positive deployment is obtained by forced ejection of the&lt;br /&gt;
&lt;br /&gt;
extractiou or pilot chutes into good airflow past the vertical stabilizer by either mortar or&lt;br /&gt;
&lt;br /&gt;
drogue gun ejection. A mortar can eject large, heavy parachutes but creates large leaction&lt;br /&gt;
&lt;br /&gt;
forces and needs considerable space for installation. Drogue gun ejection is effective, but is&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
limited to the deployment of small, lightweight parachutes such as pilot chutes. Drogue gun ejected pilot chutes are selected for initiating main parachute deployment. To ensure proper&lt;br /&gt;
&lt;br /&gt;
clearance of the vertical stabilizer, the pilot chutes are ejeLted 45 degrees upward, backward&lt;br /&gt;
&lt;br /&gt;
and outward past the vertical stabilizer. The parachute installation in the drone fuselage&lt;br /&gt;
&lt;br /&gt;
requires cross-wind deployment and therefore forced ejection of the main parachute&lt;br /&gt;
&lt;br /&gt;
deployment bags. Four different methods have been used successfully to accomplish forced&lt;br /&gt;
&lt;br /&gt;
ejection: (1) using ejector springs enclosed in a textile cylinder. (2) gas-inflating nonporous&lt;br /&gt;
&lt;br /&gt;
ejector bags, (3) catapulting the bag out of the compartment, or (4) using a lift-web&lt;br /&gt;
&lt;br /&gt;
arrangement as discussed in section 6.1.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The deployment system selected consists of a drogue gun deployed pilot chute, an&lt;br /&gt;
&lt;br /&gt;
extraction parachute, and a main parachute deployment bag lifted from the parachute&lt;br /&gt;
&lt;br /&gt;
compartment by lift webs. When the hinged compartment doors open, two drogue gun slugs&lt;br /&gt;
&lt;br /&gt;
are fired 45 degrees upward and aft; each slug deploys a pilot chute sufficiently behind the&lt;br /&gt;
&lt;br /&gt;
drone into good airflow. These pilot chutes in turn extract two extraction chutes stowed on top of the main parachute deployment bags. The extraction chutes extract and deploy the two main 0&lt;br /&gt;
&lt;br /&gt;
parachutes left and right of the vertical stabilizers. Lift webs and unsymmetrical bag handles&lt;br /&gt;
&lt;br /&gt;
lift the main parachute bags out of the drone compartment and extract the main parachute&lt;br /&gt;
&lt;br /&gt;
past the vertical stabilizer (see Figure 7-3)&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.3.5 Extraction Parachute Assembly&lt;br /&gt;
&lt;br /&gt;
The two extraction parachutes must properly deploy the two main parachutes. The size of&lt;br /&gt;
&lt;br /&gt;
the extraction parachutes and their location in the wake of the drone is determined as follows:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
A stable, 7.4-foot-diameter ringslot parachute is selected. &lt;br /&gt;
&lt;br /&gt;
The weight of the ringslot extraction parachute can be estimated from section 6.7 to 2.5 pounds, and the weight of the extraction parachute assembly including riser and deployment bag to 1.5 . 2.5 pounds = 3.75 pounds. The weight of a single 72.7-foot-diameter main parachute, as determined from section 6.7, is 54 pounds. This weight estimate assumes an efficiently designed main canopy that has a combination of tape and radial seams to carry the radial loads and has other, similar weight-saving design features. The arrangement of the extraction parachute in relation to the drone is shown in Figure 7-5. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.3.6 Pilot Parachute Assembly &lt;br /&gt;
&lt;br /&gt;
The extraction parachute assembly weight of 3.75 pounds is too heavy to be deployed by a drogue-gun slug; therefore, a small pilot chute is selected for initial deployment by the drogue-gun slug. This pilot chute, in turn, will deploy the extraction parachute.&lt;br /&gt;
&lt;br /&gt;
Evaluation of past good and poor deployments has led to the rule that the extraction force of the pilot chute should be greater than or equal to four times the weight of the unit to be extracted; in this case, the extraction parachute assembly. So that the pilot chute has enough force, a pilot chute is selected that will produce, at the minimum deployment speed of 150 KEAS, an extraction force equal to five times the weight of the extraction parachute assembly: 5. 3.75 pounds - 18.75 pounds. The minimum dynamic pressure at 150 KEAS is&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.3.7 Main Parachute Forces&lt;br /&gt;
&lt;br /&gt;
7.3.7.1 Requirements &lt;br /&gt;
&lt;br /&gt;
Drone weight ............................................. W D = 4800 lb&lt;br /&gt;
&lt;br /&gt;
Maximum deployment speed .............................. vo = 200 KEAS &lt;br /&gt;
&lt;br /&gt;
Minimum deployment speed ........................ Vo minimum = 150 KEAS &lt;br /&gt;
&lt;br /&gt;
Maximum allowable total parachute force (two main parachutes) ................................... FT = 16,000 lb &lt;br /&gt;
&lt;br /&gt;
Deployment altitude .................................. H = 2000 to 7000 ft &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.3.7.2 Velocity-Altitude Profile &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Section 5.5 states that the maximum opening force of the main parachute occurs at maximum deployment altitude. Figure 7-8 shows a velocity-altitude-versus-time profile for a typical vehicle recovery system. &lt;br /&gt;
&lt;br /&gt;
The maximum dynamic pressure, qo, occurs at the 200-KEAS deployment velocity &lt;br /&gt;
&lt;br /&gt;
2. The Pflanz method is quite accurate for all conditions including high altitude, but neglects the effect of gravity. Parachutes opened in vertical descent will have a 1-g (one weight unit) higher force than calculated. It is necessary to calculate the canopy filling times for the various reefed stages (see section 5.4.3) and to determine the drag-area-versus-time profile for the specific parachute (see section 5.4.4). This method permits the investigation of variations in filling times and drag-area-versus-time profiles. &lt;br /&gt;
&lt;br /&gt;
3. The force-trajectory-time computer method includes the effects of altitude, gravity, and changing trajectory angle. This method requires determination of a drag-area-versus-time profile for the entire parachute opening sequence (see Figure 5-52). Computers permit multiple runs with changes in times, drag-area-versus-time profiles, starting velocities, and altitudes.&lt;br /&gt;
&lt;br /&gt;
7.3.7.4 Reefed Opening Forces&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
To  save trajectory time, the reef-d pardchute is disreefed at a dynamic pressure 10 to 20% higher than the terminal reefed dynamic pressure. Therefore,&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Results of changing the canopy inflation time, tf, and the drag-area-versus-time profile, n, are shown in Thble 7-2. Reference 5-76, the Pflanz report, provides a more detailed study of the effect of canopy fill time and drag-area-increase-versus-time profile on the magnitude of the parachute force&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Force-Trajectory-Time Computer Method &lt;br /&gt;
&lt;br /&gt;
The program established oy NWC determines as a function of time the parachute forces, the vehicle deceleration, and the space-positioning (trajectory) data in a two-axis system. The method requires a drag-area-versus-time profile for the individual parachutes and the total vehicle system (Figure 7-9). This profile was previously shown in Figure 5-52. Figure 7-9 includes the change in air-vehicle drag caused by the change in vehicle attitude during the parachute opening process&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.3.7.6 Comments on Calculated Opening Forces 1. The reefed opening force for the single parachute is higher than thie contractor-requested maximum allowable force per parachute of 8000 pounds&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
2. The average disreef force is approximately 1500 pounds lower than the reefed force. Therefore, it appears logical to lower the reefed force and increase the disreef force. Although this adjustment probably cannot be made within the 8000-pound limit, 8500 pounds appears to be an obtainable goal. &lt;br /&gt;
&lt;br /&gt;
3. To meet the contractor requirement of an 8000-pound maximum force limit per parachute, two-stage reefing is required. &lt;br /&gt;
&lt;br /&gt;
4. It appears practical to determine in drop tests if a 2.0 to 2.1% reefed drag area can be obtained. This drag area would decrease the reefed opening force and somewhat increase the disreef force. However, reaching an average maximum force of less than 8000 pounds appears doubtful. &lt;br /&gt;
&lt;br /&gt;
5. In the calculations, both parachutes are assumed to have equal opening forces. In reality, opening forces of the two parachutes can differ because of variations in filling time. lead-ann-lag chute behavior caused by blanketing, and resultant nonuniform canopy inflation. 7-22 NWC TP 6575 &lt;br /&gt;
&lt;br /&gt;
The fast-opening Apollo ringsail-type main parachutes had a load distribution among the three parachutes of 40-40-20. The individual parachutes, therefore, had to be overdesigned in a 40/33 ratio. However, the total parachute force load taken by the vehicle hard points did not exceed the calculated average load because of the high-low variation of the individual parachutes. &lt;br /&gt;
&lt;br /&gt;
The two slower-opening extended-skirt parachutes used for this application are more uniform in their load distribution. A cursory analysis of available test data indicates that a 55/45 load distribution between the two parachutes and a no-overload condition for the vehicle hard points should be an acceptable load distribution. &lt;br /&gt;
&lt;br /&gt;
A contractor-subcontractor agreement is required to determine whether the individual parachutes should be designed for the 55/45 load variation or whether this overload can be accommodated by the 1.5 safety factor and the additional safety provided by the normal overstrength of textile specification materials.&lt;br /&gt;
&lt;br /&gt;
7.3.7.7 Snatch Forces &lt;br /&gt;
&lt;br /&gt;
The snatch force is caused by the acceleration of the mass of the parachute assembly to the velocity of the forebody (drone). A canopy, partially inflated at line stretch, increases the mass of the parachute by the mass of the air included in the canopy; this can increase the snatch force (mass shock) considerably.  &lt;br /&gt;
&lt;br /&gt;
Two  principal rules should be followed to keep the snatch force within allowable limits.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
1. Keep the parachute canopy closed until line (canopy) stretch occurs by use of a deployment bag o! %kirt restrictor.&lt;br /&gt;
&lt;br /&gt;
2. Accelerate I!: mass of the parachute assembly in incremental steps. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Known means of accomplishing these goals are discussed in Chapter 6.1. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The difference between a poor deployment and a deployment that accomplishes the first rule and partially accomplishes ' second is illustrated in Figure 5-54, which shows snatch and opening forces for the C-9 p. tchute with and without the quarter deployment bag. The deployment method outlined in ! tilon 7.3.4 should hold snatch forces at a level below the parachute opening forces. &lt;br /&gt;
&lt;br /&gt;
A method for calculating ,tch forces is described in Reference 2.2, the 1963 edition of the USAF parachute handbook. : nreferred method for calculating parachute deployment. including the snatch force, is cont.iiiici in J. W Purvis's AIAA paper, &amp;quot;Improved Prediction of Parachute Line Sail During I incs-First Deployment&amp;quot; (Reference 5.86)&lt;br /&gt;
&lt;br /&gt;
7.3.8 Parachute Stress Analysis &lt;br /&gt;
&lt;br /&gt;
7.3.8.1 Parachute Design Data&lt;br /&gt;
&lt;br /&gt;
A total parachute assembly is shown in Figure 7-10.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.3.8.2 Parachute Forces &lt;br /&gt;
&lt;br /&gt;
The maximum reefed opening force, FR, is 9255 pounds. The maximum disreef opening force, F., is 7404 pounds. The maximum design force for stressing the parachute assembly, FI, is 9255 pounds.&lt;br /&gt;
&lt;br /&gt;
The forces obtained in computer runs are selected as the most accurate forces for stressing the parachute assembly and its components. Based on multiple computer runs, a diligent choice must be made for the most likable forces.&lt;br /&gt;
&lt;br /&gt;
7.3.83 Main-Parachute Safety and Design Factors &lt;br /&gt;
&lt;br /&gt;
Section 6.4 is used as a guide for selecting the safety, load, loss, and design factors in Table 7.4&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
1. Connection of suspension lines to riser legs and drone hardpoints is made easier if the number of suspension lines are a multiple of 4 or 8. &lt;br /&gt;
&lt;br /&gt;
2. The gore at the skirt should not be wider than 3.5 feet for packing reasons. &lt;br /&gt;
&lt;br /&gt;
3. The canopy should have no fewer than 12 gores to avoid gore distortion during inflation. &lt;br /&gt;
&lt;br /&gt;
4. Radial ribbons or radial seams should not overlap at the vent; overlapping causes bunching of material and associated sewing problems. &lt;br /&gt;
&lt;br /&gt;
5. The strengths of available suspension-line types may affect the gore selection. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Table 7-5 shows the required suspension line strength and the resultant gore width as functions of the number of gore/suspension lines used. &lt;br /&gt;
&lt;br /&gt;
7-25 NWC TP 6575&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The width of the goie of the skirt on conical, full-extended-skirt (CFES) parachutes is about 85% of the maximum gore width, Eo. Sixty-four suspension lines are selected in accordance with MIL-C-7515, TIpe XI, with 300-pound tensile strength. This selection provides a margin of safety (MS) of&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The suspension line will be attached to the canopy skirt in a loop connection. &lt;br /&gt;
&lt;br /&gt;
7.3.8.5 Canopy Stress&lt;br /&gt;
&lt;br /&gt;
No precise method has been d.-veloped for calculating the stress in a circular, solid-material, bias-construction canopy.&lt;br /&gt;
&lt;br /&gt;
Section 6.4 describes a semi-empirical method for determining the required fabric strength of a solid material canopy in pounds per unit width using the stress in a pressure vessel as an analogy. The stress in a cylindrical vessel, expressed as force per unit length, is&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
where p is the pressure in the cylindrical vessel and r is the vessel radius. Using this analogy and considering the canopy gore as part of a pressure vessel, the required material strength of the canopy per unit width is obtained&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The maximum stress actually occurs during reefed inflation because of the smaller inflated diameter:&lt;br /&gt;
&lt;br /&gt;
7.3.8.6 Canopy Reinforcing Tapes &lt;br /&gt;
&lt;br /&gt;
1. Skirt Tape. The skirt tape should Iv. equal or greater in strength than the individual suspension lines but not less than 1000 pounds, and 1-inch-wide tape should be used for parachutes larger than 20 feet in diameter. &lt;br /&gt;
&lt;br /&gt;
The nylon tape selected is 1-inch-wide MIL-T-5038, Type IV, with 1000-pound strength. Proper connection of the skirt tape to the radial seam (tape) and the suspension line must be ensured.&lt;br /&gt;
&lt;br /&gt;
2. Vent Tape. From the geometric design of the parachute vent (Figure 7-11). the force in the vent tape, FVT, is calculated&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
A 1-inch-wide, 4000-pound webbing (MIL-W-5625) or 7/8-inch-wide, 3100-pound webbing (MIL-W-5625) is selected. &lt;br /&gt;
&lt;br /&gt;
3. Vent Lines. The strength of the vent line- should be equal to or greater than 60% of the strength of the radials&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.3.8.7 Design of Radials &lt;br /&gt;
&lt;br /&gt;
The following four types of radial designs are in use: &lt;br /&gt;
&lt;br /&gt;
1. Radial seams with suspension lines running in channels over the canopy and attached at the vent and the skirt as on the canopy of the C-9 personnel parachute. &lt;br /&gt;
&lt;br /&gt;
2. Suspension lines running on top of the radials over the canopy and sewn at full length to the canopy as on many heavy-duty ribtx'n parachutes. &lt;br /&gt;
&lt;br /&gt;
3. Radial tapes sewn on top of or inside the radial seams, and suspension lines attached to the radial tapes by sewing or by skirt loops (NB-7 and T-10 canopies). &lt;br /&gt;
&lt;br /&gt;
4. Radial ribbons on ribbon parachutes designed to take the total radial load with suspension lines sewn onto d e radials or connected by a skirt loop. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The following are some comments on the design of radials: &lt;br /&gt;
&lt;br /&gt;
1. Making the strength of the radials 1:qtlal to 80% of the strength of the suspension lines has been satisfactory on thousands of ribbon parachutes. &lt;br /&gt;
&lt;br /&gt;
2. When tapes or suspension lines are sewn at full length to the radials, care must be taken that fullness in the radials ensures that the radial tapes or the suspension lines are the primary load carrying members. For an explanation of fullness, see section 6.6.4. &lt;br /&gt;
&lt;br /&gt;
3. Uniform material distribution is of utmost importance when sewn tapes or lines are used for radial reinforcemetnt. &lt;br /&gt;
&lt;br /&gt;
For the radial design of the main parachute, we use a tape with 80% strength of the suspension lint (0.8. 300 lb - 240 Ib) sewn on top of the radial scam. A 250-pound strength, 'A-inch-wide tape is selected in accordance with MIL-T-5038, 7ýpe III. Thpe and radial seams are marked every 24 inches for proper material distribution&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.3.8.8 Check for Proper Gore Fullness &lt;br /&gt;
&lt;br /&gt;
When the first parachute of a new design has been completed in the manufacturing shop, a gore fullness check in accordance with Figure 7-12 should be conducted. A slight amount of slack should be noticeable in the canopy fabric in both directions when all four corners of a gore are pulled radially outward. Slack indicates that the main loads are carried by the radials and reinforcing tapes and not by the canopy fabric. Stress folds in the canopy indicate faults in the design or manufacture of the parachute&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
’&lt;br /&gt;
&lt;br /&gt;
This is a large vent opening for a reefed parachute. Several criteria may be used to determine the size of the canopy vent as follows: &lt;br /&gt;
&lt;br /&gt;
1. Unreefed parachutes with vents up to 1% of the canopy surface area, So, have been operated successfully.&lt;br /&gt;
&lt;br /&gt;
2. Reefed parachutes require a vent diameter, DV, smaller than the reefing line circle, diameter DR, of the parachute; Dv is smaller than DR (see section 5.6, Figure 5-66). &lt;br /&gt;
&lt;br /&gt;
3. The radials at the vent should not overlap. A 1-inch free space between radials is desirable (see Figure 7-14)&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Stress in the canopy gore area can be relieved by making the gore at the vent 10% wider than the calculated gore dimension, ev. Therefore, ev* - 1.1 . ev - 1.1(1.6) = 1.76 inches. The vent tape is sewn to the vent at the original ev dimension, thereby gathering the vent 10% and creating a stress-relieving arcing in the gore fabric next to the vent. See Figure 7-15 for an example of final gore dimensions.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.3.10 Pocket Bands The pocket bands used on every gore make canopy inflation more uniform and eliminates long and short filling times. A narrow tape is used as the pocket band, which will :ot affect the average length of the canopy filling time. Data on the dimensioning of pocket bands are given in section 6.4. As shown in Figure 7-16, the pocket band dimensions are&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The diameter of the reefing line circle, DR, is larger than the 3.64-foot vent diameter of the canopy, Dv. This difference in diameters is an important design requirement (see section 7.3.9).&lt;br /&gt;
&lt;br /&gt;
7.3.11.2 Strength of the Reefing Line&lt;br /&gt;
&lt;br /&gt;
The force in the reefing line is determined according to information in section 5.6.8. Test items 22 and 23 in Figure 5-76 closely resemble the main parachute used here. A reefing-lineforce-to-reefed-parachute-force ratio of 2.5% is selected for this assembly. Therefore, the force in the reefing line is&lt;br /&gt;
&lt;br /&gt;
(0.025)FR = 0.025(9255 Ib) = 231.4 lb&lt;br /&gt;
&lt;br /&gt;
The design factor, DF, for the reefing system was determined in section 7.3.8, Table 7-4, to be 2.74.&lt;br /&gt;
&lt;br /&gt;
== 7.4 HIGH-SPEED DROGUE CHUTE ASSEMBLY ==&lt;br /&gt;
7.4.1 Requirements &lt;br /&gt;
&lt;br /&gt;
The following operational requirements govern the design of the first-stage drogue chute:&lt;br /&gt;
&lt;br /&gt;
1. The drone must be recoverable from any conceivable flight condition during the engineering test phase. &lt;br /&gt;
&lt;br /&gt;
2. An out-of-control drone or a drone that loses radio contact with the controller must be prevented from flying off the range. Recovery is initiated by an independent range signal. This type of recovery requires a high-speed deceleration parachute that can be deployed and operated when the drone is moving at maximum speed, or is in a spin, or during any other abnormal flight condition. &lt;br /&gt;
&lt;br /&gt;
This type of recovery established the following requirements for the type and size of the drogue chute:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
1. The drogue chute must have reliable operation in the velocity range from 200 knots at sea level to Mach 1.5 at 50,000 feet.&lt;br /&gt;
&lt;br /&gt;
2. Stability must be better than :: 3 degrees. &lt;br /&gt;
&lt;br /&gt;
3. Minimum weight and volume is mandatory. &lt;br /&gt;
&lt;br /&gt;
4. The drogue chute must be able to decelerate the drone to the permissible opening speed of the main parachute assemblies.&lt;br /&gt;
&lt;br /&gt;
5. The drogue chute must be suitable for the operational environment. Figure 7-17 shows the altitude-velocity flight envelope of the drone.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.2 Drogue Chute Selection &lt;br /&gt;
&lt;br /&gt;
Tables 5-1 through 5-5 in Chapter 5 list commonly used parachute types. Table 7-6 evaluates possible drogue chute candidates. Of the parachute candidates, only the conical ribbon and the hemisflo ribbon have been used successfully for similar applications.&lt;br /&gt;
&lt;br /&gt;
A 25-degree conical ribbon parachute is selected for this application. The conical ribbon parachute meets all requirements and has a higher subsonic drag coefficient than the equally&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.3 Required Drogue Chute Diameter &lt;br /&gt;
&lt;br /&gt;
The size of the fully open drogue chute is determined by the requirement that it must decelerate the 7200-pound drone to the allowable opening speed of the main parachute, which is governed by the requirement that the opening force of the two main parachutes must stay within the 9350-pound-per-chute limit established for the 200-knot opening speed of the 4800-pound drone. &lt;br /&gt;
&lt;br /&gt;
A preliminary calculation shows that a terminal velocity of about 175 KEAS is required to limit the opening load of the reefed main parachutes to 9350 pounds. A 13- to 14-footdiameter drogue chute is needed to meet this requirement. &lt;br /&gt;
&lt;br /&gt;
To reach 175 KEAS at main parachute line stretch, the drogue chute will be disconnected by an aneroid sensor at about 7000 feet mean sea level (MSL) while descending vertically from high altitude. The drone will free-fall for 0.8 second until main parachute line stretch occurs; the free-fall causes a 10-knot increase in velocity. In addition, the changing density, p, results in&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
NWC TP 6575 &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The gain in drag caused by the longer suspension lines and the 5% loss in drag caused by forebody wake (Figure 5-21) result in a final drag coefficient, CDo, for the drogue chute of &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
CDo = 0.55. 1.085 . 0.95 = 0.57&lt;br /&gt;
&lt;br /&gt;
and a corrected drogue chute diameter &lt;br /&gt;
&lt;br /&gt;
Do - 13.61 ft&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.4 Computer Analysis of Drogue Chute Performance &lt;br /&gt;
&lt;br /&gt;
At this point, a computer program should be established to determine the following performance conditions: &lt;br /&gt;
&lt;br /&gt;
1. Balance reefed and disreef parachute forces and filling times. Start at Mach 1.5 at 34,000 feet (see point () on Figure 7-17). Check final selection for a 10,000-foot-altitude condition. &lt;br /&gt;
&lt;br /&gt;
2. Determine required opening altitude for high-speed, low-altitude deployment. This requires trajectory runs with both the drogue and main parachutes. &lt;br /&gt;
&lt;br /&gt;
3. Determine maximum horizontal range, including prevailing wind conditions. &lt;br /&gt;
&lt;br /&gt;
4. Verify that the selected main parachute opening speed of 175 KEAS is reached for all important flight conditions and that, for an opening velocity of 175 KEAS, the main parachute forces stay within the allowable force limit of 9255 pounds. &lt;br /&gt;
&lt;br /&gt;
5. Include opening of the air bags with a 6.0-second inflation time in some of the trajectories. Inflation starts after main parachute opening. &lt;br /&gt;
&lt;br /&gt;
The prime contractor should point out any special flight conditions that may require parachute recovery. The prime contractor will probably also perform recovery computer runs to determine for which flight conditions and from what altitudes recovery can be accomplished. &lt;br /&gt;
&lt;br /&gt;
7.4.5 Flight Emergency Recovery Conditions &lt;br /&gt;
&lt;br /&gt;
Certain flight conditions other than recovery command from the flight controller or the range safety officer may result in automatic on-board recovery command. These conditions include &lt;br /&gt;
&lt;br /&gt;
1. Loss of RF link. &lt;br /&gt;
&lt;br /&gt;
2. Loss of engine power (glide on internal power). &lt;br /&gt;
&lt;br /&gt;
3. High accelerations in x, y, and z caused by out-of-control flight conditions or in-flightafflicted damage on target drones. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7-38&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
NWC TP 6575 &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.6 Drogue Chute Opening Forces &lt;br /&gt;
&lt;br /&gt;
Parachute opening forces should be obtained from the computer program. However, a hand calculation is required for defining the force range before setting up the computer program. Furthermore, canopy filling times and force coefficient, C,. must be determined before computer runs (see section 5.4). &lt;br /&gt;
&lt;br /&gt;
Determining the drogue chute opening forces with the W/CDS method is normally sufficiently accurate for high-canopy-loading drogue chutes. If no computer backup is available, the Pflanz method (see section 5.4.6) will provide good force data.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.6.1 Drogue Chute Reefed Opening Forces When the W/CDS method is used, the reefed opening force, FR, is calculated to&lt;br /&gt;
&lt;br /&gt;
and the maximum allowable drogue chute drag area with a 2Z000 force limit is calculated to&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
where &lt;br /&gt;
&lt;br /&gt;
FR, the maximum allowable force, is 22,000 lb &lt;br /&gt;
&lt;br /&gt;
q, the maximum dynamic pressure, is 813.9 lb/ft2 &lt;br /&gt;
&lt;br /&gt;
For supersonic application, Figure 5-50 in section 5.4 shows CK = C' . X1 for the supersonic deployment of conical ribbon parachutes. Most applicable are the data for the Mercury and the Cook conical ribbon parachutes, which were deployed at velocities up to Mach 1.6. CK factors of 1.3 to 1.75 have been measured in supersonic deployment of conical ribbon parachutes. Forebody wake and poor deployment greatly affect the force coefficient. Mortar deployment often produces bag strip-off before canopy stretch, causing premature partial canopy inflation and a high X1 factor. Rocket extraction or drogue gun/pilot chute deployment, both resulting in canopy stretch before skirt inflation, generally avoid this problem. A force coefficient C, = 1.25 is selected.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The canopy loading of the reefed drogue chute is&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The required reefing-line length for obtaining this drag area can be determined from Figure 5-73, section 5.6.6, using the method of section 7.3.11.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.6.2 Drogue Chute Disreef Opening Force &lt;br /&gt;
&lt;br /&gt;
An important factor to determine is reefing time. A long time is required to reach close to terminal velocity before disreef. A practical approach, based on experience, is to select the 1.1-times-terminal-velocity point for disreef. If this time is too long, then a shorter reefing time is required, resulting in a higher disreef velocity and forces&lt;br /&gt;
&lt;br /&gt;
The terminal velocity of the reefed parachute is&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
and disreef force, Fo, is calculated&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Both forces FR and Fo are close to the allowable force limit of 22,000 pounds. Because loads vary 5 to 10%, slight overloads may occur. However, the 7200-pound drone weight is the take-off weight. Off-range recovery and conceivable emergencies will occur at lighter drone weights, resulting in lower parachute forces.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.7 Drogue Chute Stress Analysis and Design &lt;br /&gt;
&lt;br /&gt;
Dimensioning of the various components of the parachute assembly involves three primary tasks (1) establishing design and safety factors, (2) determining the loads and stresses in the assembly components, and (3) dimensioning all assembly members. The methods used for these tasks are described in section 6.4. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.7.1 Drogue Chute Safety, Load, Loss, and Design Factors &lt;br /&gt;
&lt;br /&gt;
The method used is similar to the one developed in section 6.4. Table 7-7 shows safety, load, and loss factors in relation to design factor.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.7.2 Number of Gores and Suspension-Line Strength &lt;br /&gt;
&lt;br /&gt;
The drogue chute will be designed for a maximumn force, Fo, of 22,000 pounds in the reefed and full-open stages. The suspension-line arrangement was selected in accordance with Table 7-8.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.7.2 Number of Gores and Suspension-Line Strength &lt;br /&gt;
&lt;br /&gt;
The drogue chute will be designed for a maximumn force, Fo, of 22,000 pounds in the reefed and full-open stages. The suspension-line arrangement was selected in accordance with Table 7-8.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
A canopy with 24 gores and 3000-pound-individual-strength suspension lines is selected primarily for gore width and vent diameter. The relatively large vent must be covered with wide vent lines held in place by proper connections. &lt;br /&gt;
&lt;br /&gt;
The method described in section 6.4 is used for preliminary dimensioning of the horizontal ribbons. In this method, the expression Fo/(CDS)p is an indication of the pressure in the parachute canopy; the gore width, es, is an indication of the gore radius. A smaller gore width and resultant gore radius causes lower stress in the individual horizontal ribbons for a given internal pressure. Figure 6-41 shows boundary curves for the required horizontal ribbon strength. These data, based on analysis of many tested ribbon parachutes, were first presented in Reference 5.39 and subsequently updated by the author. &lt;br /&gt;
&lt;br /&gt;
For the reefed parachute,&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The gore width of the reefed parachute is obtained from the following consideration. The reefed drag area is equivalent to the drag area of a parachute with the following nominal diameter (DRJ):&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The equivalent nominal diameter for the reefed parachute is&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Two-inch-wide ribbon with 460-pound strength, MIL-T-5608, Trype DII, is selected for the upper canopy part, and 2-inch-wide ribbon with 300-pound strength, MIL-T-5608, Type CV, is used for the lower part of the canopy. This drogue parachute will be subjected to high-frequency ribbon flutter during its high-speed descent from altitude, which may include a descent on the drogue chute from 50,000 to 7000 feet. Disintegration of horizontal and vertical ribbon and the stitching connecting the ribbons has occurred in the past during long-duration, high-speed applications of reefed and unreefed ribbon chutes. This high-frequency flutter is especially pronounced on the uninflated part of reefed ribbon parachutes. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Experience has shown that the following design features will counteract this problem: &lt;br /&gt;
&lt;br /&gt;
1. Tight spacing of vertical ribbons. &lt;br /&gt;
&lt;br /&gt;
2. wo vertical ribbons, one on each side of horizontal ribbon. &lt;br /&gt;
&lt;br /&gt;
3. Three rows of stitching with F-F thread in the vertical ribbon. All three features are used in this canopy design. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.7.3 Design of Radials, Vent and Skirt Tape, and Vent Lines &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Radials.Based on experience, radials are designed to have 80% of the strength of the suspension lines; 0.8 3000 = 2400 pounds. Three 2-inch-wide tapes of MIL-T-5608 form each radial; two 1000-pound Class Eli tapes and one 460-pound Class DII tape give each radial a combined strength of 2460 pounds. It may be possible to use only two 1000-pound strength tapes that have 80% of the actual load of 2548 pounds. &lt;br /&gt;
&lt;br /&gt;
Skirt and Vent Tape. In accordance with the discussion in section 7.6.6, the selected skirt tape is equal in strength to the suspension line but is 2 inches wide. Nylon tape (MIL-T-5608, Class E, lype V) with 3000-pound strength meets this requirement.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The required strength of the vent tape is&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Because some of this load will be taken by the vent lines, a double 4000-pound webbing is chosen in accordance with MIL-W-2756, lype IL. &lt;br /&gt;
&lt;br /&gt;
Special attention is required to obtain a design that achieves proper connection between radial tape, vent tape, and vent lines. &lt;br /&gt;
&lt;br /&gt;
Vent lines. The vent lines should have 60% of the strength of the radial tapes and be 5% shorter than the finished vent diameter. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.7.4 Drogue Chute Riser Design &lt;br /&gt;
&lt;br /&gt;
The drogue chute riser is formed of bundled suspension lines. This design eliminates the 20% connection loss, u, on the parachute side and permits a highly efficient connection on the drone side. The individual lines must be secured against each other to prevent flutter abrasion. Each line runs from a loop on the canopy radial, down the riser, around the drone connection point, and up the riser to an opposite radial-tape loop. Tests should be made to determine the strength of the radial-tape and suspension-line-loop connection and the individual loop around the drone hard point. A wrap-around keeper is used on the riser suspension line transfer point.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.8.1 Canopy Porosity &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The porosity of a ribbon canopy is defined as the percentage ratio of openings in the canopy plus the material porosity divided by the total canopy surface area. Canopy porosity affects parachute stability, drag, and opening process. A canopy with high porosity provides for good parachute stability, and uniform, low force inflation, but also lower drag than a canopy with lower porosity. Too high a canopy porosity may result in no or only partial canopy inflation.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The operational porosity limit decreases with decreasing parachute diameter from about 35% total porosity for a stable 3-foot-diameter parachute to about 12% porosity for a 100-foot-diameter parachute (see Figure 6-23 (a) and Table 6-3). Section 6.2.4 discusses the effect of canopy porosity on the design and performance of ribbon parachutes. &lt;br /&gt;
&lt;br /&gt;
Properly designed conical ribbon parachutes with the correct porosity have an oscillation equal to or less than 2 to 3 degrees; a drag coefficient, CDo, of 0.55; and an opening-force coefficient, C., of 1.05 to 1.07 for subsonic applications with low forebody drag, such as experienced in wind-tunnel tests. &lt;br /&gt;
&lt;br /&gt;
The vertical ribbon spacing discussed in section 7.4.8.2 is of utmost importance for supersonic application. A canopy porosity of 25 to 26% in accordance with Figure 6-23, Curve III, and Thble 6-3 is recommended for this application. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.8.2 Vertical Ribbon Spacing &lt;br /&gt;
&lt;br /&gt;
Ribbon parachutes in the past were designed with individual gores, and the gores were connected with radial ribbons and several rows of stitching. This arrangement created the &amp;quot;venetian blind effect&amp;quot; shown in Figure 7-19. The venetian blind effect increases the effective canopy porosity discussed in section 6.2.4. &lt;br /&gt;
&lt;br /&gt;
More recently, ribbon canopies have been designed with continuous horizontal ribbons, a design that offers savings in weight and cost. This design is described in detail in section 7.4.10. &lt;br /&gt;
&lt;br /&gt;
Figure 7-20 shows the basic arrangement of a canopy gore and ribbon grid consisting of horizontal and vertical ribbons.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Section 6.2.4 explains the relationship of canopy loading, W/(CDS)p; effective porosity, Ne; and vertical ribbon spacing, a. Ribbon parachutes used as final descent parachutes use a vertical ribbon spacing to horizontal ribbon width a/B of 2.5 to 4.0. This spacing allows advantage to be taken of the change in effective porosity. High-canopy-loading ribbon parachutes, such as first-stage drogue chutes, use a vertical ribbon spacingof I to 2 to avoid the negative effects of the change in effective porosity. A narrow vertical ribbon spacing of 1.25 times the width of the horizontal ribbon width will be used for the drogue chute.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
All previous gore dimensions and the dimensions shown in Figure 7-21 are preliminary. The horizontal ribbon spacing, b, is controlled by the required porosity, k. Required changes in horizontal ribbon spacing may result in slight changez in gore and canopy dimensions.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.9.2 Preliminary Gore-Porosity Check &lt;br /&gt;
&lt;br /&gt;
Two methods of calculating gore porosity are in use. The older method, described in Reference 5.39, has been updated in this chapter. This method allows calculation of the porosity for preliminary design purposes when no final gore drawings are available. Reference 2.2 shows how to calculate canopy porosity if a drawing is available based on the ratio of open spaces to total canopy area. Both methods include an estimation of the ribbon (material) porosity&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The porosity of a ribbon grid with variations in the distance of the horizontal ribbons is now calculated. The total porosity is estimated, and the most likable horizontal ribbon distance is selected for the first gore-porosity check (Thble 7-9). The widths of the vertical ribbon, A, and the horizontal ribbon, B, are fixed values. The ratio of vertical ribbon spacing, to horizontal ribbon width, a/B, was previously selected to 1.25, which is equal to 2.5 inches. A horizontal ribbon distance, b, of 1.1 inches is selected as first approach based on data in Thble 7-9.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
To avoid a decrease in parachute diameter, 26 horizontal ribbons are selected, changing the gore dimensions from those shown in Figure 7-21 to those shown in Figure 7-22.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.9.S General Comments on Gore Design and Porosity Selection &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The canopy gore design-total canopy porosity, XT; spacing of vertical ribbon; size of vent; and pocket-band arrangement-are the primary design features that determine the aerodynamic performance of the parachute. The most important characteristics of parachute performance are stability, smooth opening, drag, and opening-force coefficients. Determining porosity under a no-load condition is rather unrealistic, because most of the important aerodynamic characteristics occur under high-load conditions (opening shock) or medium-load conditions (descent). However, since the beginning of parachute development, aerodynamic parachute characteristics obtained in wind-tunnel and free-flight tests have been related to fixed design dimensions such as diameter and porosity. &lt;br /&gt;
&lt;br /&gt;
Determining the effective porosity caused by the changing load during the opening process and by the venetian-blind effect of the ribbon grid design is practically impossible. Furthermore, the change in effective porosity is similar on all ribbon parachutes because of the similarities of the ribbon grid designs, load factors, and related changes in material elongation that cause deformation of the ribbon grids and the parachute canopies. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.9.6 Computer Programs for Determining Gore Design and Porosity Calculation &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Both gore design and porosity calculations can be determined by computer programs. Organizations involved in frequent design of ribbon parachutes should establish these programs. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.10 Ribbon Parachute Canopies with Continuous Horizontal Ribbons &lt;br /&gt;
&lt;br /&gt;
Ribbon parachute canopies are frequently designed and manufactured with continuous horizontal ribbons either in single or two-section canopies. The continuous ribbon Jesign decreases weight and volume, increases the strength of the horizontal ribbon-radial connection, and simplifies manufacturing. Continuous horizontal ribbons change the porosity characteristics of the canopy. &lt;br /&gt;
&lt;br /&gt;
Figure 7-19 shows how the individual horizontal ribbons orient themselves in a canopy manufactured from individual triangular gores. In the inflated canopy, the horizontal ribbons in the canopy crown area orient parallel to the canopy design. However, in the skirt area, the canopy design line is almost parallel to the airflow. This design, usually called the &amp;quot;venetian blind effect,&amp;quot; causes ti:e longer leading edge of each horizoatal ribbon to bulge out and position the ribbon with a positive angle of attack to the airflow. The result is an increase in effective porosity under high dynamic pressure conditions. The venetian blind effect is discussed in section 6.2.4, and the influence of canopy loading on the change in effective porosity is shown in Figure 6-24.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Designing canopies with continuous horizontal ribbons changes the venetian blind effect. Returning to Figure 7.19, it is obvious that continuous horizontal ribbons in the canopy skirt area do not bulge out since leading and trailing ribbon edges have the same length and do not position themselves with an angle of attack to the airflow. However, in the crown area of the canopy where each gore forms a triangle, the equal length of the leading and trailing ribbon edges now gives each ribbon a negative angle of attack thereby increasing the effective porosity in the canopy crown area. The effect is minimized by large number of gores arid by the use of a center vertical ribbon, or a miniradial, as Sandia engineers call it. &lt;br /&gt;
&lt;br /&gt;
Discussion with Sandia and industry personnel indicates that no measurable difference has been found in the aerodynamic characteristics of ribbon parachute canopies designed with individual gores or with continuous horizontal ribbons so long as the canopies contain a large number of gores and a center vertical ribbon. However, a slight delay in initial inflation seems to occur on small parachutes with a small number of gores. Closer spacing of vertical ribbons in the canopy crown area should counteract this delay. Another method of counteracting the delay is by gathering the trailing edges of horizontal ribbons with several rows of stitching and using a lower porosity in the crown area. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.11 Use of Kevlar Fabrics &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Many modern ribbon parachutes use Kevlar suspension lines, risers, and canopy skirt, lateral, and vent tapes, which results in a decrease in weight and volume. Section 6.5.5 discusses all aspects of working with Kevlar in the design of parachute assemblies. This includes physical characteristics of Kevlar fibers and fabrics, available Kevlar fabrics, and experience ;il designing in Kevlar. Section 6.6.5 should be studied before designing in Kevlar.&lt;/div&gt;</summary>
		<author><name>TuanHTruong</name></author>
	</entry>
	<entry>
		<id>https://mediawiki.aerodecelerator.org/index.php?title=Recovery_System_Design&amp;diff=39</id>
		<title>Recovery System Design</title>
		<link rel="alternate" type="text/html" href="https://mediawiki.aerodecelerator.org/index.php?title=Recovery_System_Design&amp;diff=39"/>
		<updated>2024-05-07T21:21:57Z</updated>

		<summary type="html">&lt;p&gt;TuanHTruong: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;= DESIGN OF A PARACHUTE RECOVERY AND LANDING SYSTEM =&lt;br /&gt;
This chapter deals with the design of a parachute recovery and landing attenuation system for a military reconnaissance drone. The prime emphasis in the design of this system is on undamaged recovery of the drone from the total flight performance envelope during the development and test phase, on undamaged recovery after a completed mission during military operations, and on multiple use of the recovery system. An engineering team conducts performance and system analyses and chooses what recovery concept to use, what types of parachutes to select for high-speed deceleration and for final recovery, and what impact-attenuation system is best for the particular application. This chapter covers the selection process for concepts and components. Different engineers may make different selections based on experiences with particular types of parachutes or deployment concepts; experience is always a viable reason for selecting a particular approach. However, using the selection criteria shown in Figure 2-6. the designer must put reliability of operation, undamaged recovery, reusability of the landing system, and minimum weight and volume at the top of the list of requirements. &lt;br /&gt;
&lt;br /&gt;
== 7.1 REQUIREMENTS ==&lt;br /&gt;
7.1.1 System Requirements &lt;br /&gt;
&lt;br /&gt;
An unmanned air vehicle used for military reconnaissance must be recovered after a completed mission in rough terrain, undamaged and ready for multiple reuse. The recovery system must be able to &lt;br /&gt;
1. Recover the air vehicle after the completed mission when the vehicle has landed in rough terrain at altitudes from sea level to 5000 feet.&lt;br /&gt;
2. Recover the drone during the engineering test phase from all controlled and uncontrolled flight conditions. &lt;br /&gt;
3. Serve as a range-safety device to prevent the air vehicle from leaving the boundaries of the test range. &lt;br /&gt;
&lt;br /&gt;
The air vehicle has a takeoff weight of 7200 pounds and a landing weight, after the i completed mission, of 4800 pounds. Undamaged landing shall be possible in rough terrain with rocks up to 8 inches in diameter. Replacement parts and refurbishment cost shall be kept to a minimum.  &lt;br /&gt;
&lt;br /&gt;
7.1.2 Requirements for Normal Operation &lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|Drone weight at recovery after completed mission&lt;br /&gt;
|W&amp;lt;sub&amp;gt;d&amp;lt;/sub&amp;gt; = 4800 lb&lt;br /&gt;
|-&lt;br /&gt;
|Recovery velocity&lt;br /&gt;
|v&amp;lt;sub&amp;gt;o&amp;lt;/sub&amp;gt; = 150 to 200 KEAS&lt;br /&gt;
|-&lt;br /&gt;
|Minimum recovery altitude&lt;br /&gt;
|H&amp;lt;sub&amp;gt;o&amp;lt;/sub&amp;gt; = 2000 ft above ground level (AGL)&lt;br /&gt;
|-&lt;br /&gt;
|Maximum ground level&lt;br /&gt;
|H = 5000 ft&lt;br /&gt;
|-&lt;br /&gt;
|Maximum allowable total parachute force&lt;br /&gt;
|F&amp;lt;sub&amp;gt;o&amp;lt;/sub&amp;gt; = 16,000 lb&lt;br /&gt;
|-&lt;br /&gt;
|Maximum allowable impact deceleration at landing&lt;br /&gt;
|a = 9.0 ''g''&amp;lt;nowiki/&amp;gt;'s&lt;br /&gt;
|} &lt;br /&gt;
&lt;br /&gt;
7.1.3 Requirements for Emergency Operation &lt;br /&gt;
&lt;br /&gt;
Emergency operation includes recovery during the test phase from takeoff to landing and also includes recovery for range-safety reasons. &lt;br /&gt;
&lt;br /&gt;
Drone weight at takeoff .................................. Wdma = 7200 lb &lt;br /&gt;
&lt;br /&gt;
Maximum recovery velocity at mean sea level (MSL) ................................... vo = 490 KEAS &lt;br /&gt;
&lt;br /&gt;
Maximum recovery velocity at 38,000 to 50,000 ft altitude ........................................ vo = 1.5 Mach &lt;br /&gt;
&lt;br /&gt;
Maximum dynamic pressure .............................. qmm = 812 lb/ft2 &lt;br /&gt;
&lt;br /&gt;
Maximum allowable parachute force ........................ F0 = 22,000 lb  &lt;br /&gt;
&lt;br /&gt;
7.1.4 Requirements Analysis &lt;br /&gt;
&lt;br /&gt;
Three primary requirements pace the design of the recovery system: &lt;br /&gt;
&lt;br /&gt;
1. The drone must be able to land in rocky but level terrain without damage. &lt;br /&gt;
&lt;br /&gt;
2. Refurbishment cost and time shall be kept to a minimum. &lt;br /&gt;
&lt;br /&gt;
3. Recovery must be possible from all flight conditions during the flight test phase, including cases where the out-of-control drone flies off the range.  &lt;br /&gt;
&lt;br /&gt;
== 7.2 LANDING ANALYSIS AND IMPACT-ATTENUATION SYSTEM ==&lt;br /&gt;
7.2.1 Landing Analysis &lt;br /&gt;
&lt;br /&gt;
Three known recovery concepts prevent damage during landing in rocky terrain: &lt;br /&gt;
&lt;br /&gt;
1. Midair retrieval.&lt;br /&gt;
&lt;br /&gt;
2. Dual air bags or dual frangibles.&lt;br /&gt;
&lt;br /&gt;
3. Retrorockets combined with small, nondeflatable air bags.&lt;br /&gt;
&lt;br /&gt;
The need for retrieval helicopters or retrieval aircraft makes Method 1, midair retrieval, impractical. The other two methods are affected by the deceleration distance required to meet the 9-g limit. &lt;br /&gt;
&lt;br /&gt;
In section 6.8 of this manual, the required deceleration distance(s) is determined to be&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;s=\frac{{V_{e_1}}^2-{V_{e_2}}^2}{2g(n\eta-1)}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;{V_{e_1}}&amp;lt;/math&amp;gt; = velocity of the drone descending on the parachute (rate of descent), ft/s&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;V_{e_2}&amp;lt;/math&amp;gt; = permissible impact velocity, ft/s&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;g&amp;lt;/math&amp;gt; = acceleration of gravity, ft/s2&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\eta&amp;lt;/math&amp;gt; = effectiveness of the impact attenuation system used, dimensionless&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;n&amp;lt;/math&amp;gt; = allowable impact deceleration, ratio &amp;lt;math&amp;gt;n=\frac{a}{g}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Figure 6-68 of Chapter 6 shows the range of various impact attenuation systems as a&lt;br /&gt;
&lt;br /&gt;
function of rate of descent and allowable ground impact deceleration. The information&lt;br /&gt;
&lt;br /&gt;
indicates that air bags may be the most practical concept for this application. A cursory&lt;br /&gt;
&lt;br /&gt;
analysis indicates that a rate of descent of 25 ft/s at 5000 fee: altitude will result in a close to&lt;br /&gt;
&lt;br /&gt;
optimum weight ratio of the combined parachute air bag system (see Figure 6-83). Properly&lt;br /&gt;
&lt;br /&gt;
designed air bags will have an effectiveness of 65% as shown in the stroke-pressure diagram in&lt;br /&gt;
&lt;br /&gt;
Figure 6-78 and allow ground contact or final velocity of close to 0 ft/s.&lt;br /&gt;
&lt;br /&gt;
0&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.3&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
With these assumptions, the required effective air bag deceleration stroke is obtained&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
This deceleration distance is too short for a parachute retrorocket system because of the&lt;br /&gt;
&lt;br /&gt;
required timing accuracy and rocket burning time. Retrorocket systems are most practical for deceleration distances greater than 4 or 5 feet. Crushable and frangible impact attenuators are suitable for deceleration distances of less than 15 inches. Air bag systems work best for deceleration distances of 24 to 48 inches. The original assumption that an air bag concept maybe the most practical approach for this air vehicle is therefore confirmed.&lt;br /&gt;
&lt;br /&gt;
7.2.2 Impact Attenuator System&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The design of impact attenuator systems is discussed in section 6.8 of this manual.&lt;br /&gt;
&lt;br /&gt;
Figure 7-1 shows the reconnaissance drone and the air-bag attenuator systems that consist of two deflatable, two-compartment wing-bag bags (A); a single-compartment, deflatable nose bag (B); and a nondeflatable nose-buffer bag (C). The wing bags, the primary energy absorbers, need the already calculated 24-inch effective-deceleration stroke. For design reasons, 33 inches must be added to the bag height, 19 inches for the distance from the wing underside to the underside of the jet ,i rlucts, 10 inches for ground clearance, and 4 inches for bag bottom curvature. These additio:;. result in a total bag lihight of 57 inches. To ensure landing stability, an air bag height-to-diameter ratio of 1.25 is selected for the two wing bags, resulting in a bag diameter of 48 inches. The cross-hatched lower part of the two wing bags (see Figure 7-1) deflates at impact, but the upper part stays inflated and keeps the drone off the ground. The nose bag, B, helps to absorb the impact and deflates, and the nose of the drone&lt;br /&gt;
&lt;br /&gt;
comes to rest on the nondeflatable buffer bag, C. All air bags are inflated from 3000 psi nitrogen containers using aspirators for a 50/50 nitrogen air mixture. The air bags are prepressurized to 2 psi for full bag inflation prior to landing. Multiple blowout valves consisting of staggered blowout rubber disks around the circumference of the air bags control the bag deflation to stay within the 9-g deceleration limit.&lt;br /&gt;
&lt;br /&gt;
The weight of the impact-attenuation system-air bags, nitrogen containers, plumbing, and A/C containers-is estimated from section 6.7 to be 2.2% of the total drone weight, or 105.6 pounds. The air bags should be stored in containers that can be easily removed from the drone for repacking. Air bags must be deployed after the main parachutes are fully open to prevent air-bag damage caused by high dynamic pressure. Air-bag deployment begins with simultaneous pyroejecting of the removable air-bag-container covers and opening of the nitrogen-container valves. The wing bags, the primary nose bag, and the nose-buffer bag inflate. At ground contact, the bags compress, increasing the pressure inside the bags. At a preselected pressure level, the blowout valves (rubber disks, metal disks, or rubber-type sleeves) open and limit the maximum drone deceleration to the preselected level.&lt;br /&gt;
&lt;br /&gt;
7-4&lt;br /&gt;
&lt;br /&gt;
== 7.3 MAIN PARACHUTE SYSTEM ==&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.3.1 Main Parachute System Requirements&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Section 2.4 defines the criteria for parachute type selection. Requirements for low weight and volume rule out the low-drag slotted parachutes (ribbon, ringslot, and ringsail) as well as guide-surface and cross parachutes (see Tables 5.2 and 5.3). Parachute deployment past the vertical stabilizer rules out a single parachute in favor of a cluster of two parachutes deployed independently left and right of the vertical stabilizer. No cluster experience is available with annular or cross parachutes, and no reefing experience is available with annular parachutes. Cross parachutes cannot be reefed to the low reefing ratios required for this application. Extended-skirt and polyconical parachutes have been used successfully in clusters of large, reefed parachutes.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7-6&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
A cluster of two conical full extended skirt parachutes is most suitable for this system. In&lt;br /&gt;
&lt;br /&gt;
section 5.2, Figures 5.24 and 5-25 show that properly designed extended-skirt parachutes have&lt;br /&gt;
&lt;br /&gt;
drag coefficients equal to 0.8 to 0.9 in the 20- to 25-ft/s rate of descent range. Available data&lt;br /&gt;
&lt;br /&gt;
(Reference 5.23) indicate that a cluster of two extended-skirt parachutes is sufficiently stable&lt;br /&gt;
&lt;br /&gt;
for use with air bags. Extended-skirt parachutes have a low opening-force coefficient of 1.4,&lt;br /&gt;
&lt;br /&gt;
compared to an opening-force coefficient of 1.8 for conical and triconical parachutes.&lt;br /&gt;
&lt;br /&gt;
Extended-skirt parachutes can also be reefed to low reefing ratios, a requirement for final&lt;br /&gt;
&lt;br /&gt;
descent parachutes (see Chapter 5, Figure 5-72).&lt;br /&gt;
&lt;br /&gt;
73.3 Parachute Diameter&lt;br /&gt;
&lt;br /&gt;
The rate of descent at 5000 feet altitude was selected to 25 ft/s (see section 7.3.1). The&lt;br /&gt;
&lt;br /&gt;
equivalent rate of descent at sea level is&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The drag coefficient, CDo, for a conical full extended skirt parachute with a 23.2-ft/s rate of&lt;br /&gt;
&lt;br /&gt;
descent and a suspension-line ratio, [.e/Do, of 1.0 is obtained from Figure 5-25&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
A suspension-line ratio of 1.15 is selected. This is the longest practical length for extended skirt&lt;br /&gt;
&lt;br /&gt;
parachutes (see Figure 5-20).&lt;br /&gt;
&lt;br /&gt;
The length of the riser, Lr, depends on its installation in the drone; the riser should be long&lt;br /&gt;
&lt;br /&gt;
enough to extend beyond the fuselage and vertical stabilizer of the drone (see Figure 7-2),&lt;br /&gt;
&lt;br /&gt;
which gives the final configuration of the parachute cluster, including risers and parachutes.&lt;br /&gt;
&lt;br /&gt;
7.3.4 Parachute Deployment System&lt;br /&gt;
&lt;br /&gt;
A cluster of two main parachutes is selected and deployed left and right of the vertical&lt;br /&gt;
&lt;br /&gt;
stabilizer to avoid hang-up or damage of a single parachute by the vertical stabilizer. Each&lt;br /&gt;
&lt;br /&gt;
parachute needs its own extraction and deployment system to properly deploy past the&lt;br /&gt;
&lt;br /&gt;
stabilizer and to avoid interference with the other main parachute during deployment and&lt;br /&gt;
&lt;br /&gt;
inflation.&lt;br /&gt;
&lt;br /&gt;
TWo fast-opening extraction parachutes are used on each main parachute. Stable&lt;br /&gt;
&lt;br /&gt;
parachutes will minimize interferenc, during deployment. Experience with past recovery&lt;br /&gt;
&lt;br /&gt;
systems has shown that the most positive deployment is obtained by forced ejection of the&lt;br /&gt;
&lt;br /&gt;
extractiou or pilot chutes into good airflow past the vertical stabilizer by either mortar or&lt;br /&gt;
&lt;br /&gt;
drogue gun ejection. A mortar can eject large, heavy parachutes but creates large leaction&lt;br /&gt;
&lt;br /&gt;
forces and needs considerable space for installation. Drogue gun ejection is effective, but is&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
limited to the deployment of small, lightweight parachutes such as pilot chutes. Drogue gun ejected pilot chutes are selected for initiating main parachute deployment. To ensure proper&lt;br /&gt;
&lt;br /&gt;
clearance of the vertical stabilizer, the pilot chutes are ejeLted 45 degrees upward, backward&lt;br /&gt;
&lt;br /&gt;
and outward past the vertical stabilizer. The parachute installation in the drone fuselage&lt;br /&gt;
&lt;br /&gt;
requires cross-wind deployment and therefore forced ejection of the main parachute&lt;br /&gt;
&lt;br /&gt;
deployment bags. Four different methods have been used successfully to accomplish forced&lt;br /&gt;
&lt;br /&gt;
ejection: (1) using ejector springs enclosed in a textile cylinder. (2) gas-inflating nonporous&lt;br /&gt;
&lt;br /&gt;
ejector bags, (3) catapulting the bag out of the compartment, or (4) using a lift-web&lt;br /&gt;
&lt;br /&gt;
arrangement as discussed in section 6.1.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The deployment system selected consists of a drogue gun deployed pilot chute, an&lt;br /&gt;
&lt;br /&gt;
extraction parachute, and a main parachute deployment bag lifted from the parachute&lt;br /&gt;
&lt;br /&gt;
compartment by lift webs. When the hinged compartment doors open, two drogue gun slugs&lt;br /&gt;
&lt;br /&gt;
are fired 45 degrees upward and aft; each slug deploys a pilot chute sufficiently behind the&lt;br /&gt;
&lt;br /&gt;
drone into good airflow. These pilot chutes in turn extract two extraction chutes stowed on top of the main parachute deployment bags. The extraction chutes extract and deploy the two main 0&lt;br /&gt;
&lt;br /&gt;
parachutes left and right of the vertical stabilizers. Lift webs and unsymmetrical bag handles&lt;br /&gt;
&lt;br /&gt;
lift the main parachute bags out of the drone compartment and extract the main parachute&lt;br /&gt;
&lt;br /&gt;
past the vertical stabilizer (see Figure 7-3)&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.3.5 Extraction Parachute Assembly&lt;br /&gt;
&lt;br /&gt;
The two extraction parachutes must properly deploy the two main parachutes. The size of&lt;br /&gt;
&lt;br /&gt;
the extraction parachutes and their location in the wake of the drone is determined as follows:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
A stable, 7.4-foot-diameter ringslot parachute is selected. &lt;br /&gt;
&lt;br /&gt;
The weight of the ringslot extraction parachute can be estimated from section 6.7 to 2.5 pounds, and the weight of the extraction parachute assembly including riser and deployment bag to 1.5 . 2.5 pounds = 3.75 pounds. The weight of a single 72.7-foot-diameter main parachute, as determined from section 6.7, is 54 pounds. This weight estimate assumes an efficiently designed main canopy that has a combination of tape and radial seams to carry the radial loads and has other, similar weight-saving design features. The arrangement of the extraction parachute in relation to the drone is shown in Figure 7-5. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.3.6 Pilot Parachute Assembly &lt;br /&gt;
&lt;br /&gt;
The extraction parachute assembly weight of 3.75 pounds is too heavy to be deployed by a drogue-gun slug; therefore, a small pilot chute is selected for initial deployment by the drogue-gun slug. This pilot chute, in turn, will deploy the extraction parachute.&lt;br /&gt;
&lt;br /&gt;
Evaluation of past good and poor deployments has led to the rule that the extraction force of the pilot chute should be greater than or equal to four times the weight of the unit to be extracted; in this case, the extraction parachute assembly. So that the pilot chute has enough force, a pilot chute is selected that will produce, at the minimum deployment speed of 150 KEAS, an extraction force equal to five times the weight of the extraction parachute assembly: 5. 3.75 pounds - 18.75 pounds. The minimum dynamic pressure at 150 KEAS is&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.3.7 Main Parachute Forces&lt;br /&gt;
&lt;br /&gt;
7.3.7.1 Requirements &lt;br /&gt;
&lt;br /&gt;
Drone weight ............................................. W D = 4800 lb&lt;br /&gt;
&lt;br /&gt;
Maximum deployment speed .............................. vo = 200 KEAS &lt;br /&gt;
&lt;br /&gt;
Minimum deployment speed ........................ Vo minimum = 150 KEAS &lt;br /&gt;
&lt;br /&gt;
Maximum allowable total parachute force (two main parachutes) ................................... FT = 16,000 lb &lt;br /&gt;
&lt;br /&gt;
Deployment altitude .................................. H = 2000 to 7000 ft &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.3.7.2 Velocity-Altitude Profile &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Section 5.5 states that the maximum opening force of the main parachute occurs at maximum deployment altitude. Figure 7-8 shows a velocity-altitude-versus-time profile for a typical vehicle recovery system. &lt;br /&gt;
&lt;br /&gt;
The maximum dynamic pressure, qo, occurs at the 200-KEAS deployment velocity &lt;br /&gt;
&lt;br /&gt;
2. The Pflanz method is quite accurate for all conditions including high altitude, but neglects the effect of gravity. Parachutes opened in vertical descent will have a 1-g (one weight unit) higher force than calculated. It is necessary to calculate the canopy filling times for the various reefed stages (see section 5.4.3) and to determine the drag-area-versus-time profile for the specific parachute (see section 5.4.4). This method permits the investigation of variations in filling times and drag-area-versus-time profiles. &lt;br /&gt;
&lt;br /&gt;
3. The force-trajectory-time computer method includes the effects of altitude, gravity, and changing trajectory angle. This method requires determination of a drag-area-versus-time profile for the entire parachute opening sequence (see Figure 5-52). Computers permit multiple runs with changes in times, drag-area-versus-time profiles, starting velocities, and altitudes.&lt;br /&gt;
&lt;br /&gt;
7.3.7.4 Reefed Opening Forces&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
To  save trajectory time, the reef-d pardchute is disreefed at a dynamic pressure 10 to 20% higher than the terminal reefed dynamic pressure. Therefore,&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Results of changing the canopy inflation time, tf, and the drag-area-versus-time profile, n, are shown in Thble 7-2. Reference 5-76, the Pflanz report, provides a more detailed study of the effect of canopy fill time and drag-area-increase-versus-time profile on the magnitude of the parachute force&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Force-Trajectory-Time Computer Method &lt;br /&gt;
&lt;br /&gt;
The program established oy NWC determines as a function of time the parachute forces, the vehicle deceleration, and the space-positioning (trajectory) data in a two-axis system. The method requires a drag-area-versus-time profile for the individual parachutes and the total vehicle system (Figure 7-9). This profile was previously shown in Figure 5-52. Figure 7-9 includes the change in air-vehicle drag caused by the change in vehicle attitude during the parachute opening process&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.3.7.6 Comments on Calculated Opening Forces 1. The reefed opening force for the single parachute is higher than thie contractor-requested maximum allowable force per parachute of 8000 pounds&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
2. The average disreef force is approximately 1500 pounds lower than the reefed force. Therefore, it appears logical to lower the reefed force and increase the disreef force. Although this adjustment probably cannot be made within the 8000-pound limit, 8500 pounds appears to be an obtainable goal. &lt;br /&gt;
&lt;br /&gt;
3. To meet the contractor requirement of an 8000-pound maximum force limit per parachute, two-stage reefing is required. &lt;br /&gt;
&lt;br /&gt;
4. It appears practical to determine in drop tests if a 2.0 to 2.1% reefed drag area can be obtained. This drag area would decrease the reefed opening force and somewhat increase the disreef force. However, reaching an average maximum force of less than 8000 pounds appears doubtful. &lt;br /&gt;
&lt;br /&gt;
5. In the calculations, both parachutes are assumed to have equal opening forces. In reality, opening forces of the two parachutes can differ because of variations in filling time. lead-ann-lag chute behavior caused by blanketing, and resultant nonuniform canopy inflation. 7-22 NWC TP 6575 &lt;br /&gt;
&lt;br /&gt;
The fast-opening Apollo ringsail-type main parachutes had a load distribution among the three parachutes of 40-40-20. The individual parachutes, therefore, had to be overdesigned in a 40/33 ratio. However, the total parachute force load taken by the vehicle hard points did not exceed the calculated average load because of the high-low variation of the individual parachutes. &lt;br /&gt;
&lt;br /&gt;
The two slower-opening extended-skirt parachutes used for this application are more uniform in their load distribution. A cursory analysis of available test data indicates that a 55/45 load distribution between the two parachutes and a no-overload condition for the vehicle hard points should be an acceptable load distribution. &lt;br /&gt;
&lt;br /&gt;
A contractor-subcontractor agreement is required to determine whether the individual parachutes should be designed for the 55/45 load variation or whether this overload can be accommodated by the 1.5 safety factor and the additional safety provided by the normal overstrength of textile specification materials.&lt;br /&gt;
&lt;br /&gt;
7.3.7.7 Snatch Forces &lt;br /&gt;
&lt;br /&gt;
The snatch force is caused by the acceleration of the mass of the parachute assembly to the velocity of the forebody (drone). A canopy, partially inflated at line stretch, increases the mass of the parachute by the mass of the air included in the canopy; this can increase the snatch force (mass shock) considerably.  &lt;br /&gt;
&lt;br /&gt;
Two  principal rules should be followed to keep the snatch force within allowable limits.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
1. Keep the parachute canopy closed until line (canopy) stretch occurs by use of a deployment bag o! %kirt restrictor.&lt;br /&gt;
&lt;br /&gt;
2. Accelerate I!: mass of the parachute assembly in incremental steps. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Known means of accomplishing these goals are discussed in Chapter 6.1. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The difference between a poor deployment and a deployment that accomplishes the first rule and partially accomplishes ' second is illustrated in Figure 5-54, which shows snatch and opening forces for the C-9 p. tchute with and without the quarter deployment bag. The deployment method outlined in ! tilon 7.3.4 should hold snatch forces at a level below the parachute opening forces. &lt;br /&gt;
&lt;br /&gt;
A method for calculating ,tch forces is described in Reference 2.2, the 1963 edition of the USAF parachute handbook. : nreferred method for calculating parachute deployment. including the snatch force, is cont.iiiici in J. W Purvis's AIAA paper, &amp;quot;Improved Prediction of Parachute Line Sail During I incs-First Deployment&amp;quot; (Reference 5.86)&lt;br /&gt;
&lt;br /&gt;
7.3.8 Parachute Stress Analysis &lt;br /&gt;
&lt;br /&gt;
7.3.8.1 Parachute Design Data&lt;br /&gt;
&lt;br /&gt;
A total parachute assembly is shown in Figure 7-10.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.3.8.2 Parachute Forces &lt;br /&gt;
&lt;br /&gt;
The maximum reefed opening force, FR, is 9255 pounds. The maximum disreef opening force, F., is 7404 pounds. The maximum design force for stressing the parachute assembly, FI, is 9255 pounds.&lt;br /&gt;
&lt;br /&gt;
The forces obtained in computer runs are selected as the most accurate forces for stressing the parachute assembly and its components. Based on multiple computer runs, a diligent choice must be made for the most likable forces.&lt;br /&gt;
&lt;br /&gt;
7.3.83 Main-Parachute Safety and Design Factors &lt;br /&gt;
&lt;br /&gt;
Section 6.4 is used as a guide for selecting the safety, load, loss, and design factors in Table 7.4&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
1. Connection of suspension lines to riser legs and drone hardpoints is made easier if the number of suspension lines are a multiple of 4 or 8. &lt;br /&gt;
&lt;br /&gt;
2. The gore at the skirt should not be wider than 3.5 feet for packing reasons. &lt;br /&gt;
&lt;br /&gt;
3. The canopy should have no fewer than 12 gores to avoid gore distortion during inflation. &lt;br /&gt;
&lt;br /&gt;
4. Radial ribbons or radial seams should not overlap at the vent; overlapping causes bunching of material and associated sewing problems. &lt;br /&gt;
&lt;br /&gt;
5. The strengths of available suspension-line types may affect the gore selection. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Table 7-5 shows the required suspension line strength and the resultant gore width as functions of the number of gore/suspension lines used. &lt;br /&gt;
&lt;br /&gt;
7-25 NWC TP 6575&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The width of the goie of the skirt on conical, full-extended-skirt (CFES) parachutes is about 85% of the maximum gore width, Eo. Sixty-four suspension lines are selected in accordance with MIL-C-7515, TIpe XI, with 300-pound tensile strength. This selection provides a margin of safety (MS) of&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The suspension line will be attached to the canopy skirt in a loop connection. &lt;br /&gt;
&lt;br /&gt;
7.3.8.5 Canopy Stress&lt;br /&gt;
&lt;br /&gt;
No precise method has been d.-veloped for calculating the stress in a circular, solid-material, bias-construction canopy.&lt;br /&gt;
&lt;br /&gt;
Section 6.4 describes a semi-empirical method for determining the required fabric strength of a solid material canopy in pounds per unit width using the stress in a pressure vessel as an analogy. The stress in a cylindrical vessel, expressed as force per unit length, is&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
where p is the pressure in the cylindrical vessel and r is the vessel radius. Using this analogy and considering the canopy gore as part of a pressure vessel, the required material strength of the canopy per unit width is obtained&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The maximum stress actually occurs during reefed inflation because of the smaller inflated diameter:&lt;br /&gt;
&lt;br /&gt;
7.3.8.6 Canopy Reinforcing Tapes &lt;br /&gt;
&lt;br /&gt;
1. Skirt Tape. The skirt tape should Iv. equal or greater in strength than the individual suspension lines but not less than 1000 pounds, and 1-inch-wide tape should be used for parachutes larger than 20 feet in diameter. &lt;br /&gt;
&lt;br /&gt;
The nylon tape selected is 1-inch-wide MIL-T-5038, Type IV, with 1000-pound strength. Proper connection of the skirt tape to the radial seam (tape) and the suspension line must be ensured.&lt;br /&gt;
&lt;br /&gt;
2. Vent Tape. From the geometric design of the parachute vent (Figure 7-11). the force in the vent tape, FVT, is calculated&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
A 1-inch-wide, 4000-pound webbing (MIL-W-5625) or 7/8-inch-wide, 3100-pound webbing (MIL-W-5625) is selected. &lt;br /&gt;
&lt;br /&gt;
3. Vent Lines. The strength of the vent line- should be equal to or greater than 60% of the strength of the radials&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.3.8.7 Design of Radials &lt;br /&gt;
&lt;br /&gt;
The following four types of radial designs are in use: &lt;br /&gt;
&lt;br /&gt;
1. Radial seams with suspension lines running in channels over the canopy and attached at the vent and the skirt as on the canopy of the C-9 personnel parachute. &lt;br /&gt;
&lt;br /&gt;
2. Suspension lines running on top of the radials over the canopy and sewn at full length to the canopy as on many heavy-duty ribtx'n parachutes. &lt;br /&gt;
&lt;br /&gt;
3. Radial tapes sewn on top of or inside the radial seams, and suspension lines attached to the radial tapes by sewing or by skirt loops (NB-7 and T-10 canopies). &lt;br /&gt;
&lt;br /&gt;
4. Radial ribbons on ribbon parachutes designed to take the total radial load with suspension lines sewn onto d e radials or connected by a skirt loop. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The following are some comments on the design of radials: &lt;br /&gt;
&lt;br /&gt;
1. Making the strength of the radials 1:qtlal to 80% of the strength of the suspension lines has been satisfactory on thousands of ribbon parachutes. &lt;br /&gt;
&lt;br /&gt;
2. When tapes or suspension lines are sewn at full length to the radials, care must be taken that fullness in the radials ensures that the radial tapes or the suspension lines are the primary load carrying members. For an explanation of fullness, see section 6.6.4. &lt;br /&gt;
&lt;br /&gt;
3. Uniform material distribution is of utmost importance when sewn tapes or lines are used for radial reinforcemetnt. &lt;br /&gt;
&lt;br /&gt;
For the radial design of the main parachute, we use a tape with 80% strength of the suspension lint (0.8. 300 lb - 240 Ib) sewn on top of the radial scam. A 250-pound strength, 'A-inch-wide tape is selected in accordance with MIL-T-5038, 7ýpe III. Thpe and radial seams are marked every 24 inches for proper material distribution&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.3.8.8 Check for Proper Gore Fullness &lt;br /&gt;
&lt;br /&gt;
When the first parachute of a new design has been completed in the manufacturing shop, a gore fullness check in accordance with Figure 7-12 should be conducted. A slight amount of slack should be noticeable in the canopy fabric in both directions when all four corners of a gore are pulled radially outward. Slack indicates that the main loads are carried by the radials and reinforcing tapes and not by the canopy fabric. Stress folds in the canopy indicate faults in the design or manufacture of the parachute&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
’&lt;br /&gt;
&lt;br /&gt;
This is a large vent opening for a reefed parachute. Several criteria may be used to determine the size of the canopy vent as follows: &lt;br /&gt;
&lt;br /&gt;
1. Unreefed parachutes with vents up to 1% of the canopy surface area, So, have been operated successfully.&lt;br /&gt;
&lt;br /&gt;
2. Reefed parachutes require a vent diameter, DV, smaller than the reefing line circle, diameter DR, of the parachute; Dv is smaller than DR (see section 5.6, Figure 5-66). &lt;br /&gt;
&lt;br /&gt;
3. The radials at the vent should not overlap. A 1-inch free space between radials is desirable (see Figure 7-14)&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Stress in the canopy gore area can be relieved by making the gore at the vent 10% wider than the calculated gore dimension, ev. Therefore, ev* - 1.1 . ev - 1.1(1.6) = 1.76 inches. The vent tape is sewn to the vent at the original ev dimension, thereby gathering the vent 10% and creating a stress-relieving arcing in the gore fabric next to the vent. See Figure 7-15 for an example of final gore dimensions.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.3.10 Pocket Bands The pocket bands used on every gore make canopy inflation more uniform and eliminates long and short filling times. A narrow tape is used as the pocket band, which will :ot affect the average length of the canopy filling time. Data on the dimensioning of pocket bands are given in section 6.4. As shown in Figure 7-16, the pocket band dimensions are&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The diameter of the reefing line circle, DR, is larger than the 3.64-foot vent diameter of the canopy, Dv. This difference in diameters is an important design requirement (see section 7.3.9).&lt;br /&gt;
&lt;br /&gt;
7.3.11.2 Strength of the Reefing Line&lt;br /&gt;
&lt;br /&gt;
The force in the reefing line is determined according to information in section 5.6.8. Test items 22 and 23 in Figure 5-76 closely resemble the main parachute used here. A reefing-lineforce-to-reefed-parachute-force ratio of 2.5% is selected for this assembly. Therefore, the force in the reefing line is&lt;br /&gt;
&lt;br /&gt;
(0.025)FR = 0.025(9255 Ib) = 231.4 lb&lt;br /&gt;
&lt;br /&gt;
The design factor, DF, for the reefing system was determined in section 7.3.8, Table 7-4, to be 2.74.&lt;br /&gt;
&lt;br /&gt;
== 7.4 HIGH-SPEED DROGUE CHUTE ASSEMBLY ==&lt;br /&gt;
7.4.1 Requirements &lt;br /&gt;
&lt;br /&gt;
The following operational requirements govern the design of the first-stage drogue chute:&lt;br /&gt;
&lt;br /&gt;
1. The drone must be recoverable from any conceivable flight condition during the engineering test phase. &lt;br /&gt;
&lt;br /&gt;
2. An out-of-control drone or a drone that loses radio contact with the controller must be prevented from flying off the range. Recovery is initiated by an independent range signal. This type of recovery requires a high-speed deceleration parachute that can be deployed and operated when the drone is moving at maximum speed, or is in a spin, or during any other abnormal flight condition. &lt;br /&gt;
&lt;br /&gt;
This type of recovery established the following requirements for the type and size of the drogue chute:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
1. The drogue chute must have reliable operation in the velocity range from 200 knots at sea level to Mach 1.5 at 50,000 feet.&lt;br /&gt;
&lt;br /&gt;
2. Stability must be better than :: 3 degrees. &lt;br /&gt;
&lt;br /&gt;
3. Minimum weight and volume is mandatory. &lt;br /&gt;
&lt;br /&gt;
4. The drogue chute must be able to decelerate the drone to the permissible opening speed of the main parachute assemblies.&lt;br /&gt;
&lt;br /&gt;
5. The drogue chute must be suitable for the operational environment. Figure 7-17 shows the altitude-velocity flight envelope of the drone.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.2 Drogue Chute Selection &lt;br /&gt;
&lt;br /&gt;
Tables 5-1 through 5-5 in Chapter 5 list commonly used parachute types. Table 7-6 evaluates possible drogue chute candidates. Of the parachute candidates, only the conical ribbon and the hemisflo ribbon have been used successfully for similar applications.&lt;br /&gt;
&lt;br /&gt;
A 25-degree conical ribbon parachute is selected for this application. The conical ribbon parachute meets all requirements and has a higher subsonic drag coefficient than the equally&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.3 Required Drogue Chute Diameter &lt;br /&gt;
&lt;br /&gt;
The size of the fully open drogue chute is determined by the requirement that it must decelerate the 7200-pound drone to the allowable opening speed of the main parachute, which is governed by the requirement that the opening force of the two main parachutes must stay within the 9350-pound-per-chute limit established for the 200-knot opening speed of the 4800-pound drone. &lt;br /&gt;
&lt;br /&gt;
A preliminary calculation shows that a terminal velocity of about 175 KEAS is required to limit the opening load of the reefed main parachutes to 9350 pounds. A 13- to 14-footdiameter drogue chute is needed to meet this requirement. &lt;br /&gt;
&lt;br /&gt;
To reach 175 KEAS at main parachute line stretch, the drogue chute will be disconnected by an aneroid sensor at about 7000 feet mean sea level (MSL) while descending vertically from high altitude. The drone will free-fall for 0.8 second until main parachute line stretch occurs; the free-fall causes a 10-knot increase in velocity. In addition, the changing density, p, results in&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
NWC TP 6575 &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The gain in drag caused by the longer suspension lines and the 5% loss in drag caused by forebody wake (Figure 5-21) result in a final drag coefficient, CDo, for the drogue chute of &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
CDo = 0.55. 1.085 . 0.95 = 0.57&lt;br /&gt;
&lt;br /&gt;
and a corrected drogue chute diameter &lt;br /&gt;
&lt;br /&gt;
Do - 13.61 ft&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.4 Computer Analysis of Drogue Chute Performance &lt;br /&gt;
&lt;br /&gt;
At this point, a computer program should be established to determine the following performance conditions: &lt;br /&gt;
&lt;br /&gt;
1. Balance reefed and disreef parachute forces and filling times. Start at Mach 1.5 at 34,000 feet (see point () on Figure 7-17). Check final selection for a 10,000-foot-altitude condition. &lt;br /&gt;
&lt;br /&gt;
2. Determine required opening altitude for high-speed, low-altitude deployment. This requires trajectory runs with both the drogue and main parachutes. &lt;br /&gt;
&lt;br /&gt;
3. Determine maximum horizontal range, including prevailing wind conditions. &lt;br /&gt;
&lt;br /&gt;
4. Verify that the selected main parachute opening speed of 175 KEAS is reached for all important flight conditions and that, for an opening velocity of 175 KEAS, the main parachute forces stay within the allowable force limit of 9255 pounds. &lt;br /&gt;
&lt;br /&gt;
5. Include opening of the air bags with a 6.0-second inflation time in some of the trajectories. Inflation starts after main parachute opening. &lt;br /&gt;
&lt;br /&gt;
The prime contractor should point out any special flight conditions that may require parachute recovery. The prime contractor will probably also perform recovery computer runs to determine for which flight conditions and from what altitudes recovery can be accomplished. &lt;br /&gt;
&lt;br /&gt;
7.4.5 Flight Emergency Recovery Conditions &lt;br /&gt;
&lt;br /&gt;
Certain flight conditions other than recovery command from the flight controller or the range safety officer may result in automatic on-board recovery command. These conditions include &lt;br /&gt;
&lt;br /&gt;
1. Loss of RF link. &lt;br /&gt;
&lt;br /&gt;
2. Loss of engine power (glide on internal power). &lt;br /&gt;
&lt;br /&gt;
3. High accelerations in x, y, and z caused by out-of-control flight conditions or in-flightafflicted damage on target drones. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7-38&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
NWC TP 6575 &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.6 Drogue Chute Opening Forces &lt;br /&gt;
&lt;br /&gt;
Parachute opening forces should be obtained from the computer program. However, a hand calculation is required for defining the force range before setting up the computer program. Furthermore, canopy filling times and force coefficient, C,. must be determined before computer runs (see section 5.4). &lt;br /&gt;
&lt;br /&gt;
Determining the drogue chute opening forces with the W/CDS method is normally sufficiently accurate for high-canopy-loading drogue chutes. If no computer backup is available, the Pflanz method (see section 5.4.6) will provide good force data.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.6.1 Drogue Chute Reefed Opening Forces When the W/CDS method is used, the reefed opening force, FR, is calculated to&lt;br /&gt;
&lt;br /&gt;
and the maximum allowable drogue chute drag area with a 2Z000 force limit is calculated to&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
where &lt;br /&gt;
&lt;br /&gt;
FR, the maximum allowable force, is 22,000 lb &lt;br /&gt;
&lt;br /&gt;
q, the maximum dynamic pressure, is 813.9 lb/ft2 &lt;br /&gt;
&lt;br /&gt;
For supersonic application, Figure 5-50 in section 5.4 shows CK = C' . X1 for the supersonic deployment of conical ribbon parachutes. Most applicable are the data for the Mercury and the Cook conical ribbon parachutes, which were deployed at velocities up to Mach 1.6. CK factors of 1.3 to 1.75 have been measured in supersonic deployment of conical ribbon parachutes. Forebody wake and poor deployment greatly affect the force coefficient. Mortar deployment often produces bag strip-off before canopy stretch, causing premature partial canopy inflation and a high X1 factor. Rocket extraction or drogue gun/pilot chute deployment, both resulting in canopy stretch before skirt inflation, generally avoid this problem. A force coefficient C, = 1.25 is selected.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The canopy loading of the reefed drogue chute is&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The required reefing-line length for obtaining this drag area can be determined from Figure 5-73, section 5.6.6, using the method of section 7.3.11.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.6.2 Drogue Chute Disreef Opening Force &lt;br /&gt;
&lt;br /&gt;
An important factor to determine is reefing time. A long time is required to reach close to terminal velocity before disreef. A practical approach, based on experience, is to select the 1.1-times-terminal-velocity point for disreef. If this time is too long, then a shorter reefing time is required, resulting in a higher disreef velocity and forces&lt;br /&gt;
&lt;br /&gt;
The terminal velocity of the reefed parachute is&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
and disreef force, Fo, is calculated&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Both forces FR and Fo are close to the allowable force limit of 22,000 pounds. Because loads vary 5 to 10%, slight overloads may occur. However, the 7200-pound drone weight is the take-off weight. Off-range recovery and conceivable emergencies will occur at lighter drone weights, resulting in lower parachute forces.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.7 Drogue Chute Stress Analysis and Design &lt;br /&gt;
&lt;br /&gt;
Dimensioning of the various components of the parachute assembly involves three primary tasks (1) establishing design and safety factors, (2) determining the loads and stresses in the assembly components, and (3) dimensioning all assembly members. The methods used for these tasks are described in section 6.4. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.7.1 Drogue Chute Safety, Load, Loss, and Design Factors &lt;br /&gt;
&lt;br /&gt;
The method used is similar to the one developed in section 6.4. Table 7-7 shows safety, load, and loss factors in relation to design factor.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.7.2 Number of Gores and Suspension-Line Strength &lt;br /&gt;
&lt;br /&gt;
The drogue chute will be designed for a maximumn force, Fo, of 22,000 pounds in the reefed and full-open stages. The suspension-line arrangement was selected in accordance with Table 7-8.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.7.2 Number of Gores and Suspension-Line Strength &lt;br /&gt;
&lt;br /&gt;
The drogue chute will be designed for a maximumn force, Fo, of 22,000 pounds in the reefed and full-open stages. The suspension-line arrangement was selected in accordance with Table 7-8.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
A canopy with 24 gores and 3000-pound-individual-strength suspension lines is selected primarily for gore width and vent diameter. The relatively large vent must be covered with wide vent lines held in place by proper connections. &lt;br /&gt;
&lt;br /&gt;
The method described in section 6.4 is used for preliminary dimensioning of the horizontal ribbons. In this method, the expression Fo/(CDS)p is an indication of the pressure in the parachute canopy; the gore width, es, is an indication of the gore radius. A smaller gore width and resultant gore radius causes lower stress in the individual horizontal ribbons for a given internal pressure. Figure 6-41 shows boundary curves for the required horizontal ribbon strength. These data, based on analysis of many tested ribbon parachutes, were first presented in Reference 5.39 and subsequently updated by the author. &lt;br /&gt;
&lt;br /&gt;
For the reefed parachute,&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The gore width of the reefed parachute is obtained from the following consideration. The reefed drag area is equivalent to the drag area of a parachute with the following nominal diameter (DRJ):&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The equivalent nominal diameter for the reefed parachute is&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Two-inch-wide ribbon with 460-pound strength, MIL-T-5608, Trype DII, is selected for the upper canopy part, and 2-inch-wide ribbon with 300-pound strength, MIL-T-5608, Type CV, is used for the lower part of the canopy. This drogue parachute will be subjected to high-frequency ribbon flutter during its high-speed descent from altitude, which may include a descent on the drogue chute from 50,000 to 7000 feet. Disintegration of horizontal and vertical ribbon and the stitching connecting the ribbons has occurred in the past during long-duration, high-speed applications of reefed and unreefed ribbon chutes. This high-frequency flutter is especially pronounced on the uninflated part of reefed ribbon parachutes. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Experience has shown that the following design features will counteract this problem: &lt;br /&gt;
&lt;br /&gt;
1. Tight spacing of vertical ribbons. &lt;br /&gt;
&lt;br /&gt;
2. wo vertical ribbons, one on each side of horizontal ribbon. &lt;br /&gt;
&lt;br /&gt;
3. Three rows of stitching with F-F thread in the vertical ribbon. All three features are used in this canopy design. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.7.3 Design of Radials, Vent and Skirt Tape, and Vent Lines &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Radials.Based on experience, radials are designed to have 80% of the strength of the suspension lines; 0.8 3000 = 2400 pounds. Three 2-inch-wide tapes of MIL-T-5608 form each radial; two 1000-pound Class Eli tapes and one 460-pound Class DII tape give each radial a combined strength of 2460 pounds. It may be possible to use only two 1000-pound strength tapes that have 80% of the actual load of 2548 pounds. &lt;br /&gt;
&lt;br /&gt;
Skirt and Vent Tape. In accordance with the discussion in section 7.6.6, the selected skirt tape is equal in strength to the suspension line but is 2 inches wide. Nylon tape (MIL-T-5608, Class E, lype V) with 3000-pound strength meets this requirement.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The required strength of the vent tape is&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Because some of this load will be taken by the vent lines, a double 4000-pound webbing is chosen in accordance with MIL-W-2756, lype IL. &lt;br /&gt;
&lt;br /&gt;
Special attention is required to obtain a design that achieves proper connection between radial tape, vent tape, and vent lines. &lt;br /&gt;
&lt;br /&gt;
Vent lines. The vent lines should have 60% of the strength of the radial tapes and be 5% shorter than the finished vent diameter. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.7.4 Drogue Chute Riser Design &lt;br /&gt;
&lt;br /&gt;
The drogue chute riser is formed of bundled suspension lines. This design eliminates the 20% connection loss, u, on the parachute side and permits a highly efficient connection on the drone side. The individual lines must be secured against each other to prevent flutter abrasion. Each line runs from a loop on the canopy radial, down the riser, around the drone connection point, and up the riser to an opposite radial-tape loop. Tests should be made to determine the strength of the radial-tape and suspension-line-loop connection and the individual loop around the drone hard point. A wrap-around keeper is used on the riser suspension line transfer point.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.8.1 Canopy Porosity &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The porosity of a ribbon canopy is defined as the percentage ratio of openings in the canopy plus the material porosity divided by the total canopy surface area. Canopy porosity affects parachute stability, drag, and opening process. A canopy with high porosity provides for good parachute stability, and uniform, low force inflation, but also lower drag than a canopy with lower porosity. Too high a canopy porosity may result in no or only partial canopy inflation.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The operational porosity limit decreases with decreasing parachute diameter from about 35% total porosity for a stable 3-foot-diameter parachute to about 12% porosity for a 100-foot-diameter parachute (see Figure 6-23 (a) and Table 6-3). Section 6.2.4 discusses the effect of canopy porosity on the design and performance of ribbon parachutes. &lt;br /&gt;
&lt;br /&gt;
Properly designed conical ribbon parachutes with the correct porosity have an oscillation equal to or less than 2 to 3 degrees; a drag coefficient, CDo, of 0.55; and an opening-force coefficient, C., of 1.05 to 1.07 for subsonic applications with low forebody drag, such as experienced in wind-tunnel tests. &lt;br /&gt;
&lt;br /&gt;
The vertical ribbon spacing discussed in section 7.4.8.2 is of utmost importance for supersonic application. A canopy porosity of 25 to 26% in accordance with Figure 6-23, Curve III, and Thble 6-3 is recommended for this application. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.8.2 Vertical Ribbon Spacing &lt;br /&gt;
&lt;br /&gt;
Ribbon parachutes in the past were designed with individual gores, and the gores were connected with radial ribbons and several rows of stitching. This arrangement created the &amp;quot;venetian blind effect&amp;quot; shown in Figure 7-19. The venetian blind effect increases the effective canopy porosity discussed in section 6.2.4. &lt;br /&gt;
&lt;br /&gt;
More recently, ribbon canopies have been designed with continuous horizontal ribbons, a design that offers savings in weight and cost. This design is described in detail in section 7.4.10. &lt;br /&gt;
&lt;br /&gt;
Figure 7-20 shows the basic arrangement of a canopy gore and ribbon grid consisting of horizontal and vertical ribbons.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Section 6.2.4 explains the relationship of canopy loading, W/(CDS)p; effective porosity, Ne; and vertical ribbon spacing, a. Ribbon parachutes used as final descent parachutes use a vertical ribbon spacing to horizontal ribbon width a/B of 2.5 to 4.0. This spacing allows advantage to be taken of the change in effective porosity. High-canopy-loading ribbon parachutes, such as first-stage drogue chutes, use a vertical ribbon spacingof I to 2 to avoid the negative effects of the change in effective porosity. A narrow vertical ribbon spacing of 1.25 times the width of the horizontal ribbon width will be used for the drogue chute.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
All previous gore dimensions and the dimensions shown in Figure 7-21 are preliminary. The horizontal ribbon spacing, b, is controlled by the required porosity, k. Required changes in horizontal ribbon spacing may result in slight changez in gore and canopy dimensions.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.9.2 Preliminary Gore-Porosity Check &lt;br /&gt;
&lt;br /&gt;
Two methods of calculating gore porosity are in use. The older method, described in Reference 5.39, has been updated in this chapter. This method allows calculation of the porosity for preliminary design purposes when no final gore drawings are available. Reference 2.2 shows how to calculate canopy porosity if a drawing is available based on the ratio of open spaces to total canopy area. Both methods include an estimation of the ribbon (material) porosity&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The porosity of a ribbon grid with variations in the distance of the horizontal ribbons is now calculated. The total porosity is estimated, and the most likable horizontal ribbon distance is selected for the first gore-porosity check (Thble 7-9). The widths of the vertical ribbon, A, and the horizontal ribbon, B, are fixed values. The ratio of vertical ribbon spacing, to horizontal ribbon width, a/B, was previously selected to 1.25, which is equal to 2.5 inches. A horizontal ribbon distance, b, of 1.1 inches is selected as first approach based on data in Thble 7-9.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
To avoid a decrease in parachute diameter, 26 horizontal ribbons are selected, changing the gore dimensions from those shown in Figure 7-21 to those shown in Figure 7-22.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.9.S General Comments on Gore Design and Porosity Selection &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The canopy gore design-total canopy porosity, XT; spacing of vertical ribbon; size of vent; and pocket-band arrangement-are the primary design features that determine the aerodynamic performance of the parachute. The most important characteristics of parachute performance are stability, smooth opening, drag, and opening-force coefficients. Determining porosity under a no-load condition is rather unrealistic, because most of the important aerodynamic characteristics occur under high-load conditions (opening shock) or medium-load conditions (descent). However, since the beginning of parachute development, aerodynamic parachute characteristics obtained in wind-tunnel and free-flight tests have been related to fixed design dimensions such as diameter and porosity. &lt;br /&gt;
&lt;br /&gt;
Determining the effective porosity caused by the changing load during the opening process and by the venetian-blind effect of the ribbon grid design is practically impossible. Furthermore, the change in effective porosity is similar on all ribbon parachutes because of the similarities of the ribbon grid designs, load factors, and related changes in material elongation that cause deformation of the ribbon grids and the parachute canopies. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.9.6 Computer Programs for Determining Gore Design and Porosity Calculation &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Both gore design and porosity calculations can be determined by computer programs. Organizations involved in frequent design of ribbon parachutes should establish these programs. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.10 Ribbon Parachute Canopies with Continuous Horizontal Ribbons &lt;br /&gt;
&lt;br /&gt;
Ribbon parachute canopies are frequently designed and manufactured with continuous horizontal ribbons either in single or two-section canopies. The continuous ribbon Jesign decreases weight and volume, increases the strength of the horizontal ribbon-radial connection, and simplifies manufacturing. Continuous horizontal ribbons change the porosity characteristics of the canopy. &lt;br /&gt;
&lt;br /&gt;
Figure 7-19 shows how the individual horizontal ribbons orient themselves in a canopy manufactured from individual triangular gores. In the inflated canopy, the horizontal ribbons in the canopy crown area orient parallel to the canopy design. However, in the skirt area, the canopy design line is almost parallel to the airflow. This design, usually called the &amp;quot;venetian blind effect,&amp;quot; causes ti:e longer leading edge of each horizoatal ribbon to bulge out and position the ribbon with a positive angle of attack to the airflow. The result is an increase in effective porosity under high dynamic pressure conditions. The venetian blind effect is discussed in section 6.2.4, and the influence of canopy loading on the change in effective porosity is shown in Figure 6-24.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Designing canopies with continuous horizontal ribbons changes the venetian blind effect. Returning to Figure 7.19, it is obvious that continuous horizontal ribbons in the canopy skirt area do not bulge out since leading and trailing ribbon edges have the same length and do not position themselves with an angle of attack to the airflow. However, in the crown area of the canopy where each gore forms a triangle, the equal length of the leading and trailing ribbon edges now gives each ribbon a negative angle of attack thereby increasing the effective porosity in the canopy crown area. The effect is minimized by large number of gores arid by the use of a center vertical ribbon, or a miniradial, as Sandia engineers call it. &lt;br /&gt;
&lt;br /&gt;
Discussion with Sandia and industry personnel indicates that no measurable difference has been found in the aerodynamic characteristics of ribbon parachute canopies designed with individual gores or with continuous horizontal ribbons so long as the canopies contain a large number of gores and a center vertical ribbon. However, a slight delay in initial inflation seems to occur on small parachutes with a small number of gores. Closer spacing of vertical ribbons in the canopy crown area should counteract this delay. Another method of counteracting the delay is by gathering the trailing edges of horizontal ribbons with several rows of stitching and using a lower porosity in the crown area. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.11 Use of Kevlar Fabrics &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Many modern ribbon parachutes use Kevlar suspension lines, risers, and canopy skirt, lateral, and vent tapes, which results in a decrease in weight and volume. Section 6.5.5 discusses all aspects of working with Kevlar in the design of parachute assemblies. This includes physical characteristics of Kevlar fibers and fabrics, available Kevlar fabrics, and experience ;il designing in Kevlar. Section 6.6.5 should be studied before designing in Kevlar.&lt;/div&gt;</summary>
		<author><name>TuanHTruong</name></author>
	</entry>
	<entry>
		<id>https://mediawiki.aerodecelerator.org/index.php?title=Parachute_Aerodynamics&amp;diff=38</id>
		<title>Parachute Aerodynamics</title>
		<link rel="alternate" type="text/html" href="https://mediawiki.aerodecelerator.org/index.php?title=Parachute_Aerodynamics&amp;diff=38"/>
		<updated>2024-05-07T18:30:39Z</updated>

		<summary type="html">&lt;p&gt;TuanHTruong: /* 4.7 REFERENCE MATERIAL */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&lt;br /&gt;
= CHAPTER 4: AERODYNAMICS AS RELATED TO PARACHUTES =&lt;br /&gt;
== 4.1 PROPERTIES OF THE ATMOSPHERE ==&lt;br /&gt;
All forces acting on parachutes and all movements of parachutes are affected by the atmosphere, or air, surrounding the Earth. The air at the Earth's surface is approximately 78% nitrogen; 21% oxygen; and 1% a mixture of gases such as argon, neon, helium, water vapor, and carbon dioxide. This chemical composition remains relatively constant to an altitude of about 160,000 feet (50 kilometers). The following air qualities are of major significance in the dynamics of bodies moving in the atmosphere:&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
!Air quality&lt;br /&gt;
!Symbol&lt;br /&gt;
!Dimension&lt;br /&gt;
|-&lt;br /&gt;
|Specific weight of air&lt;br /&gt;
|w&lt;br /&gt;
|lb/ft&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;, kg/m&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;&lt;br /&gt;
|-&lt;br /&gt;
|Static pressure&lt;br /&gt;
|p&lt;br /&gt;
|atm, lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;, Pa, bar, torr&lt;br /&gt;
|-&lt;br /&gt;
|Temperature&lt;br /&gt;
|T&lt;br /&gt;
|&amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F, &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;C&lt;br /&gt;
|-&lt;br /&gt;
|Mass density&lt;br /&gt;
|&amp;lt;math&amp;gt;\rho&amp;lt;/math&amp;gt;&lt;br /&gt;
|slugs/ft&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;, kg s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;/m&amp;lt;sup&amp;gt;4&amp;lt;/sup&amp;gt;&lt;br /&gt;
|-&lt;br /&gt;
|Gravity&lt;br /&gt;
|''g''&lt;br /&gt;
|ft/s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;, m/s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
|-&lt;br /&gt;
|Speed of sound&lt;br /&gt;
|C&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt;&lt;br /&gt;
|ft/s, m/s&lt;br /&gt;
|}&lt;br /&gt;
All of these qualities are altitude-dependent and may vary slightly on the Earth's surface with geographic latitude because of variations of the Earth's radius caused by the centrifugal forces of the rotation of the Earth. All standard data used herein refer to a latitude of 45 degrees. Sea level is defined as mean sea level (MSL). To compare performance data on an equal basis, the United States Bureau of Standards has defined standard day conditions as follows:&lt;br /&gt;
&lt;br /&gt;
* Temperature = 15 degrees Celsius (&amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;C) or 59 degrees Fahrenheit (&amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F)&lt;br /&gt;
* Pressure = 760 millimeters (mm) of mercury (Hg) or 29.9213 inches (in.) Hg&lt;br /&gt;
&lt;br /&gt;
=== 4.1.1 Specific Weight of Air ===&lt;br /&gt;
For standard day conditions of 59 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F temperature and a pressure of 29.9213 in. Hg, the specific weight of air, w, is 0.07648 lb/ft&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt; or 1.2250 kg/m&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;. The specific weight of air changes with pressure, temperature, and humidity. Further data can be found in References 3.4 and 4.1, and in technical handbooks.&lt;br /&gt;
&lt;br /&gt;
=== 4.1.2 Static Pressure ===&lt;br /&gt;
Static pressure depends on geographic latitude, weather conditions, and altitude. The static pressure at any altitude results from the weight of the air above that altitude. For MSL and standard day conditions, the pressure, p&amp;lt;sub&amp;gt;o&amp;lt;/sub&amp;gt;, is 29.9213 in. Hg = 760 mm Hg = 1.0 atmosphere (atm). For conversion to Pascal, torr, or bar, see the conversion tables in section 3.2.&lt;br /&gt;
&lt;br /&gt;
=== 4.1.3 Temperature ===&lt;br /&gt;
Temperatures are defined in the English and metric systems in the so-called absolute and engineering scales. The absolute temperature minimum at 0 degrees, pressure is 0 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;K = -273.16 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;C, and 0 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;R = -459.69 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F. This is also written&lt;br /&gt;
&lt;br /&gt;
* Degrees Kelvin = degrees Celsius + 273.16&lt;br /&gt;
* Degrees Rankine = degrees Fahrenheit + 459.69&lt;br /&gt;
&lt;br /&gt;
The freezing point of water is 32 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F or 0 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;C. The boiling point of water is 212 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F or 100 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;C.&lt;br /&gt;
&lt;br /&gt;
=== 4.1.4 Mass Density of Air ===&lt;br /&gt;
Mass density defines the amount of mass contained in a unit volume of air. The mass density, &amp;lt;math&amp;gt;\rho&amp;lt;/math&amp;gt;, of air is of special importance in aerodynamic calculations.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\rho = \frac{specific\ weight\ of\ air,\ w}{acceleration\ of\ gravity,\ g} = \frac{lb/ft^3}{ft/s^2} = \frac{kg\ s^2}{m^4}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;slug = \frac{weight}{acceleration\ of\ gravity} = \frac{lb}{ft/s^2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Frequently the density ratio, &amp;lt;math&amp;gt;\sigma&amp;lt;/math&amp;gt;, is used&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\sigma = \frac{ambient\ air\ density,\ \rho}{standard\ sea-level\ density, \rho_o}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The factor, &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;1/\sqrt{\rho/\rho_o}&amp;lt;/math&amp;gt;, determines the increase in parachute rate of descent with altitude. The density at 40,000 feet is ¼ of the MSL density, and the density at 100,000 feet is 1/75 of the MSL density. Therefore, the parachute rate of descent is about twice as high at 40,000 feet and about nine times as high at 100,000 feet. MSL density is 0.00237689 slugs/ft&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;, or 0.1249 kg s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;/m&amp;lt;sup&amp;gt;4&amp;lt;/sup&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
=== 4.1.5 Gravity ===&lt;br /&gt;
Any mass attracts another mass with a force called gravity. If the Earth were surrounded by a vacuum, a body suspended above the Earth and released would fall toward the center of the Earth with increasing velocity caused by the acceleration of gravity, ''g''. In reality, the falling body is decelerated by its air drag until the air drag, D, equals the weight of the body, W, and an equilibrium velocity is reached; for parachutes, this is called the steady-state rate of descent.&lt;br /&gt;
&lt;br /&gt;
The acceleration of gravity, ''g'', at sea lavel is&lt;br /&gt;
&lt;br /&gt;
* ''g'' = 32.174 ft/s2 or 9.80665 m/s2.&lt;br /&gt;
&lt;br /&gt;
The value g = 9.08665 m/s is standardized internationally but is accurate only for a latitude of 45 degrees.&lt;br /&gt;
&lt;br /&gt;
With increasing altitude above the Earth's surface, the acceleration of gravity decreases in accordance with the equation&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;g = g_o(\frac{r}{r+h})^2&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
* ''g'' = acceleration of gravity at any altitude, ft/s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
* g&amp;lt;sub&amp;gt;o&amp;lt;/sub&amp;gt; = acceleration of gravity at sea level, ft/s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
* r = average Earth radius = 2.08556 x 10&amp;lt;sup&amp;gt;7&amp;lt;/sup&amp;gt; ft&lt;br /&gt;
* h = altitude above sea level, ft&lt;br /&gt;
&lt;br /&gt;
For other planets and heavenly bodies, the acceleration of gravity varies with the mass of the body. For example, the acceleration of gravity on Mars is about 1/3 of the acceleration of gravity on Earth. For more details on planets and heavenly bodies, see page XII of Reference 2.1.&lt;br /&gt;
&lt;br /&gt;
=== 4.1.6 Kinematic Viscosity ===&lt;br /&gt;
The coefficient of viscosity, &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt;, defines the shearing stresses in a gas or liquid and is sometimes called the resistance to continuous deformation. In aerodynamics, the coefficient of viscosity is combined with the mass density to form the kinematic viscosity, &amp;lt;math&amp;gt;\nu&amp;lt;/math&amp;gt;, where&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\nu = \frac{coefficient\ of\ viscosity,\ \mu}{mass\ density,\ \rho} = 0.0001576\ ft^2/s\ at\ sea\ level&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The kinematic viscosity, &amp;lt;math&amp;gt;\nu&amp;lt;/math&amp;gt;, is altitude dependent and is used to calculate the Reynolds number, Re.&lt;br /&gt;
&lt;br /&gt;
=== 4.1.7 Reynolds Number ===&lt;br /&gt;
The Reynolds number, Re, defines the relationship of mass forces to viscous friction forces in liquids and gases. It is calculated as&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Re = \frac{v\cdot l}{\nu} = \frac{velocity\ (ft/s)\cdot characteristic\ length\ (ft)}{kinematic\ viscosity\ (ft^2/s)}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Reynolds number is an important criterion in subsonic, noncompressible flow, and allows comparison of model tests with full-scale flight tests. A Reynolds number effect on parachutes working in separated, turbulent flow has not yet been established, as shown in section 5.2. The following chart shows the Reynolds numbers for various air vehicles.&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
!Subject&lt;br /&gt;
!Insect&lt;br /&gt;
!Glider&lt;br /&gt;
!DC-3&lt;br /&gt;
!B-747&lt;br /&gt;
!Drogue&lt;br /&gt;
Chute&lt;br /&gt;
!Main &lt;br /&gt;
Parachute&lt;br /&gt;
!WTT&lt;br /&gt;
Model&lt;br /&gt;
|-&lt;br /&gt;
|Re&lt;br /&gt;
|6 • 10&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;&lt;br /&gt;
|2.5 • 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&lt;br /&gt;
|24 • 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&lt;br /&gt;
|100 • 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&lt;br /&gt;
|50 • 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&lt;br /&gt;
|20 • 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&lt;br /&gt;
|2 • 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
=== 4.1.8 Mach Number ===&lt;br /&gt;
Mach number is an important parameter of supersonic flight; it states how much faster than the speed of sound the air vehicle travels.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Mach\ number,\ M = \frac{flight\ velocity,\ v}{speed\ of\ sound, c_s}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The speed of sound is the velocity at which a pressure disturbance, such as the sound of the human voice, travels in any medium. The speed of sound varies considerably in different gases, liquids, and metals.&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|Speed of sound in air in MSL&lt;br /&gt;
|C&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt; = 1116.46 ft/s = 340.38 m/s&lt;br /&gt;
|-&lt;br /&gt;
|Speed of sound in water&lt;br /&gt;
|C&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt; = 4749 ft/s = 1461.21 m/s&lt;br /&gt;
|-&lt;br /&gt;
|Speed of sound in iron&lt;br /&gt;
|C&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt; = 16,410 ft/s = 5710.7 m/s&lt;br /&gt;
|}&lt;br /&gt;
The speed of sound depends on temperature and the chemical composition of the medium, A widely used equation for speed of sound in air is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;C_s = 41.4\sqrt{\gamma\cdot T}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
* &amp;lt;math&amp;gt;C_s&amp;lt;/math&amp;gt; = speed of sound in dry air, ft/s&lt;br /&gt;
* &amp;lt;math&amp;gt;\gamma&amp;lt;/math&amp;gt; = ratio of specific heat, equal to 1.4 for dry air, dimensionless&lt;br /&gt;
* &amp;lt;math&amp;gt;T&amp;lt;/math&amp;gt; = temperature in Fahrenheit absolute, equal to 459.67 + &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F&lt;br /&gt;
&lt;br /&gt;
The speed of sound changes with altitude, as temperature (see Figure 3-1). The drag of streamlined bodies such as missiles, airfoils, and airplanes increases considerably as their velocities approach Mach 1. Depending on the configuration of the body, supersonic compressibility effects may occur in the 0.75 to 0.85 Mach range, causing local supersonic flow, shock waves, flow separation, and concomitant increases in drag and changes in stability.&lt;br /&gt;
&lt;br /&gt;
Parachutes that operate in separated flow over the entire velocity range do not show the typical drag increase when operating close to or beyond Mach 1. Supersonic parachute behavior is discussed in detail in section 5.8.&lt;br /&gt;
&lt;br /&gt;
== 4.2 CONTINUITY LAW AND BERNOULLI EQUATION ==&lt;br /&gt;
&lt;br /&gt;
=== 4.2.1 Continuity L.aw ===&lt;br /&gt;
Air is thought to flow in layers called streamlines. Figure 4-1 shows streamlines as layers of air without air transfer between individual layers. ne air is shown as being incompressible, a valid assumption for subsonic flow.&lt;br /&gt;
&lt;br /&gt;
[Insert Figure 4-1] 	&lt;br /&gt;
&lt;br /&gt;
If exchange of air does not occur across the streamline boundaries, the amount of air entering the streamline at point 1 must also exit at point 2, as shown in Figure 4-1. Because the cross section at point 2 is smaller than the cross section at point 1, the air must exit at a higher velocity. The following equation defines this condition:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;v_1\cdot S_1\cdot \rho_1 = v_2\cdot S_2\cdot \rho_2&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S&amp;lt;/math&amp;gt; = cross section of the streamline&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;v&amp;lt;/math&amp;gt; = velocity in the streamline&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\rho&amp;lt;/math&amp;gt; = density of the air flowing in the streamline&lt;br /&gt;
&lt;br /&gt;
This equation, which governs the flow in and around a body in gases and liquids, is important in aerodynamics and is called the Continuity Law. For incompressible subsonic flow, it can be simplified to &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;v_1\cdot S_1 = v_2\cdot S_2&amp;lt;/math&amp;gt; &lt;br /&gt;
&lt;br /&gt;
Whenever the cross section narrows, the velocity increases; when the cross section widens, the velocity decreases.&lt;br /&gt;
&lt;br /&gt;
=== 4.2.2 Bernoulli Equation ===&lt;br /&gt;
Figure 4-2 illustrates a streamline with the cross section, S, the velocity, v, and the pressure, p. If the air is incompressible, the downstream is v + Av. and the pressure is p + AP. If the air is inviscid, the inertia forces caused by the acceleration of air from v to v + Av must be balanced by differential pressure forces.&lt;br /&gt;
&lt;br /&gt;
[Insert Figure 4-2]FIGURE 4-2 Pressure and Velocity Distribution in a Streamline Element. 	&lt;br /&gt;
&lt;br /&gt;
The following equation can be written&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;p\cdot S-(p+\Delta p)S = m\cdot \frac{dv}{dt}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Simplified, the above equation yields&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;dp = - \rho vdv&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
and&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;p = - \frac{1}{2}\rho v^2 + C&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The above equation allows the following consideration: If p is pressure, then &amp;lt;math&amp;gt;1/2\ \rho v^2&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;C&amp;lt;/math&amp;gt; must also be pressure. The equation &amp;lt;math&amp;gt;1/2\ \rho v^2&amp;lt;/math&amp;gt; includes a velocity and is referred to as the dynamic pressure, or sometimes as velocity or impact pressure.&lt;br /&gt;
&lt;br /&gt;
Pressure, &amp;lt;math&amp;gt;p&amp;lt;/math&amp;gt;, is defined as static pressure; &amp;lt;math&amp;gt;1/2\ \rho v^2&amp;lt;/math&amp;gt; as dynamic pressure; and the sum of both, &amp;lt;math&amp;gt;C&amp;lt;/math&amp;gt;, as the total pressure or&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;p+\frac{1}{2} \rho v^2 = H&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
and&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;p_1 + \frac{1}{2} \rho {v_1}^2 = p_2 + \frac{1}{2} \rho {v_2}^2&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;H&amp;lt;/math&amp;gt; is the total pressure of the system, lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Dynamic pressure, &amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt;, is a frequently used quantity in aerodynamics:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;q = \frac{1}{2} \rho v^2&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
* &amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt; = dynamic pressure, lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
* &amp;lt;math&amp;gt;\rho&amp;lt;/math&amp;gt; =  air density, slugs/ft&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;&lt;br /&gt;
* &amp;lt;math&amp;gt;v&amp;lt;/math&amp;gt; =  velocity at a point of undisturbed flow, ft/s&lt;br /&gt;
&lt;br /&gt;
The following formulas are used for calculating the sea-level dynamic pressure if the velocity is given in ft/s, knots, mph, or km/h, respectively:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;q=\frac{v^2}{841.4}(ft/s), q=\frac{v^2}{295}(knots), q=\frac{v^2}{391.2}(mph), q=\frac{v^2}{1013.1}(km/h)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
                                              &lt;br /&gt;
&lt;br /&gt;
== 4.3 NEWTON'S THREE OF MOTION ==&lt;br /&gt;
Engineering mechanics are governed by the following three laws of Isaac Newton:&lt;br /&gt;
&lt;br /&gt;
1.  A body remains at rest or in an unaccelerated state of motion unless acted upon.&lt;br /&gt;
&lt;br /&gt;
2.  A force acting upon a body will produce an acceleration in the direction of the force.&lt;br /&gt;
&lt;br /&gt;
3.  An action in one direction will produce an equal reaction in the opposite direction.&lt;br /&gt;
&lt;br /&gt;
The first law is self-explanatory. The second law may be expressed by the equation&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;F=m\cdot a&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;F&amp;lt;/math&amp;gt; = force in pounds acting on the mass, lb&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;m&amp;lt;/math&amp;gt; = mass of body that the force is acting upon, slugs&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; = acceleration in ft/s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; resulting from the force, F&lt;br /&gt;
&lt;br /&gt;
The mass, m, of a body is obtained by&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;m=\frac{W}{g}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;W&amp;lt;/math&amp;gt; = weight of the body, lb&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;g&amp;lt;/math&amp;gt; = acceleration of gravity, ft/s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The mass, therefore, has the dimension of&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;m = \frac{W}{g}=\frac{lb}{ft/s^2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
This unit of mass is the slug.&lt;br /&gt;
&lt;br /&gt;
The equation of Newton's second law can now be written&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;F=\frac{W}{g}\cdot a,\ or\ F=W\frac{a}{g}&amp;lt;/math&amp;gt; 	&lt;br /&gt;
&lt;br /&gt;
The factor a/g is frequently called the load factor, G, and tells how much larger a force is than a force equivalent to the weight of the body. It is customary in parachute work to state that the maximum parachute force allowed is G • W or (a/g) • W. It is appropriate to write&lt;br /&gt;
&lt;br /&gt;
Maximum allowable parachute force, &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;F=W\frac{a}{g},\ or\ W\cdot G&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Figure 4-3 illustrates Newton's third law, explaining the principle of the rocket that can produce thrust in a perfect vacuum.&lt;br /&gt;
&lt;br /&gt;
A mass, m, ejected from a rocket at the velocity, v, per unit time, t, will produce a force, F, which in turn will create a reaction force, R, of equal magnitude but acting in the opposite direction.&lt;br /&gt;
&lt;br /&gt;
== 4.4 FORCES ACTING ON A BODY MOVING THROUGH AIR ==&lt;br /&gt;
&lt;br /&gt;
=== 4.4.1 Symmetrical Body ===&lt;br /&gt;
A body moving through air experiences forces caused by air pressure acting on the body. The same forces if the body moves through air, such as a descending parachute, or if the body is fixed and the air moves against the body, such as a parachute or an airfoil in a wind tunnel (Figure 44).&lt;br /&gt;
&lt;br /&gt;
         	 &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
A stable parachute in a wind tunnel experiences only the force called &amp;quot;drag&amp;quot; in the direction of the airflow. drag force, D, is calculated to&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;D=q\cdot S\cdot C_D&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;D&amp;lt;/math&amp;gt; = drag, lb&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt; = dynamic pressure, lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S&amp;lt;/math&amp;gt; = total surface area of the parachute canopy, ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;C_D&amp;lt;/math&amp;gt; = coefficient of drag,  dimensionless&lt;br /&gt;
&lt;br /&gt;
The dynamic pressure, q, can be calculated from section 4.2.2. The surface area of the canopy, S, is selected as a reference area. The drag coefficient, C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, is a form factor that indicates the drag characteristic of a specific shape. Most aerodynamic bodies are designed for low drag or a low drag coefficient. Parachutes, generally, are designed for high drag; therefore, a high drag coefficient is desirable. this difference in drag is demonstrated by the two bodies shown in Figure 4-5.&lt;br /&gt;
&lt;br /&gt;
            	&lt;br /&gt;
&lt;br /&gt;
Both bodies have the same cross section perpendicular to the airflow. The cylindrical. streamlined body has a smooth airflow over its total body length, resulting in a drag coefficient. C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, of 0.05 to 0.1, depending on slenderness ratio, surface roughness, and shape. The drag coefficient of all streamlined bodies is much affected by Reynolds number and Mach number. The open hemisphere, which is similar to a parachute canopy, has a drag coefficient, C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, of 1.3 to 1.4 for the same body cross section. The difference in drag is explained by the smooth airflow around the streamlined body and a separated, turbulent flow around the open hemisphere. The drag of bodies with separated flow, like parachute canopies, is little affected by Reynolds number.&lt;br /&gt;
&lt;br /&gt;
=== 4.4.2 Airflow Around an Asymmetrical Body (Airfoil) ===&lt;br /&gt;
Figure 4-6 shows an airfoil fixed at an angle of attack, a. against the airflow in a wind tunnel. This airfoil creates a drag force, D, in the direction of the flow; a lift force L perpendicular to the direction of the flow; and a moment, M. around the attachment point of the airfoil. fie sign convention of moments and forces shown are positive. Lift and drag can be combined for the resultant force, R.&lt;br /&gt;
&lt;br /&gt;
FIGURE. 4-6, Wind-Tunnel Forces Acting on an Airfoil.&lt;br /&gt;
&lt;br /&gt;
The lift, L is calculated&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;L = q\cdot S\cdot C_L&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; = measured lift, lb&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt; = dynamic pressure, lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S&amp;lt;/math&amp;gt; = reference area, ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;C_L&amp;lt;/math&amp;gt; = lift coefficient, dimensionless&lt;br /&gt;
&lt;br /&gt;
The moment is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;M=q\cdot S\cdot c_m\cdot c&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Where&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;M&amp;lt;/math&amp;gt; = measured lift, lb&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt; = dynamic pressure, lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S&amp;lt;/math&amp;gt; = reference area, ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;c_m&amp;lt;/math&amp;gt; = moment coefficient, dimensionless&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;c&amp;lt;/math&amp;gt; = average chord width of the wing, ft&lt;br /&gt;
&lt;br /&gt;
The reference area, S, is defined by agreement. For streamlined bodies, the maximum body cross section is used. Airfoils use the planform of the wing, and parachutes use the canopy surface area. The selection of the wing planform and the parachute surface area as references was made for practical reasons. The wing planform for a specific wing is fixed, whereas the cross section of the wing in the direction of the flow changes with the angle of attack. Similarly, the surface area of the parachute canopy is fixed; however, the frontal projected area of the inflated parachute canopy changes with airspeed, porosity, line length, and type of parachute.&lt;br /&gt;
&lt;br /&gt;
Forces and moments acting on an airfoil or a parachute canopy may be presented in several ways. The two most frequently used methods, as shown in Figure 4-7, are with forces oriented to the axis of flight and with forces oriented to the axis of the airfoil.&lt;br /&gt;
&lt;br /&gt;
The tangential force, and the normal force, N, are calculated&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;T = C_T\cdot S\cdot q&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
and 	&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;N = C_N\cdot S\cdot q&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
C&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; = tangential force coefficient, dimensionless&lt;br /&gt;
&lt;br /&gt;
C&amp;lt;sub&amp;gt;N&amp;lt;/sub&amp;gt; = normal force coefficient, dimensionless&lt;br /&gt;
&lt;br /&gt;
The resultant force, R, and the moment, M, in both presentations have the same direction and the same magnitude. The airflow fixed system is preferred for aerodynamic performance calculations, and the airfoil fixed system for wing stress calculations. me aerodynamic coefficients C&amp;lt;sub&amp;gt;L&amp;lt;/sub&amp;gt;, C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, C&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, C&amp;lt;sub&amp;gt;N&amp;lt;/sub&amp;gt;, and C&amp;lt;sub&amp;gt;m&amp;lt;/sub&amp;gt; can easily be determined in wind•tunnel measurements.&lt;br /&gt;
&lt;br /&gt;
Figure 4-8 shows the relationship of both force systems on a parachute. By definition, a negative moment is stabilizing, as illustrated in Figure 4-8. It is interesting to note that in Europe the stabilizing moment is defined as positive. Wind-tunnel installations frequently measure normal and tangential force instead of lift and drag. If α, T, and N are known, the drag D, can be calculated&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;D=T\cdot cos(\alpha)+N\cdot sin(\alpha)&amp;lt;/math&amp;gt;For a parachute with an angle of attack, &amp;lt;math&amp;gt;\alpha&amp;lt;/math&amp;gt;, equal to zero, the drag force and the tangential force are synonymous.&lt;br /&gt;
&lt;br /&gt;
Figure 4-9 shows the coefficients C&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, and C&amp;lt;sub&amp;gt;m&amp;lt;/sub&amp;gt; versus angle of attack for stable and unstable parachutes.&lt;br /&gt;
&lt;br /&gt;
The coefficient presentation shows two interesting facts. The slope of the moment coefficient curve, dC&amp;lt;sub&amp;gt;m&amp;lt;/sub&amp;gt;/dα, for the unstable parachute is positive between -25 degrees and + 25 degrees; this is, by definition, destabilizing. This parachute will oscillate approximately ± 25&lt;br /&gt;
&lt;br /&gt;
FIGURE 4-9. Coefficients C&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, and C&amp;lt;sub&amp;gt;M&amp;lt;/sub&amp;gt; Versus Angle of Attack, α, for a Stable and Unstable Parachute.&lt;br /&gt;
&lt;br /&gt;
degrees. The slope of the moment, dC&amp;lt;sub&amp;gt;m&amp;lt;/sub&amp;gt;/dα, for the stable parachute is negative over the total angle of attack; this is, by definition, stabilizing. The steeper the negative dC&amp;lt;sub&amp;gt;m&amp;lt;/sub&amp;gt;/dα slope, the greater is the stabilizing tendency of the parachute, and the better is its damping capability against unstabilizing forces such as sudden gusts of wind.&lt;br /&gt;
&lt;br /&gt;
Figure 4-10, from Reference 4.1, demonstrates the effect of airflow around a cylinder and an airfoil. The circulation around a rotating cylinder creates lift caused by the increase in velocity on one side of the cylinder and a decrease on the opposite side. This is called the Magnus effect.&lt;br /&gt;
&lt;br /&gt;
== 4.5 EQUILIBRIUM OF FORCES IN STUDY DESCENT OR FLIGHT ==&lt;br /&gt;
&lt;br /&gt;
=== 4.5.1 Parachute in Steady Descent ===&lt;br /&gt;
A stable parachute in unaccelerated descent has an equilibrium between the total drag of the parachute and the load, Dr, and the weight of the load and the parachute assembly, WT (Figure 4-11). &lt;br /&gt;
&lt;br /&gt;
For steady descent&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
D&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; = total drag, 1b&lt;br /&gt;
&lt;br /&gt;
D&amp;lt;sub&amp;gt;P&amp;lt;/sub&amp;gt; = drag of parachute, 1b&lt;br /&gt;
&lt;br /&gt;
W&amp;lt;sub&amp;gt;C&amp;lt;/sub&amp;gt; = weight of load. 1b&lt;br /&gt;
&lt;br /&gt;
In most cases, the drag of the load can be neglected in relation to the large drag of the parachute, With drag, D — (C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;S)&amp;lt;sub&amp;gt;p&amp;lt;/sub&amp;gt; • p/2• v&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; and D&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; = W&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;. and solving for v, the important equation for rate of descent, v&amp;lt;sub&amp;gt;e&amp;lt;/sub&amp;gt;, is obtained,&lt;br /&gt;
&lt;br /&gt;
Rate of descent,&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
FIGURE 4-11. Forces Acting on a Parachute in Steady Descent.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
or in parachute terminology for rate of descent at sea level&lt;br /&gt;
&lt;br /&gt;
and rate of descent at any altitude&lt;br /&gt;
&lt;br /&gt;
For 1/, see column 4 in Table 3-3,&lt;br /&gt;
&lt;br /&gt;
In the equation for rate of descent. V&amp;lt;sub&amp;gt;e&amp;lt;/sub&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
W&amp;lt;sub&amp;gt;T =&amp;lt;/sub&amp;gt; weight of load and parachute assembly, 1b&lt;br /&gt;
&lt;br /&gt;
S&amp;lt;sub&amp;gt;o&amp;lt;/sub&amp;gt; = canopy surface area, ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
C&amp;lt;sub&amp;gt;Do&amp;lt;/sub&amp;gt; = parachute drag coefficient related to S&amp;lt;sub&amp;gt;o&amp;lt;/sub&amp;gt;&lt;br /&gt;
&lt;br /&gt;
p = air density at a specific altitude in slugs/ft&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;, as shown in Table 3-3&lt;br /&gt;
&lt;br /&gt;
During descent from altitude, the parachute system is constantly decelerated because of the increasing air density. This can be ignored for slowly descending main parachutes. However, for drogue chute systems that descend at 200 ft/s or faster, the constant deceleration may result in velocities 3 to 5% higher than the steady rate of descent.&lt;br /&gt;
&lt;br /&gt;
=== 4.5.2 Gliding Parachutes ===&lt;br /&gt;
Figure 4-12 shows the balance of forces on a gliding parachute. The total weight of the system, W&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; . must be balanced by the resultant force. R. However, a lifting force is required for glide. To satisfy the force balance&lt;br /&gt;
&lt;br /&gt;
R = C&amp;lt;sub&amp;gt;R&amp;lt;/sub&amp;gt; * S * p/2 * v&lt;br /&gt;
&lt;br /&gt;
Trajectory velocity, V&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, is calculated&lt;br /&gt;
&lt;br /&gt;
Horizontal velocity is calculated&lt;br /&gt;
&lt;br /&gt;
V&amp;lt;sub&amp;gt;H&amp;lt;/sub&amp;gt; = V&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; • cosø, and vertical velocity, v&amp;lt;sub&amp;gt;v&amp;lt;/sub&amp;gt; = V&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; • sinø&lt;br /&gt;
&lt;br /&gt;
The glide ratio is obtained from&lt;br /&gt;
&lt;br /&gt;
Analysis of Figure 4-12 indicates that the larger the ratio of lift to drag, the better the glide ratio, I./D A high resultant coefficient, C&amp;lt;sub&amp;gt;R&amp;lt;/sub&amp;gt;, results in a low glide or trajectory V&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, desirable for landing. A small C&amp;lt;sub&amp;gt;R&amp;lt;/sub&amp;gt; results in a high glide velocity, V&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, which is desirable for flying toward a target, compensating for head winds, or covering a distance quickly. Generally, gliding parachutes follow the same aerodynamic rules as low-aspect-ratio wings.&lt;br /&gt;
&lt;br /&gt;
           	   	&lt;br /&gt;
&lt;br /&gt;
FIGUR E 4-12, Forces Acting on a Gliding Parachute&lt;br /&gt;
&lt;br /&gt;
=== 4.5.3 Parasite Drag and Induced Drag ===&lt;br /&gt;
The drag acting on a lift-producing air vehicle, such as a gliding parachute or an aircraft, has two primary components: the parasite drag, D&amp;lt;sub&amp;gt;P&amp;lt;/sub&amp;gt; , and the induced drag. D&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Parasite drag is produced by the form drag from individual components such as the suspension lines, canopy, and the jumper of a gliding parachute, and the fuselage, tail sectiora, and control surfaces of an airplane. Large surfaces produce surface friction drag as part of the parasite drag.&lt;br /&gt;
&lt;br /&gt;
Induced drag is caused by the lifting action of the parachute canopy or the aircraft wing. Section 4.7 includes books with detailed discussions of induced drag.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Total drag, D&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, can be defined as&lt;br /&gt;
&lt;br /&gt;
or, in the coefficient form&lt;br /&gt;
&lt;br /&gt;
The parasite drag, D&amp;lt;sub&amp;gt;p&amp;lt;/sub&amp;gt;, and the coefficient, C&amp;lt;sub&amp;gt;DP&amp;lt;/sub&amp;gt;, can be determined in wind-tunnel tests or calculated as the sum of the individual component drags.&lt;br /&gt;
&lt;br /&gt;
The induced drag coefficient, C&amp;lt;sub&amp;gt;Di&amp;lt;/sub&amp;gt; , of a gliding parachute canopy or a wing profile can be calculated&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
C = coefficient of induced drag, dimensionless&lt;br /&gt;
&lt;br /&gt;
The expression b&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;/S is defined as the aspect ratio of a wing or parachute with the notation AR b&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;/S. Therefore&lt;br /&gt;
&lt;br /&gt;
The equation for induced drag indicates that increasing the aspect ratio, AR, reduces the induced drag coefficient,  , and therefore reduces the drag, D. ms, in turn, increases the glide ratio, L/D. Increasing the glide ratio by increasing the aspect ratio is optimized on high-performance sailplanes with aspect ratios higher than 20. Increasing the glide ratio of gliding parachutes by increasing the aspect ratio has limitations, which are discussed in section 5.9.&lt;br /&gt;
&lt;br /&gt;
=== 4.5.4 Aircraft in Horizontal Flight ===&lt;br /&gt;
Figure 4-13 shows forces and moments on an aircraft in steady, horizontal flight. In steady, horizontal flight, an equilibrium exists between all forces and moments acting on the aircraft. Lift on the wing and tail, L&amp;lt;sub&amp;gt;W&amp;lt;/sub&amp;gt; and L&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;. and the weight of the aircraft, W&amp;lt;sub&amp;gt;A&amp;lt;/sub&amp;gt;, balance in the vertical plane. Thrust, T and drag. D, balance each other in the horizontal plane, and the positive or negative moment, M, is balanced by the positive or negative lift of the tail multiplied by the moment arm, L&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
FIGURE 4-13. Forces and Moments Acting on an Aircraft in Steady night,&lt;br /&gt;
&lt;br /&gt;
Any imbalance in these forces results in descent or climb in the vertical plane or faster or slower speed in the horizontal plane. A change in the lift of the elevator initiates climb or descent. Thrust, T, is the prime contributor for climb or descent and faster or slower speed, However, a balance of forces must always be maintained for horizontal flight or steady rate oi climb or descent.&lt;br /&gt;
&lt;br /&gt;
== 4.6 WIND-TUNNEL TESTING OF PARACHUTES ==&lt;br /&gt;
Wind tunnels are an effective tool for testing air vehicles and air-vehicle components and have been used successfully for testing parachutes and parachute systems. Experience has shown that certain rules apply for the wind-tunnel testing of parachutes. Small parachutes manufactured from textiles cannot be made sufficiently similar to large parachutes in geometric design and flexibility, Lightweight material. required to obtain design similarity, is difficult to manufacture or is unobtainable.&lt;br /&gt;
&lt;br /&gt;
One cardinal rule has been established through many years of parachute wind-tunnel testing: A modification that changes the performance of a model parachute in wind-tunnel testing produces the same type and percentage of performance change in a large parachute. This rule is true for drag. stability, and opening-force characteristics.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
=== 4.6.1 Blowers ===&lt;br /&gt;
The simple air blower (Figure 4-14) is a proven tool for preliminary parachute testing of a chiefly qualitative nature. Unless special test conditions prevail, parachutes tested should be a minimum of 1.5 to 2 feet in diameter to obtain meaningful results.&lt;br /&gt;
&lt;br /&gt;
                                                                    &lt;br /&gt;
&lt;br /&gt;
 FIGURE 4-14. Typical Air Blower.&lt;br /&gt;
&lt;br /&gt;
An air blower is a preliminary test too! because it permits quick parachute• configuration changes and excellent visual observation.&lt;br /&gt;
&lt;br /&gt;
=== 4.6.2 Open-Throat, No-Return Wind Tunnels ===&lt;br /&gt;
The open-throat, no-return wind tunnel shown in Figure 4-15 permits exact measurements if parachutes of sufficient size are used. Parachutes 3 feet or more in diameter are well suited for obtaining good, quantitative test results.&lt;br /&gt;
&lt;br /&gt;
              FIGURE 4-15. Open-Throat, No-Return Wind Tunnel&lt;br /&gt;
&lt;br /&gt;
In air blowers and open-throat wind tunnels, the velocity at the skirt of the parachute (Section a-a of Figures 4-14 and 4-15) is lower than the velocity at the nozzle exit of the wind tunnel (Section b&amp;lt;sup&amp;gt;-&amp;lt;/sup&amp;gt;b of Figures 4-14 and 4-15), Care must be taken to measure the parachute test&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
velocity at Section a-a and not at Section b-b, the customary attachment point for airfoils and models.&lt;br /&gt;
&lt;br /&gt;
Wind tunnels frequently cannot test at the descent velocity of most main parachutes of 20 to 30 feet per second. Obtaining proper test results at this low is hampered by a poor velocity distribution in the wind-tunnel-test section, and by the weight of the test parachute. The latter has a tendency to pull the parachute downward, thereby providing a negative angle of attack, lusting unstable parachutes at higher presents the problem that the drag coefficient C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, of unstable parachutes is sensitive. The drag coefficient of unstable parachutes is described in section 5.2.&lt;br /&gt;
&lt;br /&gt;
An open-throat wind tunnel permits quick changes in parachute configuration, such as changing the suspension and reefing line lengths. Large open-throat wind tunnels that are not sealed against outside elements suffer atmospheric problems such as fog formation in the test section.&lt;br /&gt;
&lt;br /&gt;
=== 4.6.3 Closed-Throat, Full-Return Wind Tunnel ===&lt;br /&gt;
Figure 4-16 is a drawing of a full-return, closed-throat wind tunnel. fic full-return, closed-throat wind tunnel is generally considered best suited for obtaining good. qualitative, aerodynamic data, since it has a uniform distribution in the test section. A disadvantage is the difficulty in gaining access to the test section for changing the parachute configuration.&lt;br /&gt;
&lt;br /&gt;
FIGURE 4-16. Closed-Throat, Full-Reuurn Wind Tunnel.&lt;br /&gt;
&lt;br /&gt;
=== 4.6.4 General Comments for Wind-Tunnel Testing of Parachutes ===&lt;br /&gt;
1. Parachute models for wind-tunnel testing should be as large and as similar as possible in geometry and flexibility to full-scale parachutes. Parachutes of less than 1.5 feet in diameter usually lack geometric similarity and material flexibility, which results in inflation characteristics and dissimilar inflated shapes.&lt;br /&gt;
&lt;br /&gt;
2.  The finished dimensions of model parachutes must be measured as accurately as possible to determine the nominal diameter, Do, and the surface area, So. Model parachutes will shrink from 5 to 10% during manufacture because of sewing take-up, which results in a notable difference in the dimensions between the drawing and the completed parachute.&lt;br /&gt;
&lt;br /&gt;
3.  Wind&amp;lt;sup&amp;gt;-&amp;lt;/sup&amp;gt;tunnel tests of parachutes are excellent for comparing different models and modifications: also, they are the most effective means for measuring coefficients of lift, drag. and normal and tangential forces, as well as for determining the load coefficient, for infinite load.&lt;br /&gt;
&lt;br /&gt;
4.  In wind-tunnel tests, velocity decay does not occur during parachute inflation and operation; this is defined as testing under &amp;quot;infinite mass condition. &amp;quot; First-stage drogue chutes and parachutes with a canopy loading, W/C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;S. in excess of 100 lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; approach this condition. Low-canopy-loading main parachutes with rates of descent of 20 to 30 ft/s have a large velocity decay during opening, which requires careful interpretation of the opening-force data obtained in wind-tunnel tests.&lt;br /&gt;
&lt;br /&gt;
5.  In the past, to avoid wind-tunnel blockage and questionable test data. the diameter of a test parachute could not exceed about 5 to 6% of the wind-tunnel test section area. Recent Sandia investigations of single and clustered ribbon parachutes with wind-tunnel blockage ratios of up to 30% have resulted in correction methods that make it possible to test much larger parachutes (Reference 4.2).&lt;br /&gt;
&lt;br /&gt;
== 4.7 REFERENCE MATERIAL ==&lt;br /&gt;
&lt;br /&gt;
4.1 H. H. Hurt. Aerodynamics for Naval Aviators Navy Manual NAVWEPS 00 80T 80. Chief of Naval Operations, Aviation Training Division.&lt;br /&gt;
&lt;br /&gt;
4.2 J, M. Macha and R J. Buffington. &amp;quot;Wall-Interference Corrections for Parachutes in a Closed Wind Tunnel.&amp;quot; AIM Paper, April 1989. (AIM 89-0900-cp.)&lt;br /&gt;
&lt;br /&gt;
For readers interested in a more detailed study of aerodynamics, the following books are recommended.&lt;br /&gt;
&lt;br /&gt;
4.3 J, H, Dwinnel, Principle of Aerodynamics. McGraw-Hill     	Co., New York, 1949.&lt;br /&gt;
&lt;br /&gt;
4.4 J. Morane. Introduction to Theoretical and Computational Aerodynamics. John Wiley &amp;amp; Sons.&lt;br /&gt;
&lt;br /&gt;
4.5 R.S. Shevell. Fundamentals of Flight. Prentice-Hall. 1983.&lt;br /&gt;
&lt;br /&gt;
4.6 J. D. Anderson, Jr. Introduction to Flights, ILS Engineering and History. McGraw-Hill Book co., New York 1978.&lt;br /&gt;
&lt;br /&gt;
4.7 D. J. Cockrell. The Aerodynamics of Parachutes.&amp;quot; AGARDograph No. 6295, available from NASA Langley Research Center, M/S 1M), Hampton, Va., 236.&lt;/div&gt;</summary>
		<author><name>TuanHTruong</name></author>
	</entry>
	<entry>
		<id>https://mediawiki.aerodecelerator.org/index.php?title=Parachute_Aerodynamics&amp;diff=37</id>
		<title>Parachute Aerodynamics</title>
		<link rel="alternate" type="text/html" href="https://mediawiki.aerodecelerator.org/index.php?title=Parachute_Aerodynamics&amp;diff=37"/>
		<updated>2024-05-07T18:29:17Z</updated>

		<summary type="html">&lt;p&gt;TuanHTruong: /* 4.7 REFERENCE MATERIAL */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&lt;br /&gt;
= CHAPTER 4: AERODYNAMICS AS RELATED TO PARACHUTES =&lt;br /&gt;
== 4.1 PROPERTIES OF THE ATMOSPHERE ==&lt;br /&gt;
All forces acting on parachutes and all movements of parachutes are affected by the atmosphere, or air, surrounding the Earth. The air at the Earth's surface is approximately 78% nitrogen; 21% oxygen; and 1% a mixture of gases such as argon, neon, helium, water vapor, and carbon dioxide. This chemical composition remains relatively constant to an altitude of about 160,000 feet (50 kilometers). The following air qualities are of major significance in the dynamics of bodies moving in the atmosphere:&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
!Air quality&lt;br /&gt;
!Symbol&lt;br /&gt;
!Dimension&lt;br /&gt;
|-&lt;br /&gt;
|Specific weight of air&lt;br /&gt;
|w&lt;br /&gt;
|lb/ft&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;, kg/m&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;&lt;br /&gt;
|-&lt;br /&gt;
|Static pressure&lt;br /&gt;
|p&lt;br /&gt;
|atm, lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;, Pa, bar, torr&lt;br /&gt;
|-&lt;br /&gt;
|Temperature&lt;br /&gt;
|T&lt;br /&gt;
|&amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F, &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;C&lt;br /&gt;
|-&lt;br /&gt;
|Mass density&lt;br /&gt;
|&amp;lt;math&amp;gt;\rho&amp;lt;/math&amp;gt;&lt;br /&gt;
|slugs/ft&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;, kg s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;/m&amp;lt;sup&amp;gt;4&amp;lt;/sup&amp;gt;&lt;br /&gt;
|-&lt;br /&gt;
|Gravity&lt;br /&gt;
|''g''&lt;br /&gt;
|ft/s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;, m/s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
|-&lt;br /&gt;
|Speed of sound&lt;br /&gt;
|C&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt;&lt;br /&gt;
|ft/s, m/s&lt;br /&gt;
|}&lt;br /&gt;
All of these qualities are altitude-dependent and may vary slightly on the Earth's surface with geographic latitude because of variations of the Earth's radius caused by the centrifugal forces of the rotation of the Earth. All standard data used herein refer to a latitude of 45 degrees. Sea level is defined as mean sea level (MSL). To compare performance data on an equal basis, the United States Bureau of Standards has defined standard day conditions as follows:&lt;br /&gt;
&lt;br /&gt;
* Temperature = 15 degrees Celsius (&amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;C) or 59 degrees Fahrenheit (&amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F)&lt;br /&gt;
* Pressure = 760 millimeters (mm) of mercury (Hg) or 29.9213 inches (in.) Hg&lt;br /&gt;
&lt;br /&gt;
=== 4.1.1 Specific Weight of Air ===&lt;br /&gt;
For standard day conditions of 59 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F temperature and a pressure of 29.9213 in. Hg, the specific weight of air, w, is 0.07648 lb/ft&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt; or 1.2250 kg/m&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;. The specific weight of air changes with pressure, temperature, and humidity. Further data can be found in References 3.4 and 4.1, and in technical handbooks.&lt;br /&gt;
&lt;br /&gt;
=== 4.1.2 Static Pressure ===&lt;br /&gt;
Static pressure depends on geographic latitude, weather conditions, and altitude. The static pressure at any altitude results from the weight of the air above that altitude. For MSL and standard day conditions, the pressure, p&amp;lt;sub&amp;gt;o&amp;lt;/sub&amp;gt;, is 29.9213 in. Hg = 760 mm Hg = 1.0 atmosphere (atm). For conversion to Pascal, torr, or bar, see the conversion tables in section 3.2.&lt;br /&gt;
&lt;br /&gt;
=== 4.1.3 Temperature ===&lt;br /&gt;
Temperatures are defined in the English and metric systems in the so-called absolute and engineering scales. The absolute temperature minimum at 0 degrees, pressure is 0 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;K = -273.16 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;C, and 0 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;R = -459.69 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F. This is also written&lt;br /&gt;
&lt;br /&gt;
* Degrees Kelvin = degrees Celsius + 273.16&lt;br /&gt;
* Degrees Rankine = degrees Fahrenheit + 459.69&lt;br /&gt;
&lt;br /&gt;
The freezing point of water is 32 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F or 0 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;C. The boiling point of water is 212 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F or 100 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;C.&lt;br /&gt;
&lt;br /&gt;
=== 4.1.4 Mass Density of Air ===&lt;br /&gt;
Mass density defines the amount of mass contained in a unit volume of air. The mass density, &amp;lt;math&amp;gt;\rho&amp;lt;/math&amp;gt;, of air is of special importance in aerodynamic calculations.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\rho = \frac{specific\ weight\ of\ air,\ w}{acceleration\ of\ gravity,\ g} = \frac{lb/ft^3}{ft/s^2} = \frac{kg\ s^2}{m^4}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;slug = \frac{weight}{acceleration\ of\ gravity} = \frac{lb}{ft/s^2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Frequently the density ratio, &amp;lt;math&amp;gt;\sigma&amp;lt;/math&amp;gt;, is used&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\sigma = \frac{ambient\ air\ density,\ \rho}{standard\ sea-level\ density, \rho_o}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The factor, &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;1/\sqrt{\rho/\rho_o}&amp;lt;/math&amp;gt;, determines the increase in parachute rate of descent with altitude. The density at 40,000 feet is ¼ of the MSL density, and the density at 100,000 feet is 1/75 of the MSL density. Therefore, the parachute rate of descent is about twice as high at 40,000 feet and about nine times as high at 100,000 feet. MSL density is 0.00237689 slugs/ft&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;, or 0.1249 kg s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;/m&amp;lt;sup&amp;gt;4&amp;lt;/sup&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
=== 4.1.5 Gravity ===&lt;br /&gt;
Any mass attracts another mass with a force called gravity. If the Earth were surrounded by a vacuum, a body suspended above the Earth and released would fall toward the center of the Earth with increasing velocity caused by the acceleration of gravity, ''g''. In reality, the falling body is decelerated by its air drag until the air drag, D, equals the weight of the body, W, and an equilibrium velocity is reached; for parachutes, this is called the steady-state rate of descent.&lt;br /&gt;
&lt;br /&gt;
The acceleration of gravity, ''g'', at sea lavel is&lt;br /&gt;
&lt;br /&gt;
* ''g'' = 32.174 ft/s2 or 9.80665 m/s2.&lt;br /&gt;
&lt;br /&gt;
The value g = 9.08665 m/s is standardized internationally but is accurate only for a latitude of 45 degrees.&lt;br /&gt;
&lt;br /&gt;
With increasing altitude above the Earth's surface, the acceleration of gravity decreases in accordance with the equation&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;g = g_o(\frac{r}{r+h})^2&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
* ''g'' = acceleration of gravity at any altitude, ft/s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
* g&amp;lt;sub&amp;gt;o&amp;lt;/sub&amp;gt; = acceleration of gravity at sea level, ft/s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
* r = average Earth radius = 2.08556 x 10&amp;lt;sup&amp;gt;7&amp;lt;/sup&amp;gt; ft&lt;br /&gt;
* h = altitude above sea level, ft&lt;br /&gt;
&lt;br /&gt;
For other planets and heavenly bodies, the acceleration of gravity varies with the mass of the body. For example, the acceleration of gravity on Mars is about 1/3 of the acceleration of gravity on Earth. For more details on planets and heavenly bodies, see page XII of Reference 2.1.&lt;br /&gt;
&lt;br /&gt;
=== 4.1.6 Kinematic Viscosity ===&lt;br /&gt;
The coefficient of viscosity, &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt;, defines the shearing stresses in a gas or liquid and is sometimes called the resistance to continuous deformation. In aerodynamics, the coefficient of viscosity is combined with the mass density to form the kinematic viscosity, &amp;lt;math&amp;gt;\nu&amp;lt;/math&amp;gt;, where&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\nu = \frac{coefficient\ of\ viscosity,\ \mu}{mass\ density,\ \rho} = 0.0001576\ ft^2/s\ at\ sea\ level&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The kinematic viscosity, &amp;lt;math&amp;gt;\nu&amp;lt;/math&amp;gt;, is altitude dependent and is used to calculate the Reynolds number, Re.&lt;br /&gt;
&lt;br /&gt;
=== 4.1.7 Reynolds Number ===&lt;br /&gt;
The Reynolds number, Re, defines the relationship of mass forces to viscous friction forces in liquids and gases. It is calculated as&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Re = \frac{v\cdot l}{\nu} = \frac{velocity\ (ft/s)\cdot characteristic\ length\ (ft)}{kinematic\ viscosity\ (ft^2/s)}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Reynolds number is an important criterion in subsonic, noncompressible flow, and allows comparison of model tests with full-scale flight tests. A Reynolds number effect on parachutes working in separated, turbulent flow has not yet been established, as shown in section 5.2. The following chart shows the Reynolds numbers for various air vehicles.&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
!Subject&lt;br /&gt;
!Insect&lt;br /&gt;
!Glider&lt;br /&gt;
!DC-3&lt;br /&gt;
!B-747&lt;br /&gt;
!Drogue&lt;br /&gt;
Chute&lt;br /&gt;
!Main &lt;br /&gt;
Parachute&lt;br /&gt;
!WTT&lt;br /&gt;
Model&lt;br /&gt;
|-&lt;br /&gt;
|Re&lt;br /&gt;
|6 • 10&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;&lt;br /&gt;
|2.5 • 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&lt;br /&gt;
|24 • 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&lt;br /&gt;
|100 • 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&lt;br /&gt;
|50 • 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&lt;br /&gt;
|20 • 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&lt;br /&gt;
|2 • 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
=== 4.1.8 Mach Number ===&lt;br /&gt;
Mach number is an important parameter of supersonic flight; it states how much faster than the speed of sound the air vehicle travels.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Mach\ number,\ M = \frac{flight\ velocity,\ v}{speed\ of\ sound, c_s}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The speed of sound is the velocity at which a pressure disturbance, such as the sound of the human voice, travels in any medium. The speed of sound varies considerably in different gases, liquids, and metals.&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|Speed of sound in air in MSL&lt;br /&gt;
|C&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt; = 1116.46 ft/s = 340.38 m/s&lt;br /&gt;
|-&lt;br /&gt;
|Speed of sound in water&lt;br /&gt;
|C&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt; = 4749 ft/s = 1461.21 m/s&lt;br /&gt;
|-&lt;br /&gt;
|Speed of sound in iron&lt;br /&gt;
|C&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt; = 16,410 ft/s = 5710.7 m/s&lt;br /&gt;
|}&lt;br /&gt;
The speed of sound depends on temperature and the chemical composition of the medium, A widely used equation for speed of sound in air is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;C_s = 41.4\sqrt{\gamma\cdot T}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
* &amp;lt;math&amp;gt;C_s&amp;lt;/math&amp;gt; = speed of sound in dry air, ft/s&lt;br /&gt;
* &amp;lt;math&amp;gt;\gamma&amp;lt;/math&amp;gt; = ratio of specific heat, equal to 1.4 for dry air, dimensionless&lt;br /&gt;
* &amp;lt;math&amp;gt;T&amp;lt;/math&amp;gt; = temperature in Fahrenheit absolute, equal to 459.67 + &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F&lt;br /&gt;
&lt;br /&gt;
The speed of sound changes with altitude, as temperature (see Figure 3-1). The drag of streamlined bodies such as missiles, airfoils, and airplanes increases considerably as their velocities approach Mach 1. Depending on the configuration of the body, supersonic compressibility effects may occur in the 0.75 to 0.85 Mach range, causing local supersonic flow, shock waves, flow separation, and concomitant increases in drag and changes in stability.&lt;br /&gt;
&lt;br /&gt;
Parachutes that operate in separated flow over the entire velocity range do not show the typical drag increase when operating close to or beyond Mach 1. Supersonic parachute behavior is discussed in detail in section 5.8.&lt;br /&gt;
&lt;br /&gt;
== 4.2 CONTINUITY LAW AND BERNOULLI EQUATION ==&lt;br /&gt;
&lt;br /&gt;
=== 4.2.1 Continuity L.aw ===&lt;br /&gt;
Air is thought to flow in layers called streamlines. Figure 4-1 shows streamlines as layers of air without air transfer between individual layers. ne air is shown as being incompressible, a valid assumption for subsonic flow.&lt;br /&gt;
&lt;br /&gt;
[Insert Figure 4-1] 	&lt;br /&gt;
&lt;br /&gt;
If exchange of air does not occur across the streamline boundaries, the amount of air entering the streamline at point 1 must also exit at point 2, as shown in Figure 4-1. Because the cross section at point 2 is smaller than the cross section at point 1, the air must exit at a higher velocity. The following equation defines this condition:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;v_1\cdot S_1\cdot \rho_1 = v_2\cdot S_2\cdot \rho_2&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S&amp;lt;/math&amp;gt; = cross section of the streamline&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;v&amp;lt;/math&amp;gt; = velocity in the streamline&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\rho&amp;lt;/math&amp;gt; = density of the air flowing in the streamline&lt;br /&gt;
&lt;br /&gt;
This equation, which governs the flow in and around a body in gases and liquids, is important in aerodynamics and is called the Continuity Law. For incompressible subsonic flow, it can be simplified to &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;v_1\cdot S_1 = v_2\cdot S_2&amp;lt;/math&amp;gt; &lt;br /&gt;
&lt;br /&gt;
Whenever the cross section narrows, the velocity increases; when the cross section widens, the velocity decreases.&lt;br /&gt;
&lt;br /&gt;
=== 4.2.2 Bernoulli Equation ===&lt;br /&gt;
Figure 4-2 illustrates a streamline with the cross section, S, the velocity, v, and the pressure, p. If the air is incompressible, the downstream is v + Av. and the pressure is p + AP. If the air is inviscid, the inertia forces caused by the acceleration of air from v to v + Av must be balanced by differential pressure forces.&lt;br /&gt;
&lt;br /&gt;
[Insert Figure 4-2]FIGURE 4-2 Pressure and Velocity Distribution in a Streamline Element. 	&lt;br /&gt;
&lt;br /&gt;
The following equation can be written&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;p\cdot S-(p+\Delta p)S = m\cdot \frac{dv}{dt}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Simplified, the above equation yields&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;dp = - \rho vdv&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
and&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;p = - \frac{1}{2}\rho v^2 + C&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The above equation allows the following consideration: If p is pressure, then &amp;lt;math&amp;gt;1/2\ \rho v^2&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;C&amp;lt;/math&amp;gt; must also be pressure. The equation &amp;lt;math&amp;gt;1/2\ \rho v^2&amp;lt;/math&amp;gt; includes a velocity and is referred to as the dynamic pressure, or sometimes as velocity or impact pressure.&lt;br /&gt;
&lt;br /&gt;
Pressure, &amp;lt;math&amp;gt;p&amp;lt;/math&amp;gt;, is defined as static pressure; &amp;lt;math&amp;gt;1/2\ \rho v^2&amp;lt;/math&amp;gt; as dynamic pressure; and the sum of both, &amp;lt;math&amp;gt;C&amp;lt;/math&amp;gt;, as the total pressure or&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;p+\frac{1}{2} \rho v^2 = H&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
and&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;p_1 + \frac{1}{2} \rho {v_1}^2 = p_2 + \frac{1}{2} \rho {v_2}^2&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;H&amp;lt;/math&amp;gt; is the total pressure of the system, lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Dynamic pressure, &amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt;, is a frequently used quantity in aerodynamics:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;q = \frac{1}{2} \rho v^2&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
* &amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt; = dynamic pressure, lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
* &amp;lt;math&amp;gt;\rho&amp;lt;/math&amp;gt; =  air density, slugs/ft&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;&lt;br /&gt;
* &amp;lt;math&amp;gt;v&amp;lt;/math&amp;gt; =  velocity at a point of undisturbed flow, ft/s&lt;br /&gt;
&lt;br /&gt;
The following formulas are used for calculating the sea-level dynamic pressure if the velocity is given in ft/s, knots, mph, or km/h, respectively:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;q=\frac{v^2}{841.4}(ft/s), q=\frac{v^2}{295}(knots), q=\frac{v^2}{391.2}(mph), q=\frac{v^2}{1013.1}(km/h)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
                                              &lt;br /&gt;
&lt;br /&gt;
== 4.3 NEWTON'S THREE OF MOTION ==&lt;br /&gt;
Engineering mechanics are governed by the following three laws of Isaac Newton:&lt;br /&gt;
&lt;br /&gt;
1.  A body remains at rest or in an unaccelerated state of motion unless acted upon.&lt;br /&gt;
&lt;br /&gt;
2.  A force acting upon a body will produce an acceleration in the direction of the force.&lt;br /&gt;
&lt;br /&gt;
3.  An action in one direction will produce an equal reaction in the opposite direction.&lt;br /&gt;
&lt;br /&gt;
The first law is self-explanatory. The second law may be expressed by the equation&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;F=m\cdot a&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;F&amp;lt;/math&amp;gt; = force in pounds acting on the mass, lb&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;m&amp;lt;/math&amp;gt; = mass of body that the force is acting upon, slugs&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; = acceleration in ft/s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; resulting from the force, F&lt;br /&gt;
&lt;br /&gt;
The mass, m, of a body is obtained by&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;m=\frac{W}{g}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;W&amp;lt;/math&amp;gt; = weight of the body, lb&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;g&amp;lt;/math&amp;gt; = acceleration of gravity, ft/s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The mass, therefore, has the dimension of&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;m = \frac{W}{g}=\frac{lb}{ft/s^2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
This unit of mass is the slug.&lt;br /&gt;
&lt;br /&gt;
The equation of Newton's second law can now be written&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;F=\frac{W}{g}\cdot a,\ or\ F=W\frac{a}{g}&amp;lt;/math&amp;gt; 	&lt;br /&gt;
&lt;br /&gt;
The factor a/g is frequently called the load factor, G, and tells how much larger a force is than a force equivalent to the weight of the body. It is customary in parachute work to state that the maximum parachute force allowed is G • W or (a/g) • W. It is appropriate to write&lt;br /&gt;
&lt;br /&gt;
Maximum allowable parachute force, &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;F=W\frac{a}{g},\ or\ W\cdot G&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Figure 4-3 illustrates Newton's third law, explaining the principle of the rocket that can produce thrust in a perfect vacuum.&lt;br /&gt;
&lt;br /&gt;
A mass, m, ejected from a rocket at the velocity, v, per unit time, t, will produce a force, F, which in turn will create a reaction force, R, of equal magnitude but acting in the opposite direction.&lt;br /&gt;
&lt;br /&gt;
== 4.4 FORCES ACTING ON A BODY MOVING THROUGH AIR ==&lt;br /&gt;
&lt;br /&gt;
=== 4.4.1 Symmetrical Body ===&lt;br /&gt;
A body moving through air experiences forces caused by air pressure acting on the body. The same forces if the body moves through air, such as a descending parachute, or if the body is fixed and the air moves against the body, such as a parachute or an airfoil in a wind tunnel (Figure 44).&lt;br /&gt;
&lt;br /&gt;
         	 &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
A stable parachute in a wind tunnel experiences only the force called &amp;quot;drag&amp;quot; in the direction of the airflow. drag force, D, is calculated to&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;D=q\cdot S\cdot C_D&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;D&amp;lt;/math&amp;gt; = drag, lb&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt; = dynamic pressure, lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S&amp;lt;/math&amp;gt; = total surface area of the parachute canopy, ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;C_D&amp;lt;/math&amp;gt; = coefficient of drag,  dimensionless&lt;br /&gt;
&lt;br /&gt;
The dynamic pressure, q, can be calculated from section 4.2.2. The surface area of the canopy, S, is selected as a reference area. The drag coefficient, C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, is a form factor that indicates the drag characteristic of a specific shape. Most aerodynamic bodies are designed for low drag or a low drag coefficient. Parachutes, generally, are designed for high drag; therefore, a high drag coefficient is desirable. this difference in drag is demonstrated by the two bodies shown in Figure 4-5.&lt;br /&gt;
&lt;br /&gt;
            	&lt;br /&gt;
&lt;br /&gt;
Both bodies have the same cross section perpendicular to the airflow. The cylindrical. streamlined body has a smooth airflow over its total body length, resulting in a drag coefficient. C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, of 0.05 to 0.1, depending on slenderness ratio, surface roughness, and shape. The drag coefficient of all streamlined bodies is much affected by Reynolds number and Mach number. The open hemisphere, which is similar to a parachute canopy, has a drag coefficient, C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, of 1.3 to 1.4 for the same body cross section. The difference in drag is explained by the smooth airflow around the streamlined body and a separated, turbulent flow around the open hemisphere. The drag of bodies with separated flow, like parachute canopies, is little affected by Reynolds number.&lt;br /&gt;
&lt;br /&gt;
=== 4.4.2 Airflow Around an Asymmetrical Body (Airfoil) ===&lt;br /&gt;
Figure 4-6 shows an airfoil fixed at an angle of attack, a. against the airflow in a wind tunnel. This airfoil creates a drag force, D, in the direction of the flow; a lift force L perpendicular to the direction of the flow; and a moment, M. around the attachment point of the airfoil. fie sign convention of moments and forces shown are positive. Lift and drag can be combined for the resultant force, R.&lt;br /&gt;
&lt;br /&gt;
FIGURE. 4-6, Wind-Tunnel Forces Acting on an Airfoil.&lt;br /&gt;
&lt;br /&gt;
The lift, L is calculated&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;L = q\cdot S\cdot C_L&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; = measured lift, lb&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt; = dynamic pressure, lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S&amp;lt;/math&amp;gt; = reference area, ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;C_L&amp;lt;/math&amp;gt; = lift coefficient, dimensionless&lt;br /&gt;
&lt;br /&gt;
The moment is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;M=q\cdot S\cdot c_m\cdot c&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Where&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;M&amp;lt;/math&amp;gt; = measured lift, lb&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt; = dynamic pressure, lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S&amp;lt;/math&amp;gt; = reference area, ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;c_m&amp;lt;/math&amp;gt; = moment coefficient, dimensionless&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;c&amp;lt;/math&amp;gt; = average chord width of the wing, ft&lt;br /&gt;
&lt;br /&gt;
The reference area, S, is defined by agreement. For streamlined bodies, the maximum body cross section is used. Airfoils use the planform of the wing, and parachutes use the canopy surface area. The selection of the wing planform and the parachute surface area as references was made for practical reasons. The wing planform for a specific wing is fixed, whereas the cross section of the wing in the direction of the flow changes with the angle of attack. Similarly, the surface area of the parachute canopy is fixed; however, the frontal projected area of the inflated parachute canopy changes with airspeed, porosity, line length, and type of parachute.&lt;br /&gt;
&lt;br /&gt;
Forces and moments acting on an airfoil or a parachute canopy may be presented in several ways. The two most frequently used methods, as shown in Figure 4-7, are with forces oriented to the axis of flight and with forces oriented to the axis of the airfoil.&lt;br /&gt;
&lt;br /&gt;
The tangential force, and the normal force, N, are calculated&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;T = C_T\cdot S\cdot q&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
and 	&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;N = C_N\cdot S\cdot q&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
C&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; = tangential force coefficient, dimensionless&lt;br /&gt;
&lt;br /&gt;
C&amp;lt;sub&amp;gt;N&amp;lt;/sub&amp;gt; = normal force coefficient, dimensionless&lt;br /&gt;
&lt;br /&gt;
The resultant force, R, and the moment, M, in both presentations have the same direction and the same magnitude. The airflow fixed system is preferred for aerodynamic performance calculations, and the airfoil fixed system for wing stress calculations. me aerodynamic coefficients C&amp;lt;sub&amp;gt;L&amp;lt;/sub&amp;gt;, C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, C&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, C&amp;lt;sub&amp;gt;N&amp;lt;/sub&amp;gt;, and C&amp;lt;sub&amp;gt;m&amp;lt;/sub&amp;gt; can easily be determined in wind•tunnel measurements.&lt;br /&gt;
&lt;br /&gt;
Figure 4-8 shows the relationship of both force systems on a parachute. By definition, a negative moment is stabilizing, as illustrated in Figure 4-8. It is interesting to note that in Europe the stabilizing moment is defined as positive. Wind-tunnel installations frequently measure normal and tangential force instead of lift and drag. If α, T, and N are known, the drag D, can be calculated&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;D=T\cdot cos(\alpha)+N\cdot sin(\alpha)&amp;lt;/math&amp;gt;For a parachute with an angle of attack, &amp;lt;math&amp;gt;\alpha&amp;lt;/math&amp;gt;, equal to zero, the drag force and the tangential force are synonymous.&lt;br /&gt;
&lt;br /&gt;
Figure 4-9 shows the coefficients C&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, and C&amp;lt;sub&amp;gt;m&amp;lt;/sub&amp;gt; versus angle of attack for stable and unstable parachutes.&lt;br /&gt;
&lt;br /&gt;
The coefficient presentation shows two interesting facts. The slope of the moment coefficient curve, dC&amp;lt;sub&amp;gt;m&amp;lt;/sub&amp;gt;/dα, for the unstable parachute is positive between -25 degrees and + 25 degrees; this is, by definition, destabilizing. This parachute will oscillate approximately ± 25&lt;br /&gt;
&lt;br /&gt;
FIGURE 4-9. Coefficients C&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, and C&amp;lt;sub&amp;gt;M&amp;lt;/sub&amp;gt; Versus Angle of Attack, α, for a Stable and Unstable Parachute.&lt;br /&gt;
&lt;br /&gt;
degrees. The slope of the moment, dC&amp;lt;sub&amp;gt;m&amp;lt;/sub&amp;gt;/dα, for the stable parachute is negative over the total angle of attack; this is, by definition, stabilizing. The steeper the negative dC&amp;lt;sub&amp;gt;m&amp;lt;/sub&amp;gt;/dα slope, the greater is the stabilizing tendency of the parachute, and the better is its damping capability against unstabilizing forces such as sudden gusts of wind.&lt;br /&gt;
&lt;br /&gt;
Figure 4-10, from Reference 4.1, demonstrates the effect of airflow around a cylinder and an airfoil. The circulation around a rotating cylinder creates lift caused by the increase in velocity on one side of the cylinder and a decrease on the opposite side. This is called the Magnus effect.&lt;br /&gt;
&lt;br /&gt;
== 4.5 EQUILIBRIUM OF FORCES IN STUDY DESCENT OR FLIGHT ==&lt;br /&gt;
&lt;br /&gt;
=== 4.5.1 Parachute in Steady Descent ===&lt;br /&gt;
A stable parachute in unaccelerated descent has an equilibrium between the total drag of the parachute and the load, Dr, and the weight of the load and the parachute assembly, WT (Figure 4-11). &lt;br /&gt;
&lt;br /&gt;
For steady descent&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
D&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; = total drag, 1b&lt;br /&gt;
&lt;br /&gt;
D&amp;lt;sub&amp;gt;P&amp;lt;/sub&amp;gt; = drag of parachute, 1b&lt;br /&gt;
&lt;br /&gt;
W&amp;lt;sub&amp;gt;C&amp;lt;/sub&amp;gt; = weight of load. 1b&lt;br /&gt;
&lt;br /&gt;
In most cases, the drag of the load can be neglected in relation to the large drag of the parachute, With drag, D — (C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;S)&amp;lt;sub&amp;gt;p&amp;lt;/sub&amp;gt; • p/2• v&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; and D&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; = W&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;. and solving for v, the important equation for rate of descent, v&amp;lt;sub&amp;gt;e&amp;lt;/sub&amp;gt;, is obtained,&lt;br /&gt;
&lt;br /&gt;
Rate of descent,&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
FIGURE 4-11. Forces Acting on a Parachute in Steady Descent.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
or in parachute terminology for rate of descent at sea level&lt;br /&gt;
&lt;br /&gt;
and rate of descent at any altitude&lt;br /&gt;
&lt;br /&gt;
For 1/, see column 4 in Table 3-3,&lt;br /&gt;
&lt;br /&gt;
In the equation for rate of descent. V&amp;lt;sub&amp;gt;e&amp;lt;/sub&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
W&amp;lt;sub&amp;gt;T =&amp;lt;/sub&amp;gt; weight of load and parachute assembly, 1b&lt;br /&gt;
&lt;br /&gt;
S&amp;lt;sub&amp;gt;o&amp;lt;/sub&amp;gt; = canopy surface area, ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
C&amp;lt;sub&amp;gt;Do&amp;lt;/sub&amp;gt; = parachute drag coefficient related to S&amp;lt;sub&amp;gt;o&amp;lt;/sub&amp;gt;&lt;br /&gt;
&lt;br /&gt;
p = air density at a specific altitude in slugs/ft&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;, as shown in Table 3-3&lt;br /&gt;
&lt;br /&gt;
During descent from altitude, the parachute system is constantly decelerated because of the increasing air density. This can be ignored for slowly descending main parachutes. However, for drogue chute systems that descend at 200 ft/s or faster, the constant deceleration may result in velocities 3 to 5% higher than the steady rate of descent.&lt;br /&gt;
&lt;br /&gt;
=== 4.5.2 Gliding Parachutes ===&lt;br /&gt;
Figure 4-12 shows the balance of forces on a gliding parachute. The total weight of the system, W&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; . must be balanced by the resultant force. R. However, a lifting force is required for glide. To satisfy the force balance&lt;br /&gt;
&lt;br /&gt;
R = C&amp;lt;sub&amp;gt;R&amp;lt;/sub&amp;gt; * S * p/2 * v&lt;br /&gt;
&lt;br /&gt;
Trajectory velocity, V&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, is calculated&lt;br /&gt;
&lt;br /&gt;
Horizontal velocity is calculated&lt;br /&gt;
&lt;br /&gt;
V&amp;lt;sub&amp;gt;H&amp;lt;/sub&amp;gt; = V&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; • cosø, and vertical velocity, v&amp;lt;sub&amp;gt;v&amp;lt;/sub&amp;gt; = V&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; • sinø&lt;br /&gt;
&lt;br /&gt;
The glide ratio is obtained from&lt;br /&gt;
&lt;br /&gt;
Analysis of Figure 4-12 indicates that the larger the ratio of lift to drag, the better the glide ratio, I./D A high resultant coefficient, C&amp;lt;sub&amp;gt;R&amp;lt;/sub&amp;gt;, results in a low glide or trajectory V&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, desirable for landing. A small C&amp;lt;sub&amp;gt;R&amp;lt;/sub&amp;gt; results in a high glide velocity, V&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, which is desirable for flying toward a target, compensating for head winds, or covering a distance quickly. Generally, gliding parachutes follow the same aerodynamic rules as low-aspect-ratio wings.&lt;br /&gt;
&lt;br /&gt;
           	   	&lt;br /&gt;
&lt;br /&gt;
FIGUR E 4-12, Forces Acting on a Gliding Parachute&lt;br /&gt;
&lt;br /&gt;
=== 4.5.3 Parasite Drag and Induced Drag ===&lt;br /&gt;
The drag acting on a lift-producing air vehicle, such as a gliding parachute or an aircraft, has two primary components: the parasite drag, D&amp;lt;sub&amp;gt;P&amp;lt;/sub&amp;gt; , and the induced drag. D&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Parasite drag is produced by the form drag from individual components such as the suspension lines, canopy, and the jumper of a gliding parachute, and the fuselage, tail sectiora, and control surfaces of an airplane. Large surfaces produce surface friction drag as part of the parasite drag.&lt;br /&gt;
&lt;br /&gt;
Induced drag is caused by the lifting action of the parachute canopy or the aircraft wing. Section 4.7 includes books with detailed discussions of induced drag.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Total drag, D&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, can be defined as&lt;br /&gt;
&lt;br /&gt;
or, in the coefficient form&lt;br /&gt;
&lt;br /&gt;
The parasite drag, D&amp;lt;sub&amp;gt;p&amp;lt;/sub&amp;gt;, and the coefficient, C&amp;lt;sub&amp;gt;DP&amp;lt;/sub&amp;gt;, can be determined in wind-tunnel tests or calculated as the sum of the individual component drags.&lt;br /&gt;
&lt;br /&gt;
The induced drag coefficient, C&amp;lt;sub&amp;gt;Di&amp;lt;/sub&amp;gt; , of a gliding parachute canopy or a wing profile can be calculated&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
C = coefficient of induced drag, dimensionless&lt;br /&gt;
&lt;br /&gt;
The expression b&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;/S is defined as the aspect ratio of a wing or parachute with the notation AR b&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;/S. Therefore&lt;br /&gt;
&lt;br /&gt;
The equation for induced drag indicates that increasing the aspect ratio, AR, reduces the induced drag coefficient,  , and therefore reduces the drag, D. ms, in turn, increases the glide ratio, L/D. Increasing the glide ratio by increasing the aspect ratio is optimized on high-performance sailplanes with aspect ratios higher than 20. Increasing the glide ratio of gliding parachutes by increasing the aspect ratio has limitations, which are discussed in section 5.9.&lt;br /&gt;
&lt;br /&gt;
=== 4.5.4 Aircraft in Horizontal Flight ===&lt;br /&gt;
Figure 4-13 shows forces and moments on an aircraft in steady, horizontal flight. In steady, horizontal flight, an equilibrium exists between all forces and moments acting on the aircraft. Lift on the wing and tail, L&amp;lt;sub&amp;gt;W&amp;lt;/sub&amp;gt; and L&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;. and the weight of the aircraft, W&amp;lt;sub&amp;gt;A&amp;lt;/sub&amp;gt;, balance in the vertical plane. Thrust, T and drag. D, balance each other in the horizontal plane, and the positive or negative moment, M, is balanced by the positive or negative lift of the tail multiplied by the moment arm, L&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
FIGURE 4-13. Forces and Moments Acting on an Aircraft in Steady night,&lt;br /&gt;
&lt;br /&gt;
Any imbalance in these forces results in descent or climb in the vertical plane or faster or slower speed in the horizontal plane. A change in the lift of the elevator initiates climb or descent. Thrust, T, is the prime contributor for climb or descent and faster or slower speed, However, a balance of forces must always be maintained for horizontal flight or steady rate oi climb or descent.&lt;br /&gt;
&lt;br /&gt;
== 4.6 WIND-TUNNEL TESTING OF PARACHUTES ==&lt;br /&gt;
Wind tunnels are an effective tool for testing air vehicles and air-vehicle components and have been used successfully for testing parachutes and parachute systems. Experience has shown that certain rules apply for the wind-tunnel testing of parachutes. Small parachutes manufactured from textiles cannot be made sufficiently similar to large parachutes in geometric design and flexibility, Lightweight material. required to obtain design similarity, is difficult to manufacture or is unobtainable.&lt;br /&gt;
&lt;br /&gt;
One cardinal rule has been established through many years of parachute wind-tunnel testing: A modification that changes the performance of a model parachute in wind-tunnel testing produces the same type and percentage of performance change in a large parachute. This rule is true for drag. stability, and opening-force characteristics.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
=== 4.6.1 Blowers ===&lt;br /&gt;
The simple air blower (Figure 4-14) is a proven tool for preliminary parachute testing of a chiefly qualitative nature. Unless special test conditions prevail, parachutes tested should be a minimum of 1.5 to 2 feet in diameter to obtain meaningful results.&lt;br /&gt;
&lt;br /&gt;
                                                                    &lt;br /&gt;
&lt;br /&gt;
 FIGURE 4-14. Typical Air Blower.&lt;br /&gt;
&lt;br /&gt;
An air blower is a preliminary test too! because it permits quick parachute• configuration changes and excellent visual observation.&lt;br /&gt;
&lt;br /&gt;
=== 4.6.2 Open-Throat, No-Return Wind Tunnels ===&lt;br /&gt;
The open-throat, no-return wind tunnel shown in Figure 4-15 permits exact measurements if parachutes of sufficient size are used. Parachutes 3 feet or more in diameter are well suited for obtaining good, quantitative test results.&lt;br /&gt;
&lt;br /&gt;
              FIGURE 4-15. Open-Throat, No-Return Wind Tunnel&lt;br /&gt;
&lt;br /&gt;
In air blowers and open-throat wind tunnels, the velocity at the skirt of the parachute (Section a-a of Figures 4-14 and 4-15) is lower than the velocity at the nozzle exit of the wind tunnel (Section b&amp;lt;sup&amp;gt;-&amp;lt;/sup&amp;gt;b of Figures 4-14 and 4-15), Care must be taken to measure the parachute test&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
velocity at Section a-a and not at Section b-b, the customary attachment point for airfoils and models.&lt;br /&gt;
&lt;br /&gt;
Wind tunnels frequently cannot test at the descent velocity of most main parachutes of 20 to 30 feet per second. Obtaining proper test results at this low is hampered by a poor velocity distribution in the wind-tunnel-test section, and by the weight of the test parachute. The latter has a tendency to pull the parachute downward, thereby providing a negative angle of attack, lusting unstable parachutes at higher presents the problem that the drag coefficient C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, of unstable parachutes is sensitive. The drag coefficient of unstable parachutes is described in section 5.2.&lt;br /&gt;
&lt;br /&gt;
An open-throat wind tunnel permits quick changes in parachute configuration, such as changing the suspension and reefing line lengths. Large open-throat wind tunnels that are not sealed against outside elements suffer atmospheric problems such as fog formation in the test section.&lt;br /&gt;
&lt;br /&gt;
=== 4.6.3 Closed-Throat, Full-Return Wind Tunnel ===&lt;br /&gt;
Figure 4-16 is a drawing of a full-return, closed-throat wind tunnel. fic full-return, closed-throat wind tunnel is generally considered best suited for obtaining good. qualitative, aerodynamic data, since it has a uniform distribution in the test section. A disadvantage is the difficulty in gaining access to the test section for changing the parachute configuration.&lt;br /&gt;
&lt;br /&gt;
FIGURE 4-16. Closed-Throat, Full-Reuurn Wind Tunnel.&lt;br /&gt;
&lt;br /&gt;
=== 4.6.4 General Comments for Wind-Tunnel Testing of Parachutes ===&lt;br /&gt;
1. Parachute models for wind-tunnel testing should be as large and as similar as possible in geometry and flexibility to full-scale parachutes. Parachutes of less than 1.5 feet in diameter usually lack geometric similarity and material flexibility, which results in inflation characteristics and dissimilar inflated shapes.&lt;br /&gt;
&lt;br /&gt;
2.  The finished dimensions of model parachutes must be measured as accurately as possible to determine the nominal diameter, Do, and the surface area, So. Model parachutes will shrink from 5 to 10% during manufacture because of sewing take-up, which results in a notable difference in the dimensions between the drawing and the completed parachute.&lt;br /&gt;
&lt;br /&gt;
3.  Wind&amp;lt;sup&amp;gt;-&amp;lt;/sup&amp;gt;tunnel tests of parachutes are excellent for comparing different models and modifications: also, they are the most effective means for measuring coefficients of lift, drag. and normal and tangential forces, as well as for determining the load coefficient, for infinite load.&lt;br /&gt;
&lt;br /&gt;
4.  In wind-tunnel tests, velocity decay does not occur during parachute inflation and operation; this is defined as testing under &amp;quot;infinite mass condition. &amp;quot; First-stage drogue chutes and parachutes with a canopy loading, W/C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;S. in excess of 100 lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; approach this condition. Low-canopy-loading main parachutes with rates of descent of 20 to 30 ft/s have a large velocity decay during opening, which requires careful interpretation of the opening-force data obtained in wind-tunnel tests.&lt;br /&gt;
&lt;br /&gt;
5.  In the past, to avoid wind-tunnel blockage and questionable test data. the diameter of a test parachute could not exceed about 5 to 6% of the wind-tunnel test section area. Recent Sandia investigations of single and clustered ribbon parachutes with wind-tunnel blockage ratios of up to 30% have resulted in correction methods that make it possible to test much larger parachutes (Reference 4.2).&lt;br /&gt;
&lt;br /&gt;
= 4.7 REFERENCE MATERIAL =&lt;br /&gt;
4.1 H. H. Hurt. Aerodynamics for Naval Aviators Navy Manual NAVWEPS 00 80T 80. Chief of Naval Operations, Aviation Training Division.&lt;br /&gt;
&lt;br /&gt;
4.2 J, M. Macha and R J. Buffington. &amp;quot;Wall-Interference Corrections for Parachutes in a Closed Wind Tunnel.&amp;quot; AIM Paper, April 1989. (AIM 89-0900-cp.)&lt;br /&gt;
&lt;br /&gt;
For readers interested in a more detailed study of aerodynamics, the following books are recommended.&lt;br /&gt;
&lt;br /&gt;
4.3 J, H, Dwinnel, Principle of Aerodynamics. McGraw-Hill     	Co., New York, 1949.&lt;br /&gt;
&lt;br /&gt;
4.4 J. Morane. Introduction to Theoretical and Computational Aerodynamics. John Wiley &amp;amp; Sons.&lt;br /&gt;
&lt;br /&gt;
4.5 R.S. Shevell. Fundamentals of Flight. Prentice-Hall. 1983.&lt;br /&gt;
&lt;br /&gt;
4.6 J. D. Anderson, Jr. Introduction to Flights, ILS Engineering and History. McGraw-Hill Book co., New York 1978.&lt;br /&gt;
&lt;br /&gt;
4.7 D. J. Cockrell. The Aerodynamics of Parachutes.&amp;quot; AGARDograph No. 6295, available from NASA Langley Research Center, M/S 1M), Hampton, Va., 236.&lt;/div&gt;</summary>
		<author><name>TuanHTruong</name></author>
	</entry>
	<entry>
		<id>https://mediawiki.aerodecelerator.org/index.php?title=Parachute_Aerodynamics&amp;diff=36</id>
		<title>Parachute Aerodynamics</title>
		<link rel="alternate" type="text/html" href="https://mediawiki.aerodecelerator.org/index.php?title=Parachute_Aerodynamics&amp;diff=36"/>
		<updated>2024-05-07T18:27:14Z</updated>

		<summary type="html">&lt;p&gt;TuanHTruong: /* 4.7 REFERENCE MATERIAL */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&lt;br /&gt;
= CHAPTER 4: AERODYNAMICS AS RELATED TO PARACHUTES =&lt;br /&gt;
== 4.1 PROPERTIES OF THE ATMOSPHERE ==&lt;br /&gt;
All forces acting on parachutes and all movements of parachutes are affected by the atmosphere, or air, surrounding the Earth. The air at the Earth's surface is approximately 78% nitrogen; 21% oxygen; and 1% a mixture of gases such as argon, neon, helium, water vapor, and carbon dioxide. This chemical composition remains relatively constant to an altitude of about 160,000 feet (50 kilometers). The following air qualities are of major significance in the dynamics of bodies moving in the atmosphere:&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
!Air quality&lt;br /&gt;
!Symbol&lt;br /&gt;
!Dimension&lt;br /&gt;
|-&lt;br /&gt;
|Specific weight of air&lt;br /&gt;
|w&lt;br /&gt;
|lb/ft&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;, kg/m&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;&lt;br /&gt;
|-&lt;br /&gt;
|Static pressure&lt;br /&gt;
|p&lt;br /&gt;
|atm, lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;, Pa, bar, torr&lt;br /&gt;
|-&lt;br /&gt;
|Temperature&lt;br /&gt;
|T&lt;br /&gt;
|&amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F, &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;C&lt;br /&gt;
|-&lt;br /&gt;
|Mass density&lt;br /&gt;
|&amp;lt;math&amp;gt;\rho&amp;lt;/math&amp;gt;&lt;br /&gt;
|slugs/ft&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;, kg s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;/m&amp;lt;sup&amp;gt;4&amp;lt;/sup&amp;gt;&lt;br /&gt;
|-&lt;br /&gt;
|Gravity&lt;br /&gt;
|''g''&lt;br /&gt;
|ft/s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;, m/s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
|-&lt;br /&gt;
|Speed of sound&lt;br /&gt;
|C&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt;&lt;br /&gt;
|ft/s, m/s&lt;br /&gt;
|}&lt;br /&gt;
All of these qualities are altitude-dependent and may vary slightly on the Earth's surface with geographic latitude because of variations of the Earth's radius caused by the centrifugal forces of the rotation of the Earth. All standard data used herein refer to a latitude of 45 degrees. Sea level is defined as mean sea level (MSL). To compare performance data on an equal basis, the United States Bureau of Standards has defined standard day conditions as follows:&lt;br /&gt;
&lt;br /&gt;
* Temperature = 15 degrees Celsius (&amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;C) or 59 degrees Fahrenheit (&amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F)&lt;br /&gt;
* Pressure = 760 millimeters (mm) of mercury (Hg) or 29.9213 inches (in.) Hg&lt;br /&gt;
&lt;br /&gt;
=== 4.1.1 Specific Weight of Air ===&lt;br /&gt;
For standard day conditions of 59 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F temperature and a pressure of 29.9213 in. Hg, the specific weight of air, w, is 0.07648 lb/ft&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt; or 1.2250 kg/m&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;. The specific weight of air changes with pressure, temperature, and humidity. Further data can be found in References 3.4 and 4.1, and in technical handbooks.&lt;br /&gt;
&lt;br /&gt;
=== 4.1.2 Static Pressure ===&lt;br /&gt;
Static pressure depends on geographic latitude, weather conditions, and altitude. The static pressure at any altitude results from the weight of the air above that altitude. For MSL and standard day conditions, the pressure, p&amp;lt;sub&amp;gt;o&amp;lt;/sub&amp;gt;, is 29.9213 in. Hg = 760 mm Hg = 1.0 atmosphere (atm). For conversion to Pascal, torr, or bar, see the conversion tables in section 3.2.&lt;br /&gt;
&lt;br /&gt;
=== 4.1.3 Temperature ===&lt;br /&gt;
Temperatures are defined in the English and metric systems in the so-called absolute and engineering scales. The absolute temperature minimum at 0 degrees, pressure is 0 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;K = -273.16 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;C, and 0 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;R = -459.69 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F. This is also written&lt;br /&gt;
&lt;br /&gt;
* Degrees Kelvin = degrees Celsius + 273.16&lt;br /&gt;
* Degrees Rankine = degrees Fahrenheit + 459.69&lt;br /&gt;
&lt;br /&gt;
The freezing point of water is 32 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F or 0 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;C. The boiling point of water is 212 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F or 100 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;C.&lt;br /&gt;
&lt;br /&gt;
=== 4.1.4 Mass Density of Air ===&lt;br /&gt;
Mass density defines the amount of mass contained in a unit volume of air. The mass density, &amp;lt;math&amp;gt;\rho&amp;lt;/math&amp;gt;, of air is of special importance in aerodynamic calculations.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\rho = \frac{specific\ weight\ of\ air,\ w}{acceleration\ of\ gravity,\ g} = \frac{lb/ft^3}{ft/s^2} = \frac{kg\ s^2}{m^4}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;slug = \frac{weight}{acceleration\ of\ gravity} = \frac{lb}{ft/s^2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Frequently the density ratio, &amp;lt;math&amp;gt;\sigma&amp;lt;/math&amp;gt;, is used&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\sigma = \frac{ambient\ air\ density,\ \rho}{standard\ sea-level\ density, \rho_o}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The factor, &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;1/\sqrt{\rho/\rho_o}&amp;lt;/math&amp;gt;, determines the increase in parachute rate of descent with altitude. The density at 40,000 feet is ¼ of the MSL density, and the density at 100,000 feet is 1/75 of the MSL density. Therefore, the parachute rate of descent is about twice as high at 40,000 feet and about nine times as high at 100,000 feet. MSL density is 0.00237689 slugs/ft&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;, or 0.1249 kg s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;/m&amp;lt;sup&amp;gt;4&amp;lt;/sup&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
=== 4.1.5 Gravity ===&lt;br /&gt;
Any mass attracts another mass with a force called gravity. If the Earth were surrounded by a vacuum, a body suspended above the Earth and released would fall toward the center of the Earth with increasing velocity caused by the acceleration of gravity, ''g''. In reality, the falling body is decelerated by its air drag until the air drag, D, equals the weight of the body, W, and an equilibrium velocity is reached; for parachutes, this is called the steady-state rate of descent.&lt;br /&gt;
&lt;br /&gt;
The acceleration of gravity, ''g'', at sea lavel is&lt;br /&gt;
&lt;br /&gt;
* ''g'' = 32.174 ft/s2 or 9.80665 m/s2.&lt;br /&gt;
&lt;br /&gt;
The value g = 9.08665 m/s is standardized internationally but is accurate only for a latitude of 45 degrees.&lt;br /&gt;
&lt;br /&gt;
With increasing altitude above the Earth's surface, the acceleration of gravity decreases in accordance with the equation&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;g = g_o(\frac{r}{r+h})^2&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
* ''g'' = acceleration of gravity at any altitude, ft/s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
* g&amp;lt;sub&amp;gt;o&amp;lt;/sub&amp;gt; = acceleration of gravity at sea level, ft/s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
* r = average Earth radius = 2.08556 x 10&amp;lt;sup&amp;gt;7&amp;lt;/sup&amp;gt; ft&lt;br /&gt;
* h = altitude above sea level, ft&lt;br /&gt;
&lt;br /&gt;
For other planets and heavenly bodies, the acceleration of gravity varies with the mass of the body. For example, the acceleration of gravity on Mars is about 1/3 of the acceleration of gravity on Earth. For more details on planets and heavenly bodies, see page XII of Reference 2.1.&lt;br /&gt;
&lt;br /&gt;
=== 4.1.6 Kinematic Viscosity ===&lt;br /&gt;
The coefficient of viscosity, &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt;, defines the shearing stresses in a gas or liquid and is sometimes called the resistance to continuous deformation. In aerodynamics, the coefficient of viscosity is combined with the mass density to form the kinematic viscosity, &amp;lt;math&amp;gt;\nu&amp;lt;/math&amp;gt;, where&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\nu = \frac{coefficient\ of\ viscosity,\ \mu}{mass\ density,\ \rho} = 0.0001576\ ft^2/s\ at\ sea\ level&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The kinematic viscosity, &amp;lt;math&amp;gt;\nu&amp;lt;/math&amp;gt;, is altitude dependent and is used to calculate the Reynolds number, Re.&lt;br /&gt;
&lt;br /&gt;
=== 4.1.7 Reynolds Number ===&lt;br /&gt;
The Reynolds number, Re, defines the relationship of mass forces to viscous friction forces in liquids and gases. It is calculated as&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Re = \frac{v\cdot l}{\nu} = \frac{velocity\ (ft/s)\cdot characteristic\ length\ (ft)}{kinematic\ viscosity\ (ft^2/s)}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Reynolds number is an important criterion in subsonic, noncompressible flow, and allows comparison of model tests with full-scale flight tests. A Reynolds number effect on parachutes working in separated, turbulent flow has not yet been established, as shown in section 5.2. The following chart shows the Reynolds numbers for various air vehicles.&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
!Subject&lt;br /&gt;
!Insect&lt;br /&gt;
!Glider&lt;br /&gt;
!DC-3&lt;br /&gt;
!B-747&lt;br /&gt;
!Drogue&lt;br /&gt;
Chute&lt;br /&gt;
!Main &lt;br /&gt;
Parachute&lt;br /&gt;
!WTT&lt;br /&gt;
Model&lt;br /&gt;
|-&lt;br /&gt;
|Re&lt;br /&gt;
|6 • 10&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;&lt;br /&gt;
|2.5 • 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&lt;br /&gt;
|24 • 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&lt;br /&gt;
|100 • 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&lt;br /&gt;
|50 • 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&lt;br /&gt;
|20 • 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&lt;br /&gt;
|2 • 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
=== 4.1.8 Mach Number ===&lt;br /&gt;
Mach number is an important parameter of supersonic flight; it states how much faster than the speed of sound the air vehicle travels.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Mach\ number,\ M = \frac{flight\ velocity,\ v}{speed\ of\ sound, c_s}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The speed of sound is the velocity at which a pressure disturbance, such as the sound of the human voice, travels in any medium. The speed of sound varies considerably in different gases, liquids, and metals.&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|Speed of sound in air in MSL&lt;br /&gt;
|C&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt; = 1116.46 ft/s = 340.38 m/s&lt;br /&gt;
|-&lt;br /&gt;
|Speed of sound in water&lt;br /&gt;
|C&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt; = 4749 ft/s = 1461.21 m/s&lt;br /&gt;
|-&lt;br /&gt;
|Speed of sound in iron&lt;br /&gt;
|C&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt; = 16,410 ft/s = 5710.7 m/s&lt;br /&gt;
|}&lt;br /&gt;
The speed of sound depends on temperature and the chemical composition of the medium, A widely used equation for speed of sound in air is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;C_s = 41.4\sqrt{\gamma\cdot T}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
* &amp;lt;math&amp;gt;C_s&amp;lt;/math&amp;gt; = speed of sound in dry air, ft/s&lt;br /&gt;
* &amp;lt;math&amp;gt;\gamma&amp;lt;/math&amp;gt; = ratio of specific heat, equal to 1.4 for dry air, dimensionless&lt;br /&gt;
* &amp;lt;math&amp;gt;T&amp;lt;/math&amp;gt; = temperature in Fahrenheit absolute, equal to 459.67 + &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F&lt;br /&gt;
&lt;br /&gt;
The speed of sound changes with altitude, as temperature (see Figure 3-1). The drag of streamlined bodies such as missiles, airfoils, and airplanes increases considerably as their velocities approach Mach 1. Depending on the configuration of the body, supersonic compressibility effects may occur in the 0.75 to 0.85 Mach range, causing local supersonic flow, shock waves, flow separation, and concomitant increases in drag and changes in stability.&lt;br /&gt;
&lt;br /&gt;
Parachutes that operate in separated flow over the entire velocity range do not show the typical drag increase when operating close to or beyond Mach 1. Supersonic parachute behavior is discussed in detail in section 5.8.&lt;br /&gt;
&lt;br /&gt;
== 4.2 CONTINUITY LAW AND BERNOULLI EQUATION ==&lt;br /&gt;
&lt;br /&gt;
=== 4.2.1 Continuity L.aw ===&lt;br /&gt;
Air is thought to flow in layers called streamlines. Figure 4-1 shows streamlines as layers of air without air transfer between individual layers. ne air is shown as being incompressible, a valid assumption for subsonic flow.&lt;br /&gt;
&lt;br /&gt;
[Insert Figure 4-1] 	&lt;br /&gt;
&lt;br /&gt;
If exchange of air does not occur across the streamline boundaries, the amount of air entering the streamline at point 1 must also exit at point 2, as shown in Figure 4-1. Because the cross section at point 2 is smaller than the cross section at point 1, the air must exit at a higher velocity. The following equation defines this condition:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;v_1\cdot S_1\cdot \rho_1 = v_2\cdot S_2\cdot \rho_2&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S&amp;lt;/math&amp;gt; = cross section of the streamline&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;v&amp;lt;/math&amp;gt; = velocity in the streamline&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\rho&amp;lt;/math&amp;gt; = density of the air flowing in the streamline&lt;br /&gt;
&lt;br /&gt;
This equation, which governs the flow in and around a body in gases and liquids, is important in aerodynamics and is called the Continuity Law. For incompressible subsonic flow, it can be simplified to &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;v_1\cdot S_1 = v_2\cdot S_2&amp;lt;/math&amp;gt; &lt;br /&gt;
&lt;br /&gt;
Whenever the cross section narrows, the velocity increases; when the cross section widens, the velocity decreases.&lt;br /&gt;
&lt;br /&gt;
=== 4.2.2 Bernoulli Equation ===&lt;br /&gt;
Figure 4-2 illustrates a streamline with the cross section, S, the velocity, v, and the pressure, p. If the air is incompressible, the downstream is v + Av. and the pressure is p + AP. If the air is inviscid, the inertia forces caused by the acceleration of air from v to v + Av must be balanced by differential pressure forces.&lt;br /&gt;
&lt;br /&gt;
[Insert Figure 4-2]FIGURE 4-2 Pressure and Velocity Distribution in a Streamline Element. 	&lt;br /&gt;
&lt;br /&gt;
The following equation can be written&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;p\cdot S-(p+\Delta p)S = m\cdot \frac{dv}{dt}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Simplified, the above equation yields&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;dp = - \rho vdv&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
and&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;p = - \frac{1}{2}\rho v^2 + C&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The above equation allows the following consideration: If p is pressure, then &amp;lt;math&amp;gt;1/2\ \rho v^2&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;C&amp;lt;/math&amp;gt; must also be pressure. The equation &amp;lt;math&amp;gt;1/2\ \rho v^2&amp;lt;/math&amp;gt; includes a velocity and is referred to as the dynamic pressure, or sometimes as velocity or impact pressure.&lt;br /&gt;
&lt;br /&gt;
Pressure, &amp;lt;math&amp;gt;p&amp;lt;/math&amp;gt;, is defined as static pressure; &amp;lt;math&amp;gt;1/2\ \rho v^2&amp;lt;/math&amp;gt; as dynamic pressure; and the sum of both, &amp;lt;math&amp;gt;C&amp;lt;/math&amp;gt;, as the total pressure or&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;p+\frac{1}{2} \rho v^2 = H&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
and&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;p_1 + \frac{1}{2} \rho {v_1}^2 = p_2 + \frac{1}{2} \rho {v_2}^2&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;H&amp;lt;/math&amp;gt; is the total pressure of the system, lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Dynamic pressure, &amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt;, is a frequently used quantity in aerodynamics:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;q = \frac{1}{2} \rho v^2&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
* &amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt; = dynamic pressure, lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
* &amp;lt;math&amp;gt;\rho&amp;lt;/math&amp;gt; =  air density, slugs/ft&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;&lt;br /&gt;
* &amp;lt;math&amp;gt;v&amp;lt;/math&amp;gt; =  velocity at a point of undisturbed flow, ft/s&lt;br /&gt;
&lt;br /&gt;
The following formulas are used for calculating the sea-level dynamic pressure if the velocity is given in ft/s, knots, mph, or km/h, respectively:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;q=\frac{v^2}{841.4}(ft/s), q=\frac{v^2}{295}(knots), q=\frac{v^2}{391.2}(mph), q=\frac{v^2}{1013.1}(km/h)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
                                              &lt;br /&gt;
&lt;br /&gt;
== 4.3 NEWTON'S THREE OF MOTION ==&lt;br /&gt;
Engineering mechanics are governed by the following three laws of Isaac Newton:&lt;br /&gt;
&lt;br /&gt;
1.  A body remains at rest or in an unaccelerated state of motion unless acted upon.&lt;br /&gt;
&lt;br /&gt;
2.  A force acting upon a body will produce an acceleration in the direction of the force.&lt;br /&gt;
&lt;br /&gt;
3.  An action in one direction will produce an equal reaction in the opposite direction.&lt;br /&gt;
&lt;br /&gt;
The first law is self-explanatory. The second law may be expressed by the equation&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;F=m\cdot a&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;F&amp;lt;/math&amp;gt; = force in pounds acting on the mass, lb&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;m&amp;lt;/math&amp;gt; = mass of body that the force is acting upon, slugs&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; = acceleration in ft/s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; resulting from the force, F&lt;br /&gt;
&lt;br /&gt;
The mass, m, of a body is obtained by&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;m=\frac{W}{g}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;W&amp;lt;/math&amp;gt; = weight of the body, lb&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;g&amp;lt;/math&amp;gt; = acceleration of gravity, ft/s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The mass, therefore, has the dimension of&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;m = \frac{W}{g}=\frac{lb}{ft/s^2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
This unit of mass is the slug.&lt;br /&gt;
&lt;br /&gt;
The equation of Newton's second law can now be written&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;F=\frac{W}{g}\cdot a,\ or\ F=W\frac{a}{g}&amp;lt;/math&amp;gt; 	&lt;br /&gt;
&lt;br /&gt;
The factor a/g is frequently called the load factor, G, and tells how much larger a force is than a force equivalent to the weight of the body. It is customary in parachute work to state that the maximum parachute force allowed is G • W or (a/g) • W. It is appropriate to write&lt;br /&gt;
&lt;br /&gt;
Maximum allowable parachute force, &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;F=W\frac{a}{g},\ or\ W\cdot G&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Figure 4-3 illustrates Newton's third law, explaining the principle of the rocket that can produce thrust in a perfect vacuum.&lt;br /&gt;
&lt;br /&gt;
A mass, m, ejected from a rocket at the velocity, v, per unit time, t, will produce a force, F, which in turn will create a reaction force, R, of equal magnitude but acting in the opposite direction.&lt;br /&gt;
&lt;br /&gt;
== 4.4 FORCES ACTING ON A BODY MOVING THROUGH AIR ==&lt;br /&gt;
&lt;br /&gt;
=== 4.4.1 Symmetrical Body ===&lt;br /&gt;
A body moving through air experiences forces caused by air pressure acting on the body. The same forces if the body moves through air, such as a descending parachute, or if the body is fixed and the air moves against the body, such as a parachute or an airfoil in a wind tunnel (Figure 44).&lt;br /&gt;
&lt;br /&gt;
         	 &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
A stable parachute in a wind tunnel experiences only the force called &amp;quot;drag&amp;quot; in the direction of the airflow. drag force, D, is calculated to&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;D=q\cdot S\cdot C_D&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;D&amp;lt;/math&amp;gt; = drag, lb&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt; = dynamic pressure, lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S&amp;lt;/math&amp;gt; = total surface area of the parachute canopy, ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;C_D&amp;lt;/math&amp;gt; = coefficient of drag,  dimensionless&lt;br /&gt;
&lt;br /&gt;
The dynamic pressure, q, can be calculated from section 4.2.2. The surface area of the canopy, S, is selected as a reference area. The drag coefficient, C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, is a form factor that indicates the drag characteristic of a specific shape. Most aerodynamic bodies are designed for low drag or a low drag coefficient. Parachutes, generally, are designed for high drag; therefore, a high drag coefficient is desirable. this difference in drag is demonstrated by the two bodies shown in Figure 4-5.&lt;br /&gt;
&lt;br /&gt;
            	&lt;br /&gt;
&lt;br /&gt;
Both bodies have the same cross section perpendicular to the airflow. The cylindrical. streamlined body has a smooth airflow over its total body length, resulting in a drag coefficient. C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, of 0.05 to 0.1, depending on slenderness ratio, surface roughness, and shape. The drag coefficient of all streamlined bodies is much affected by Reynolds number and Mach number. The open hemisphere, which is similar to a parachute canopy, has a drag coefficient, C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, of 1.3 to 1.4 for the same body cross section. The difference in drag is explained by the smooth airflow around the streamlined body and a separated, turbulent flow around the open hemisphere. The drag of bodies with separated flow, like parachute canopies, is little affected by Reynolds number.&lt;br /&gt;
&lt;br /&gt;
=== 4.4.2 Airflow Around an Asymmetrical Body (Airfoil) ===&lt;br /&gt;
Figure 4-6 shows an airfoil fixed at an angle of attack, a. against the airflow in a wind tunnel. This airfoil creates a drag force, D, in the direction of the flow; a lift force L perpendicular to the direction of the flow; and a moment, M. around the attachment point of the airfoil. fie sign convention of moments and forces shown are positive. Lift and drag can be combined for the resultant force, R.&lt;br /&gt;
&lt;br /&gt;
FIGURE. 4-6, Wind-Tunnel Forces Acting on an Airfoil.&lt;br /&gt;
&lt;br /&gt;
The lift, L is calculated&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;L = q\cdot S\cdot C_L&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; = measured lift, lb&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt; = dynamic pressure, lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S&amp;lt;/math&amp;gt; = reference area, ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;C_L&amp;lt;/math&amp;gt; = lift coefficient, dimensionless&lt;br /&gt;
&lt;br /&gt;
The moment is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;M=q\cdot S\cdot c_m\cdot c&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Where&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;M&amp;lt;/math&amp;gt; = measured lift, lb&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt; = dynamic pressure, lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S&amp;lt;/math&amp;gt; = reference area, ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;c_m&amp;lt;/math&amp;gt; = moment coefficient, dimensionless&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;c&amp;lt;/math&amp;gt; = average chord width of the wing, ft&lt;br /&gt;
&lt;br /&gt;
The reference area, S, is defined by agreement. For streamlined bodies, the maximum body cross section is used. Airfoils use the planform of the wing, and parachutes use the canopy surface area. The selection of the wing planform and the parachute surface area as references was made for practical reasons. The wing planform for a specific wing is fixed, whereas the cross section of the wing in the direction of the flow changes with the angle of attack. Similarly, the surface area of the parachute canopy is fixed; however, the frontal projected area of the inflated parachute canopy changes with airspeed, porosity, line length, and type of parachute.&lt;br /&gt;
&lt;br /&gt;
Forces and moments acting on an airfoil or a parachute canopy may be presented in several ways. The two most frequently used methods, as shown in Figure 4-7, are with forces oriented to the axis of flight and with forces oriented to the axis of the airfoil.&lt;br /&gt;
&lt;br /&gt;
The tangential force, and the normal force, N, are calculated&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;T = C_T\cdot S\cdot q&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
and 	&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;N = C_N\cdot S\cdot q&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
C&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; = tangential force coefficient, dimensionless&lt;br /&gt;
&lt;br /&gt;
C&amp;lt;sub&amp;gt;N&amp;lt;/sub&amp;gt; = normal force coefficient, dimensionless&lt;br /&gt;
&lt;br /&gt;
The resultant force, R, and the moment, M, in both presentations have the same direction and the same magnitude. The airflow fixed system is preferred for aerodynamic performance calculations, and the airfoil fixed system for wing stress calculations. me aerodynamic coefficients C&amp;lt;sub&amp;gt;L&amp;lt;/sub&amp;gt;, C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, C&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, C&amp;lt;sub&amp;gt;N&amp;lt;/sub&amp;gt;, and C&amp;lt;sub&amp;gt;m&amp;lt;/sub&amp;gt; can easily be determined in wind•tunnel measurements.&lt;br /&gt;
&lt;br /&gt;
Figure 4-8 shows the relationship of both force systems on a parachute. By definition, a negative moment is stabilizing, as illustrated in Figure 4-8. It is interesting to note that in Europe the stabilizing moment is defined as positive. Wind-tunnel installations frequently measure normal and tangential force instead of lift and drag. If α, T, and N are known, the drag D, can be calculated&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;D=T\cdot cos(\alpha)+N\cdot sin(\alpha)&amp;lt;/math&amp;gt;For a parachute with an angle of attack, &amp;lt;math&amp;gt;\alpha&amp;lt;/math&amp;gt;, equal to zero, the drag force and the tangential force are synonymous.&lt;br /&gt;
&lt;br /&gt;
Figure 4-9 shows the coefficients C&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, and C&amp;lt;sub&amp;gt;m&amp;lt;/sub&amp;gt; versus angle of attack for stable and unstable parachutes.&lt;br /&gt;
&lt;br /&gt;
The coefficient presentation shows two interesting facts. The slope of the moment coefficient curve, dC&amp;lt;sub&amp;gt;m&amp;lt;/sub&amp;gt;/dα, for the unstable parachute is positive between -25 degrees and + 25 degrees; this is, by definition, destabilizing. This parachute will oscillate approximately ± 25&lt;br /&gt;
&lt;br /&gt;
FIGURE 4-9. Coefficients C&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, and C&amp;lt;sub&amp;gt;M&amp;lt;/sub&amp;gt; Versus Angle of Attack, α, for a Stable and Unstable Parachute.&lt;br /&gt;
&lt;br /&gt;
degrees. The slope of the moment, dC&amp;lt;sub&amp;gt;m&amp;lt;/sub&amp;gt;/dα, for the stable parachute is negative over the total angle of attack; this is, by definition, stabilizing. The steeper the negative dC&amp;lt;sub&amp;gt;m&amp;lt;/sub&amp;gt;/dα slope, the greater is the stabilizing tendency of the parachute, and the better is its damping capability against unstabilizing forces such as sudden gusts of wind.&lt;br /&gt;
&lt;br /&gt;
Figure 4-10, from Reference 4.1, demonstrates the effect of airflow around a cylinder and an airfoil. The circulation around a rotating cylinder creates lift caused by the increase in velocity on one side of the cylinder and a decrease on the opposite side. This is called the Magnus effect.&lt;br /&gt;
&lt;br /&gt;
== 4.5 EQUILIBRIUM OF FORCES IN STUDY DESCENT OR FLIGHT ==&lt;br /&gt;
&lt;br /&gt;
=== 4.5.1 Parachute in Steady Descent ===&lt;br /&gt;
A stable parachute in unaccelerated descent has an equilibrium between the total drag of the parachute and the load, Dr, and the weight of the load and the parachute assembly, WT (Figure 4-11). &lt;br /&gt;
&lt;br /&gt;
For steady descent&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
D&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; = total drag, 1b&lt;br /&gt;
&lt;br /&gt;
D&amp;lt;sub&amp;gt;P&amp;lt;/sub&amp;gt; = drag of parachute, 1b&lt;br /&gt;
&lt;br /&gt;
W&amp;lt;sub&amp;gt;C&amp;lt;/sub&amp;gt; = weight of load. 1b&lt;br /&gt;
&lt;br /&gt;
In most cases, the drag of the load can be neglected in relation to the large drag of the parachute, With drag, D — (C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;S)&amp;lt;sub&amp;gt;p&amp;lt;/sub&amp;gt; • p/2• v&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; and D&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; = W&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;. and solving for v, the important equation for rate of descent, v&amp;lt;sub&amp;gt;e&amp;lt;/sub&amp;gt;, is obtained,&lt;br /&gt;
&lt;br /&gt;
Rate of descent,&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
FIGURE 4-11. Forces Acting on a Parachute in Steady Descent.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
or in parachute terminology for rate of descent at sea level&lt;br /&gt;
&lt;br /&gt;
and rate of descent at any altitude&lt;br /&gt;
&lt;br /&gt;
For 1/, see column 4 in Table 3-3,&lt;br /&gt;
&lt;br /&gt;
In the equation for rate of descent. V&amp;lt;sub&amp;gt;e&amp;lt;/sub&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
W&amp;lt;sub&amp;gt;T =&amp;lt;/sub&amp;gt; weight of load and parachute assembly, 1b&lt;br /&gt;
&lt;br /&gt;
S&amp;lt;sub&amp;gt;o&amp;lt;/sub&amp;gt; = canopy surface area, ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
C&amp;lt;sub&amp;gt;Do&amp;lt;/sub&amp;gt; = parachute drag coefficient related to S&amp;lt;sub&amp;gt;o&amp;lt;/sub&amp;gt;&lt;br /&gt;
&lt;br /&gt;
p = air density at a specific altitude in slugs/ft&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;, as shown in Table 3-3&lt;br /&gt;
&lt;br /&gt;
During descent from altitude, the parachute system is constantly decelerated because of the increasing air density. This can be ignored for slowly descending main parachutes. However, for drogue chute systems that descend at 200 ft/s or faster, the constant deceleration may result in velocities 3 to 5% higher than the steady rate of descent.&lt;br /&gt;
&lt;br /&gt;
=== 4.5.2 Gliding Parachutes ===&lt;br /&gt;
Figure 4-12 shows the balance of forces on a gliding parachute. The total weight of the system, W&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; . must be balanced by the resultant force. R. However, a lifting force is required for glide. To satisfy the force balance&lt;br /&gt;
&lt;br /&gt;
R = C&amp;lt;sub&amp;gt;R&amp;lt;/sub&amp;gt; * S * p/2 * v&lt;br /&gt;
&lt;br /&gt;
Trajectory velocity, V&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, is calculated&lt;br /&gt;
&lt;br /&gt;
Horizontal velocity is calculated&lt;br /&gt;
&lt;br /&gt;
V&amp;lt;sub&amp;gt;H&amp;lt;/sub&amp;gt; = V&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; • cosø, and vertical velocity, v&amp;lt;sub&amp;gt;v&amp;lt;/sub&amp;gt; = V&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; • sinø&lt;br /&gt;
&lt;br /&gt;
The glide ratio is obtained from&lt;br /&gt;
&lt;br /&gt;
Analysis of Figure 4-12 indicates that the larger the ratio of lift to drag, the better the glide ratio, I./D A high resultant coefficient, C&amp;lt;sub&amp;gt;R&amp;lt;/sub&amp;gt;, results in a low glide or trajectory V&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, desirable for landing. A small C&amp;lt;sub&amp;gt;R&amp;lt;/sub&amp;gt; results in a high glide velocity, V&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, which is desirable for flying toward a target, compensating for head winds, or covering a distance quickly. Generally, gliding parachutes follow the same aerodynamic rules as low-aspect-ratio wings.&lt;br /&gt;
&lt;br /&gt;
           	   	&lt;br /&gt;
&lt;br /&gt;
FIGUR E 4-12, Forces Acting on a Gliding Parachute&lt;br /&gt;
&lt;br /&gt;
=== 4.5.3 Parasite Drag and Induced Drag ===&lt;br /&gt;
The drag acting on a lift-producing air vehicle, such as a gliding parachute or an aircraft, has two primary components: the parasite drag, D&amp;lt;sub&amp;gt;P&amp;lt;/sub&amp;gt; , and the induced drag. D&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Parasite drag is produced by the form drag from individual components such as the suspension lines, canopy, and the jumper of a gliding parachute, and the fuselage, tail sectiora, and control surfaces of an airplane. Large surfaces produce surface friction drag as part of the parasite drag.&lt;br /&gt;
&lt;br /&gt;
Induced drag is caused by the lifting action of the parachute canopy or the aircraft wing. Section 4.7 includes books with detailed discussions of induced drag.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Total drag, D&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, can be defined as&lt;br /&gt;
&lt;br /&gt;
or, in the coefficient form&lt;br /&gt;
&lt;br /&gt;
The parasite drag, D&amp;lt;sub&amp;gt;p&amp;lt;/sub&amp;gt;, and the coefficient, C&amp;lt;sub&amp;gt;DP&amp;lt;/sub&amp;gt;, can be determined in wind-tunnel tests or calculated as the sum of the individual component drags.&lt;br /&gt;
&lt;br /&gt;
The induced drag coefficient, C&amp;lt;sub&amp;gt;Di&amp;lt;/sub&amp;gt; , of a gliding parachute canopy or a wing profile can be calculated&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
C = coefficient of induced drag, dimensionless&lt;br /&gt;
&lt;br /&gt;
The expression b&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;/S is defined as the aspect ratio of a wing or parachute with the notation AR b&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;/S. Therefore&lt;br /&gt;
&lt;br /&gt;
The equation for induced drag indicates that increasing the aspect ratio, AR, reduces the induced drag coefficient,  , and therefore reduces the drag, D. ms, in turn, increases the glide ratio, L/D. Increasing the glide ratio by increasing the aspect ratio is optimized on high-performance sailplanes with aspect ratios higher than 20. Increasing the glide ratio of gliding parachutes by increasing the aspect ratio has limitations, which are discussed in section 5.9.&lt;br /&gt;
&lt;br /&gt;
=== 4.5.4 Aircraft in Horizontal Flight ===&lt;br /&gt;
Figure 4-13 shows forces and moments on an aircraft in steady, horizontal flight. In steady, horizontal flight, an equilibrium exists between all forces and moments acting on the aircraft. Lift on the wing and tail, L&amp;lt;sub&amp;gt;W&amp;lt;/sub&amp;gt; and L&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;. and the weight of the aircraft, W&amp;lt;sub&amp;gt;A&amp;lt;/sub&amp;gt;, balance in the vertical plane. Thrust, T and drag. D, balance each other in the horizontal plane, and the positive or negative moment, M, is balanced by the positive or negative lift of the tail multiplied by the moment arm, L&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
FIGURE 4-13. Forces and Moments Acting on an Aircraft in Steady night,&lt;br /&gt;
&lt;br /&gt;
Any imbalance in these forces results in descent or climb in the vertical plane or faster or slower speed in the horizontal plane. A change in the lift of the elevator initiates climb or descent. Thrust, T, is the prime contributor for climb or descent and faster or slower speed, However, a balance of forces must always be maintained for horizontal flight or steady rate oi climb or descent.&lt;br /&gt;
&lt;br /&gt;
== 4.6 WIND-TUNNEL TESTING OF PARACHUTES ==&lt;br /&gt;
Wind tunnels are an effective tool for testing air vehicles and air-vehicle components and have been used successfully for testing parachutes and parachute systems. Experience has shown that certain rules apply for the wind-tunnel testing of parachutes. Small parachutes manufactured from textiles cannot be made sufficiently similar to large parachutes in geometric design and flexibility, Lightweight material. required to obtain design similarity, is difficult to manufacture or is unobtainable.&lt;br /&gt;
&lt;br /&gt;
One cardinal rule has been established through many years of parachute wind-tunnel testing: A modification that changes the performance of a model parachute in wind-tunnel testing produces the same type and percentage of performance change in a large parachute. This rule is true for drag. stability, and opening-force characteristics.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
=== 4.6.1 Blowers ===&lt;br /&gt;
The simple air blower (Figure 4-14) is a proven tool for preliminary parachute testing of a chiefly qualitative nature. Unless special test conditions prevail, parachutes tested should be a minimum of 1.5 to 2 feet in diameter to obtain meaningful results.&lt;br /&gt;
&lt;br /&gt;
                                                                    &lt;br /&gt;
&lt;br /&gt;
 FIGURE 4-14. Typical Air Blower.&lt;br /&gt;
&lt;br /&gt;
An air blower is a preliminary test too! because it permits quick parachute• configuration changes and excellent visual observation.&lt;br /&gt;
&lt;br /&gt;
=== 4.6.2 Open-Throat, No-Return Wind Tunnels ===&lt;br /&gt;
The open-throat, no-return wind tunnel shown in Figure 4-15 permits exact measurements if parachutes of sufficient size are used. Parachutes 3 feet or more in diameter are well suited for obtaining good, quantitative test results.&lt;br /&gt;
&lt;br /&gt;
              FIGURE 4-15. Open-Throat, No-Return Wind Tunnel&lt;br /&gt;
&lt;br /&gt;
In air blowers and open-throat wind tunnels, the velocity at the skirt of the parachute (Section a-a of Figures 4-14 and 4-15) is lower than the velocity at the nozzle exit of the wind tunnel (Section b&amp;lt;sup&amp;gt;-&amp;lt;/sup&amp;gt;b of Figures 4-14 and 4-15), Care must be taken to measure the parachute test&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
velocity at Section a-a and not at Section b-b, the customary attachment point for airfoils and models.&lt;br /&gt;
&lt;br /&gt;
Wind tunnels frequently cannot test at the descent velocity of most main parachutes of 20 to 30 feet per second. Obtaining proper test results at this low is hampered by a poor velocity distribution in the wind-tunnel-test section, and by the weight of the test parachute. The latter has a tendency to pull the parachute downward, thereby providing a negative angle of attack, lusting unstable parachutes at higher presents the problem that the drag coefficient C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, of unstable parachutes is sensitive. The drag coefficient of unstable parachutes is described in section 5.2.&lt;br /&gt;
&lt;br /&gt;
An open-throat wind tunnel permits quick changes in parachute configuration, such as changing the suspension and reefing line lengths. Large open-throat wind tunnels that are not sealed against outside elements suffer atmospheric problems such as fog formation in the test section.&lt;br /&gt;
&lt;br /&gt;
=== 4.6.3 Closed-Throat, Full-Return Wind Tunnel ===&lt;br /&gt;
Figure 4-16 is a drawing of a full-return, closed-throat wind tunnel. fic full-return, closed-throat wind tunnel is generally considered best suited for obtaining good. qualitative, aerodynamic data, since it has a uniform distribution in the test section. A disadvantage is the difficulty in gaining access to the test section for changing the parachute configuration.&lt;br /&gt;
&lt;br /&gt;
FIGURE 4-16. Closed-Throat, Full-Reuurn Wind Tunnel.&lt;br /&gt;
&lt;br /&gt;
=== 4.6.4 General Comments for Wind-Tunnel Testing of Parachutes ===&lt;br /&gt;
1. Parachute models for wind-tunnel testing should be as large and as similar as possible in geometry and flexibility to full-scale parachutes. Parachutes of less than 1.5 feet in diameter usually lack geometric similarity and material flexibility, which results in inflation characteristics and dissimilar inflated shapes.&lt;br /&gt;
&lt;br /&gt;
2.  The finished dimensions of model parachutes must be measured as accurately as possible to determine the nominal diameter, Do, and the surface area, So. Model parachutes will shrink from 5 to 10% during manufacture because of sewing take-up, which results in a notable difference in the dimensions between the drawing and the completed parachute.&lt;br /&gt;
&lt;br /&gt;
3.  Wind&amp;lt;sup&amp;gt;-&amp;lt;/sup&amp;gt;tunnel tests of parachutes are excellent for comparing different models and modifications: also, they are the most effective means for measuring coefficients of lift, drag. and normal and tangential forces, as well as for determining the load coefficient, for infinite load.&lt;br /&gt;
&lt;br /&gt;
4.  In wind-tunnel tests, velocity decay does not occur during parachute inflation and operation; this is defined as testing under &amp;quot;infinite mass condition. &amp;quot; First-stage drogue chutes and parachutes with a canopy loading, W/C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;S. in excess of 100 lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; approach this condition. Low-canopy-loading main parachutes with rates of descent of 20 to 30 ft/s have a large velocity decay during opening, which requires careful interpretation of the opening-force data obtained in wind-tunnel tests.&lt;br /&gt;
&lt;br /&gt;
5.  In the past, to avoid wind-tunnel blockage and questionable test data. the diameter of a test parachute could not exceed about 5 to 6% of the wind-tunnel test section area. Recent Sandia investigations of single and clustered ribbon parachutes with wind-tunnel blockage ratios of up to 30% have resulted in correction methods that make it possible to test much larger parachutes (Reference 4.2).&lt;br /&gt;
&lt;br /&gt;
== 4.7 REFERENCE MATERIAL ==&lt;br /&gt;
4.1 H. H. Hurt. Aerodynamics for Naval Aviators Navy Manual NAVWEPS 00 80T 80. Chief of Naval Operations, Aviation Training Division.&lt;br /&gt;
&lt;br /&gt;
4.2 J, M. Macha and R J. Buffington. &amp;quot;Wall-Interference Corrections for Parachutes in a Closed Wind Tunnel.&amp;quot; AIM Paper, April 1989. (AIM 89-0900-cp.)&lt;br /&gt;
&lt;br /&gt;
For readers interested in a more detailed study of aerodynamics, the following books are recommended.&lt;br /&gt;
&lt;br /&gt;
4.3 J, H, Dwinnel, Principle of Aerodynamics. McGraw-Hill     	Co., New York, 1949.&lt;br /&gt;
&lt;br /&gt;
4.4 J. Morane. Introduction to Theoretical and Computational Aerodynamics. John Wiley &amp;amp; Sons.&lt;br /&gt;
&lt;br /&gt;
4.5 R.S. Shevell. Fundamentals of Flight. Prentice-Hall. 1983.&lt;br /&gt;
&lt;br /&gt;
4.6 J. D. Anderson, Jr. Introduction to Flights, ILS Engineering and History. McGraw-Hill Book co., New York 1978.&lt;br /&gt;
&lt;br /&gt;
4.7 D. J. Cockrell. The Aerodynamics of Parachutes.&amp;quot; AGARDograph No. 6295, available from NASA Langley Research Center, M/S 1M), Hampton, Va., 236.&lt;/div&gt;</summary>
		<author><name>TuanHTruong</name></author>
	</entry>
	<entry>
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		<title>Parachute Aerodynamics</title>
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		<summary type="html">&lt;p&gt;TuanHTruong: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&lt;br /&gt;
= CHAPTER 4: AERODYNAMICS AS RELATED TO PARACHUTES =&lt;br /&gt;
== 4.1 PROPERTIES OF THE ATMOSPHERE ==&lt;br /&gt;
All forces acting on parachutes and all movements of parachutes are affected by the atmosphere, or air, surrounding the Earth. The air at the Earth's surface is approximately 78% nitrogen; 21% oxygen; and 1% a mixture of gases such as argon, neon, helium, water vapor, and carbon dioxide. This chemical composition remains relatively constant to an altitude of about 160,000 feet (50 kilometers). The following air qualities are of major significance in the dynamics of bodies moving in the atmosphere:&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
!Air quality&lt;br /&gt;
!Symbol&lt;br /&gt;
!Dimension&lt;br /&gt;
|-&lt;br /&gt;
|Specific weight of air&lt;br /&gt;
|w&lt;br /&gt;
|lb/ft&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;, kg/m&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;&lt;br /&gt;
|-&lt;br /&gt;
|Static pressure&lt;br /&gt;
|p&lt;br /&gt;
|atm, lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;, Pa, bar, torr&lt;br /&gt;
|-&lt;br /&gt;
|Temperature&lt;br /&gt;
|T&lt;br /&gt;
|&amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F, &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;C&lt;br /&gt;
|-&lt;br /&gt;
|Mass density&lt;br /&gt;
|&amp;lt;math&amp;gt;\rho&amp;lt;/math&amp;gt;&lt;br /&gt;
|slugs/ft&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;, kg s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;/m&amp;lt;sup&amp;gt;4&amp;lt;/sup&amp;gt;&lt;br /&gt;
|-&lt;br /&gt;
|Gravity&lt;br /&gt;
|''g''&lt;br /&gt;
|ft/s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;, m/s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
|-&lt;br /&gt;
|Speed of sound&lt;br /&gt;
|C&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt;&lt;br /&gt;
|ft/s, m/s&lt;br /&gt;
|}&lt;br /&gt;
All of these qualities are altitude-dependent and may vary slightly on the Earth's surface with geographic latitude because of variations of the Earth's radius caused by the centrifugal forces of the rotation of the Earth. All standard data used herein refer to a latitude of 45 degrees. Sea level is defined as mean sea level (MSL). To compare performance data on an equal basis, the United States Bureau of Standards has defined standard day conditions as follows:&lt;br /&gt;
&lt;br /&gt;
* Temperature = 15 degrees Celsius (&amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;C) or 59 degrees Fahrenheit (&amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F)&lt;br /&gt;
* Pressure = 760 millimeters (mm) of mercury (Hg) or 29.9213 inches (in.) Hg&lt;br /&gt;
&lt;br /&gt;
=== 4.1.1 Specific Weight of Air ===&lt;br /&gt;
For standard day conditions of 59 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F temperature and a pressure of 29.9213 in. Hg, the specific weight of air, w, is 0.07648 lb/ft&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt; or 1.2250 kg/m&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;. The specific weight of air changes with pressure, temperature, and humidity. Further data can be found in References 3.4 and 4.1, and in technical handbooks.&lt;br /&gt;
&lt;br /&gt;
=== 4.1.2 Static Pressure ===&lt;br /&gt;
Static pressure depends on geographic latitude, weather conditions, and altitude. The static pressure at any altitude results from the weight of the air above that altitude. For MSL and standard day conditions, the pressure, p&amp;lt;sub&amp;gt;o&amp;lt;/sub&amp;gt;, is 29.9213 in. Hg = 760 mm Hg = 1.0 atmosphere (atm). For conversion to Pascal, torr, or bar, see the conversion tables in section 3.2.&lt;br /&gt;
&lt;br /&gt;
=== 4.1.3 Temperature ===&lt;br /&gt;
Temperatures are defined in the English and metric systems in the so-called absolute and engineering scales. The absolute temperature minimum at 0 degrees, pressure is 0 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;K = -273.16 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;C, and 0 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;R = -459.69 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F. This is also written&lt;br /&gt;
&lt;br /&gt;
* Degrees Kelvin = degrees Celsius + 273.16&lt;br /&gt;
* Degrees Rankine = degrees Fahrenheit + 459.69&lt;br /&gt;
&lt;br /&gt;
The freezing point of water is 32 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F or 0 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;C. The boiling point of water is 212 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F or 100 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;C.&lt;br /&gt;
&lt;br /&gt;
=== 4.1.4 Mass Density of Air ===&lt;br /&gt;
Mass density defines the amount of mass contained in a unit volume of air. The mass density, &amp;lt;math&amp;gt;\rho&amp;lt;/math&amp;gt;, of air is of special importance in aerodynamic calculations.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\rho = \frac{specific\ weight\ of\ air,\ w}{acceleration\ of\ gravity,\ g} = \frac{lb/ft^3}{ft/s^2} = \frac{kg\ s^2}{m^4}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;slug = \frac{weight}{acceleration\ of\ gravity} = \frac{lb}{ft/s^2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Frequently the density ratio, &amp;lt;math&amp;gt;\sigma&amp;lt;/math&amp;gt;, is used&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\sigma = \frac{ambient\ air\ density,\ \rho}{standard\ sea-level\ density, \rho_o}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The factor, &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;1/\sqrt{\rho/\rho_o}&amp;lt;/math&amp;gt;, determines the increase in parachute rate of descent with altitude. The density at 40,000 feet is ¼ of the MSL density, and the density at 100,000 feet is 1/75 of the MSL density. Therefore, the parachute rate of descent is about twice as high at 40,000 feet and about nine times as high at 100,000 feet. MSL density is 0.00237689 slugs/ft&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;, or 0.1249 kg s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;/m&amp;lt;sup&amp;gt;4&amp;lt;/sup&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
=== 4.1.5 Gravity ===&lt;br /&gt;
Any mass attracts another mass with a force called gravity. If the Earth were surrounded by a vacuum, a body suspended above the Earth and released would fall toward the center of the Earth with increasing velocity caused by the acceleration of gravity, ''g''. In reality, the falling body is decelerated by its air drag until the air drag, D, equals the weight of the body, W, and an equilibrium velocity is reached; for parachutes, this is called the steady-state rate of descent.&lt;br /&gt;
&lt;br /&gt;
The acceleration of gravity, ''g'', at sea lavel is&lt;br /&gt;
&lt;br /&gt;
* ''g'' = 32.174 ft/s2 or 9.80665 m/s2.&lt;br /&gt;
&lt;br /&gt;
The value g = 9.08665 m/s is standardized internationally but is accurate only for a latitude of 45 degrees.&lt;br /&gt;
&lt;br /&gt;
With increasing altitude above the Earth's surface, the acceleration of gravity decreases in accordance with the equation&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;g = g_o(\frac{r}{r+h})^2&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
* ''g'' = acceleration of gravity at any altitude, ft/s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
* g&amp;lt;sub&amp;gt;o&amp;lt;/sub&amp;gt; = acceleration of gravity at sea level, ft/s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
* r = average Earth radius = 2.08556 x 10&amp;lt;sup&amp;gt;7&amp;lt;/sup&amp;gt; ft&lt;br /&gt;
* h = altitude above sea level, ft&lt;br /&gt;
&lt;br /&gt;
For other planets and heavenly bodies, the acceleration of gravity varies with the mass of the body. For example, the acceleration of gravity on Mars is about 1/3 of the acceleration of gravity on Earth. For more details on planets and heavenly bodies, see page XII of Reference 2.1.&lt;br /&gt;
&lt;br /&gt;
=== 4.1.6 Kinematic Viscosity ===&lt;br /&gt;
The coefficient of viscosity, &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt;, defines the shearing stresses in a gas or liquid and is sometimes called the resistance to continuous deformation. In aerodynamics, the coefficient of viscosity is combined with the mass density to form the kinematic viscosity, &amp;lt;math&amp;gt;\nu&amp;lt;/math&amp;gt;, where&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\nu = \frac{coefficient\ of\ viscosity,\ \mu}{mass\ density,\ \rho} = 0.0001576\ ft^2/s\ at\ sea\ level&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The kinematic viscosity, &amp;lt;math&amp;gt;\nu&amp;lt;/math&amp;gt;, is altitude dependent and is used to calculate the Reynolds number, Re.&lt;br /&gt;
&lt;br /&gt;
=== 4.1.7 Reynolds Number ===&lt;br /&gt;
The Reynolds number, Re, defines the relationship of mass forces to viscous friction forces in liquids and gases. It is calculated as&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Re = \frac{v\cdot l}{\nu} = \frac{velocity\ (ft/s)\cdot characteristic\ length\ (ft)}{kinematic\ viscosity\ (ft^2/s)}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Reynolds number is an important criterion in subsonic, noncompressible flow, and allows comparison of model tests with full-scale flight tests. A Reynolds number effect on parachutes working in separated, turbulent flow has not yet been established, as shown in section 5.2. The following chart shows the Reynolds numbers for various air vehicles.&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
!Subject&lt;br /&gt;
!Insect&lt;br /&gt;
!Glider&lt;br /&gt;
!DC-3&lt;br /&gt;
!B-747&lt;br /&gt;
!Drogue&lt;br /&gt;
Chute&lt;br /&gt;
!Main &lt;br /&gt;
Parachute&lt;br /&gt;
!WTT&lt;br /&gt;
Model&lt;br /&gt;
|-&lt;br /&gt;
|Re&lt;br /&gt;
|6 • 10&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;&lt;br /&gt;
|2.5 • 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&lt;br /&gt;
|24 • 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&lt;br /&gt;
|100 • 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&lt;br /&gt;
|50 • 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&lt;br /&gt;
|20 • 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&lt;br /&gt;
|2 • 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
=== 4.1.8 Mach Number ===&lt;br /&gt;
Mach number is an important parameter of supersonic flight; it states how much faster than the speed of sound the air vehicle travels.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Mach\ number,\ M = \frac{flight\ velocity,\ v}{speed\ of\ sound, c_s}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The speed of sound is the velocity at which a pressure disturbance, such as the sound of the human voice, travels in any medium. The speed of sound varies considerably in different gases, liquids, and metals.&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|Speed of sound in air in MSL&lt;br /&gt;
|C&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt; = 1116.46 ft/s = 340.38 m/s&lt;br /&gt;
|-&lt;br /&gt;
|Speed of sound in water&lt;br /&gt;
|C&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt; = 4749 ft/s = 1461.21 m/s&lt;br /&gt;
|-&lt;br /&gt;
|Speed of sound in iron&lt;br /&gt;
|C&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt; = 16,410 ft/s = 5710.7 m/s&lt;br /&gt;
|}&lt;br /&gt;
The speed of sound depends on temperature and the chemical composition of the medium, A widely used equation for speed of sound in air is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;C_s = 41.4\sqrt{\gamma\cdot T}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
* &amp;lt;math&amp;gt;C_s&amp;lt;/math&amp;gt; = speed of sound in dry air, ft/s&lt;br /&gt;
* &amp;lt;math&amp;gt;\gamma&amp;lt;/math&amp;gt; = ratio of specific heat, equal to 1.4 for dry air, dimensionless&lt;br /&gt;
* &amp;lt;math&amp;gt;T&amp;lt;/math&amp;gt; = temperature in Fahrenheit absolute, equal to 459.67 + &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F&lt;br /&gt;
&lt;br /&gt;
The speed of sound changes with altitude, as temperature (see Figure 3-1). The drag of streamlined bodies such as missiles, airfoils, and airplanes increases considerably as their velocities approach Mach 1. Depending on the configuration of the body, supersonic compressibility effects may occur in the 0.75 to 0.85 Mach range, causing local supersonic flow, shock waves, flow separation, and concomitant increases in drag and changes in stability.&lt;br /&gt;
&lt;br /&gt;
Parachutes that operate in separated flow over the entire velocity range do not show the typical drag increase when operating close to or beyond Mach 1. Supersonic parachute behavior is discussed in detail in section 5.8.&lt;br /&gt;
&lt;br /&gt;
== 4.2 CONTINUITY LAW AND BERNOULLI EQUATION ==&lt;br /&gt;
&lt;br /&gt;
=== 4.2.1 Continuity L.aw ===&lt;br /&gt;
Air is thought to flow in layers called streamlines. Figure 4-1 shows streamlines as layers of air without air transfer between individual layers. ne air is shown as being incompressible, a valid assumption for subsonic flow.&lt;br /&gt;
&lt;br /&gt;
[Insert Figure 4-1] 	&lt;br /&gt;
&lt;br /&gt;
If exchange of air does not occur across the streamline boundaries, the amount of air entering the streamline at point 1 must also exit at point 2, as shown in Figure 4-1. Because the cross section at point 2 is smaller than the cross section at point 1, the air must exit at a higher velocity. The following equation defines this condition:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;v_1\cdot S_1\cdot \rho_1 = v_2\cdot S_2\cdot \rho_2&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S&amp;lt;/math&amp;gt; = cross section of the streamline&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;v&amp;lt;/math&amp;gt; = velocity in the streamline&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\rho&amp;lt;/math&amp;gt; = density of the air flowing in the streamline&lt;br /&gt;
&lt;br /&gt;
This equation, which governs the flow in and around a body in gases and liquids, is important in aerodynamics and is called the Continuity Law. For incompressible subsonic flow, it can be simplified to &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;v_1\cdot S_1 = v_2\cdot S_2&amp;lt;/math&amp;gt; &lt;br /&gt;
&lt;br /&gt;
Whenever the cross section narrows, the velocity increases; when the cross section widens, the velocity decreases.&lt;br /&gt;
&lt;br /&gt;
=== 4.2.2 Bernoulli Equation ===&lt;br /&gt;
Figure 4-2 illustrates a streamline with the cross section, S, the velocity, v, and the pressure, p. If the air is incompressible, the downstream is v + Av. and the pressure is p + AP. If the air is inviscid, the inertia forces caused by the acceleration of air from v to v + Av must be balanced by differential pressure forces.&lt;br /&gt;
&lt;br /&gt;
[Insert Figure 4-2]FIGURE 4-2 Pressure and Velocity Distribution in a Streamline Element. 	&lt;br /&gt;
&lt;br /&gt;
The following equation can be written&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;p\cdot S-(p+\Delta p)S = m\cdot \frac{dv}{dt}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Simplified, the above equation yields&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;dp = - \rho vdv&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
and&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;p = - \frac{1}{2}\rho v^2 + C&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The above equation allows the following consideration: If p is pressure, then &amp;lt;math&amp;gt;1/2\ \rho v^2&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;C&amp;lt;/math&amp;gt; must also be pressure. The equation &amp;lt;math&amp;gt;1/2\ \rho v^2&amp;lt;/math&amp;gt; includes a velocity and is referred to as the dynamic pressure, or sometimes as velocity or impact pressure.&lt;br /&gt;
&lt;br /&gt;
Pressure, &amp;lt;math&amp;gt;p&amp;lt;/math&amp;gt;, is defined as static pressure; &amp;lt;math&amp;gt;1/2\ \rho v^2&amp;lt;/math&amp;gt; as dynamic pressure; and the sum of both, &amp;lt;math&amp;gt;C&amp;lt;/math&amp;gt;, as the total pressure or&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;p+\frac{1}{2} \rho v^2 = H&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
and&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;p_1 + \frac{1}{2} \rho {v_1}^2 = p_2 + \frac{1}{2} \rho {v_2}^2&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;H&amp;lt;/math&amp;gt; is the total pressure of the system, lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Dynamic pressure, &amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt;, is a frequently used quantity in aerodynamics:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;q = \frac{1}{2} \rho v^2&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
* &amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt; = dynamic pressure, lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
* &amp;lt;math&amp;gt;\rho&amp;lt;/math&amp;gt; =  air density, slugs/ft&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;&lt;br /&gt;
* &amp;lt;math&amp;gt;v&amp;lt;/math&amp;gt; =  velocity at a point of undisturbed flow, ft/s&lt;br /&gt;
&lt;br /&gt;
The following formulas are used for calculating the sea-level dynamic pressure if the velocity is given in ft/s, knots, mph, or km/h, respectively:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;q=\frac{v^2}{841.4}(ft/s), q=\frac{v^2}{295}(knots), q=\frac{v^2}{391.2}(mph), q=\frac{v^2}{1013.1}(km/h)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
                                              &lt;br /&gt;
&lt;br /&gt;
== 4.3 NEWTON'S THREE OF MOTION ==&lt;br /&gt;
Engineering mechanics are governed by the following three laws of Isaac Newton:&lt;br /&gt;
&lt;br /&gt;
1.  A body remains at rest or in an unaccelerated state of motion unless acted upon.&lt;br /&gt;
&lt;br /&gt;
2.  A force acting upon a body will produce an acceleration in the direction of the force.&lt;br /&gt;
&lt;br /&gt;
3.  An action in one direction will produce an equal reaction in the opposite direction.&lt;br /&gt;
&lt;br /&gt;
The first law is self-explanatory. The second law may be expressed by the equation&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;F=m\cdot a&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;F&amp;lt;/math&amp;gt; = force in pounds acting on the mass, lb&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;m&amp;lt;/math&amp;gt; = mass of body that the force is acting upon, slugs&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; = acceleration in ft/s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; resulting from the force, F&lt;br /&gt;
&lt;br /&gt;
The mass, m, of a body is obtained by&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;m=\frac{W}{g}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;W&amp;lt;/math&amp;gt; = weight of the body, lb&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;g&amp;lt;/math&amp;gt; = acceleration of gravity, ft/s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The mass, therefore, has the dimension of&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;m = \frac{W}{g}=\frac{lb}{ft/s^2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
This unit of mass is the slug.&lt;br /&gt;
&lt;br /&gt;
The equation of Newton's second law can now be written&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;F=\frac{W}{g}\cdot a,\ or\ F=W\frac{a}{g}&amp;lt;/math&amp;gt; 	&lt;br /&gt;
&lt;br /&gt;
The factor a/g is frequently called the load factor, G, and tells how much larger a force is than a force equivalent to the weight of the body. It is customary in parachute work to state that the maximum parachute force allowed is G • W or (a/g) • W. It is appropriate to write&lt;br /&gt;
&lt;br /&gt;
Maximum allowable parachute force, &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;F=W\frac{a}{g},\ or\ W\cdot G&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Figure 4-3 illustrates Newton's third law, explaining the principle of the rocket that can produce thrust in a perfect vacuum.&lt;br /&gt;
&lt;br /&gt;
A mass, m, ejected from a rocket at the velocity, v, per unit time, t, will produce a force, F, which in turn will create a reaction force, R, of equal magnitude but acting in the opposite direction.&lt;br /&gt;
&lt;br /&gt;
== 4.4 FORCES ACTING ON A BODY MOVING THROUGH AIR ==&lt;br /&gt;
&lt;br /&gt;
=== 4.4.1 Symmetrical Body ===&lt;br /&gt;
A body moving through air experiences forces caused by air pressure acting on the body. The same forces if the body moves through air, such as a descending parachute, or if the body is fixed and the air moves against the body, such as a parachute or an airfoil in a wind tunnel (Figure 44).&lt;br /&gt;
&lt;br /&gt;
         	 &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
A stable parachute in a wind tunnel experiences only the force called &amp;quot;drag&amp;quot; in the direction of the airflow. drag force, D, is calculated to&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;D=q\cdot S\cdot C_D&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;D&amp;lt;/math&amp;gt; = drag, lb&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt; = dynamic pressure, lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S&amp;lt;/math&amp;gt; = total surface area of the parachute canopy, ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;C_D&amp;lt;/math&amp;gt; = coefficient of drag,  dimensionless&lt;br /&gt;
&lt;br /&gt;
The dynamic pressure, q, can be calculated from section 4.2.2. The surface area of the canopy, S, is selected as a reference area. The drag coefficient, C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, is a form factor that indicates the drag characteristic of a specific shape. Most aerodynamic bodies are designed for low drag or a low drag coefficient. Parachutes, generally, are designed for high drag; therefore, a high drag coefficient is desirable. this difference in drag is demonstrated by the two bodies shown in Figure 4-5.&lt;br /&gt;
&lt;br /&gt;
            	&lt;br /&gt;
&lt;br /&gt;
Both bodies have the same cross section perpendicular to the airflow. The cylindrical. streamlined body has a smooth airflow over its total body length, resulting in a drag coefficient. C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, of 0.05 to 0.1, depending on slenderness ratio, surface roughness, and shape. The drag coefficient of all streamlined bodies is much affected by Reynolds number and Mach number. The open hemisphere, which is similar to a parachute canopy, has a drag coefficient, C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, of 1.3 to 1.4 for the same body cross section. The difference in drag is explained by the smooth airflow around the streamlined body and a separated, turbulent flow around the open hemisphere. The drag of bodies with separated flow, like parachute canopies, is little affected by Reynolds number.&lt;br /&gt;
&lt;br /&gt;
=== 4.4.2 Airflow Around an Asymmetrical Body (Airfoil) ===&lt;br /&gt;
Figure 4-6 shows an airfoil fixed at an angle of attack, a. against the airflow in a wind tunnel. This airfoil creates a drag force, D, in the direction of the flow; a lift force L perpendicular to the direction of the flow; and a moment, M. around the attachment point of the airfoil. fie sign convention of moments and forces shown are positive. Lift and drag can be combined for the resultant force, R.&lt;br /&gt;
&lt;br /&gt;
FIGURE. 4-6, Wind-Tunnel Forces Acting on an Airfoil.&lt;br /&gt;
&lt;br /&gt;
The lift, L is calculated&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;L = q\cdot S\cdot C_L&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; = measured lift, lb&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt; = dynamic pressure, lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S&amp;lt;/math&amp;gt; = reference area, ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;C_L&amp;lt;/math&amp;gt; = lift coefficient, dimensionless&lt;br /&gt;
&lt;br /&gt;
The moment is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;M=q\cdot S\cdot c_m\cdot c&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Where&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;M&amp;lt;/math&amp;gt; = measured lift, lb&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt; = dynamic pressure, lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S&amp;lt;/math&amp;gt; = reference area, ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;c_m&amp;lt;/math&amp;gt; = moment coefficient, dimensionless&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;c&amp;lt;/math&amp;gt; = average chord width of the wing, ft&lt;br /&gt;
&lt;br /&gt;
The reference area, S, is defined by agreement. For streamlined bodies, the maximum body cross section is used. Airfoils use the planform of the wing, and parachutes use the canopy surface area. The selection of the wing planform and the parachute surface area as references was made for practical reasons. The wing planform for a specific wing is fixed, whereas the cross section of the wing in the direction of the flow changes with the angle of attack. Similarly, the surface area of the parachute canopy is fixed; however, the frontal projected area of the inflated parachute canopy changes with airspeed, porosity, line length, and type of parachute.&lt;br /&gt;
&lt;br /&gt;
Forces and moments acting on an airfoil or a parachute canopy may be presented in several ways. The two most frequently used methods, as shown in Figure 4-7, are with forces oriented to the axis of flight and with forces oriented to the axis of the airfoil.&lt;br /&gt;
&lt;br /&gt;
The tangential force, and the normal force, N, are calculated&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;T = C_T\cdot S\cdot q&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
and 	&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;N = C_N\cdot S\cdot q&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
C&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; = tangential force coefficient, dimensionless&lt;br /&gt;
&lt;br /&gt;
C&amp;lt;sub&amp;gt;N&amp;lt;/sub&amp;gt; = normal force coefficient, dimensionless&lt;br /&gt;
&lt;br /&gt;
The resultant force, R, and the moment, M, in both presentations have the same direction and the same magnitude. The airflow fixed system is preferred for aerodynamic performance calculations, and the airfoil fixed system for wing stress calculations. me aerodynamic coefficients C&amp;lt;sub&amp;gt;L&amp;lt;/sub&amp;gt;, C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, C&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, C&amp;lt;sub&amp;gt;N&amp;lt;/sub&amp;gt;, and C&amp;lt;sub&amp;gt;m&amp;lt;/sub&amp;gt; can easily be determined in wind•tunnel measurements.&lt;br /&gt;
&lt;br /&gt;
Figure 4-8 shows the relationship of both force systems on a parachute. By definition, a negative moment is stabilizing, as illustrated in Figure 4-8. It is interesting to note that in Europe the stabilizing moment is defined as positive. Wind-tunnel installations frequently measure normal and tangential force instead of lift and drag. If α, T, and N are known, the drag D, can be calculated&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;D=T\cdot cos(\alpha)+N\cdot sin(\alpha)&amp;lt;/math&amp;gt;For a parachute with an angle of attack, &amp;lt;math&amp;gt;\alpha&amp;lt;/math&amp;gt;, equal to zero, the drag force and the tangential force are synonymous.&lt;br /&gt;
&lt;br /&gt;
Figure 4-9 shows the coefficients C&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, and C&amp;lt;sub&amp;gt;m&amp;lt;/sub&amp;gt; versus angle of attack for stable and unstable parachutes.&lt;br /&gt;
&lt;br /&gt;
The coefficient presentation shows two interesting facts. The slope of the moment coefficient curve, dC&amp;lt;sub&amp;gt;m&amp;lt;/sub&amp;gt;/dα, for the unstable parachute is positive between -25 degrees and + 25 degrees; this is, by definition, destabilizing. This parachute will oscillate approximately ± 25&lt;br /&gt;
&lt;br /&gt;
FIGURE 4-9. Coefficients C&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, and C&amp;lt;sub&amp;gt;M&amp;lt;/sub&amp;gt; Versus Angle of Attack, α, for a Stable and Unstable Parachute.&lt;br /&gt;
&lt;br /&gt;
degrees. The slope of the moment, dC&amp;lt;sub&amp;gt;m&amp;lt;/sub&amp;gt;/dα, for the stable parachute is negative over the total angle of attack; this is, by definition, stabilizing. The steeper the negative dC&amp;lt;sub&amp;gt;m&amp;lt;/sub&amp;gt;/dα slope, the greater is the stabilizing tendency of the parachute, and the better is its damping capability against unstabilizing forces such as sudden gusts of wind.&lt;br /&gt;
&lt;br /&gt;
Figure 4-10, from Reference 4.1, demonstrates the effect of airflow around a cylinder and an airfoil. The circulation around a rotating cylinder creates lift caused by the increase in velocity on one side of the cylinder and a decrease on the opposite side. This is called the Magnus effect.&lt;br /&gt;
&lt;br /&gt;
== 4.5 EQUILIBRIUM OF FORCES IN STUDY DESCENT OR FLIGHT ==&lt;br /&gt;
&lt;br /&gt;
=== 4.5.1 Parachute in Steady Descent ===&lt;br /&gt;
A stable parachute in unaccelerated descent has an equilibrium between the total drag of the parachute and the load, Dr, and the weight of the load and the parachute assembly, WT (Figure 4-11). &lt;br /&gt;
&lt;br /&gt;
For steady descent&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
D&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; = total drag, 1b&lt;br /&gt;
&lt;br /&gt;
D&amp;lt;sub&amp;gt;P&amp;lt;/sub&amp;gt; = drag of parachute, 1b&lt;br /&gt;
&lt;br /&gt;
W&amp;lt;sub&amp;gt;C&amp;lt;/sub&amp;gt; = weight of load. 1b&lt;br /&gt;
&lt;br /&gt;
In most cases, the drag of the load can be neglected in relation to the large drag of the parachute, With drag, D — (C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;S)&amp;lt;sub&amp;gt;p&amp;lt;/sub&amp;gt; • p/2• v&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; and D&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; = W&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;. and solving for v, the important equation for rate of descent, v&amp;lt;sub&amp;gt;e&amp;lt;/sub&amp;gt;, is obtained,&lt;br /&gt;
&lt;br /&gt;
Rate of descent,&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
FIGURE 4-11. Forces Acting on a Parachute in Steady Descent.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
or in parachute terminology for rate of descent at sea level&lt;br /&gt;
&lt;br /&gt;
and rate of descent at any altitude&lt;br /&gt;
&lt;br /&gt;
For 1/, see column 4 in Table 3-3,&lt;br /&gt;
&lt;br /&gt;
In the equation for rate of descent. V&amp;lt;sub&amp;gt;e&amp;lt;/sub&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
W&amp;lt;sub&amp;gt;T =&amp;lt;/sub&amp;gt; weight of load and parachute assembly, 1b&lt;br /&gt;
&lt;br /&gt;
S&amp;lt;sub&amp;gt;o&amp;lt;/sub&amp;gt; = canopy surface area, ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
C&amp;lt;sub&amp;gt;Do&amp;lt;/sub&amp;gt; = parachute drag coefficient related to S&amp;lt;sub&amp;gt;o&amp;lt;/sub&amp;gt;&lt;br /&gt;
&lt;br /&gt;
p = air density at a specific altitude in slugs/ft&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;, as shown in Table 3-3&lt;br /&gt;
&lt;br /&gt;
During descent from altitude, the parachute system is constantly decelerated because of the increasing air density. This can be ignored for slowly descending main parachutes. However, for drogue chute systems that descend at 200 ft/s or faster, the constant deceleration may result in velocities 3 to 5% higher than the steady rate of descent.&lt;br /&gt;
&lt;br /&gt;
=== 4.5.2 Gliding Parachutes ===&lt;br /&gt;
Figure 4-12 shows the balance of forces on a gliding parachute. The total weight of the system, W&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; . must be balanced by the resultant force. R. However, a lifting force is required for glide. To satisfy the force balance&lt;br /&gt;
&lt;br /&gt;
R = C&amp;lt;sub&amp;gt;R&amp;lt;/sub&amp;gt; * S * p/2 * v&lt;br /&gt;
&lt;br /&gt;
Trajectory velocity, V&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, is calculated&lt;br /&gt;
&lt;br /&gt;
Horizontal velocity is calculated&lt;br /&gt;
&lt;br /&gt;
V&amp;lt;sub&amp;gt;H&amp;lt;/sub&amp;gt; = V&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; • cosø, and vertical velocity, v&amp;lt;sub&amp;gt;v&amp;lt;/sub&amp;gt; = V&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; • sinø&lt;br /&gt;
&lt;br /&gt;
The glide ratio is obtained from&lt;br /&gt;
&lt;br /&gt;
Analysis of Figure 4-12 indicates that the larger the ratio of lift to drag, the better the glide ratio, I./D A high resultant coefficient, C&amp;lt;sub&amp;gt;R&amp;lt;/sub&amp;gt;, results in a low glide or trajectory V&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, desirable for landing. A small C&amp;lt;sub&amp;gt;R&amp;lt;/sub&amp;gt; results in a high glide velocity, V&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, which is desirable for flying toward a target, compensating for head winds, or covering a distance quickly. Generally, gliding parachutes follow the same aerodynamic rules as low-aspect-ratio wings.&lt;br /&gt;
&lt;br /&gt;
           	   	&lt;br /&gt;
&lt;br /&gt;
FIGUR E 4-12, Forces Acting on a Gliding Parachute&lt;br /&gt;
&lt;br /&gt;
=== 4.5.3 Parasite Drag and Induced Drag ===&lt;br /&gt;
The drag acting on a lift-producing air vehicle, such as a gliding parachute or an aircraft, has two primary components: the parasite drag, D&amp;lt;sub&amp;gt;P&amp;lt;/sub&amp;gt; , and the induced drag. D&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Parasite drag is produced by the form drag from individual components such as the suspension lines, canopy, and the jumper of a gliding parachute, and the fuselage, tail sectiora, and control surfaces of an airplane. Large surfaces produce surface friction drag as part of the parasite drag.&lt;br /&gt;
&lt;br /&gt;
Induced drag is caused by the lifting action of the parachute canopy or the aircraft wing. Section 4.7 includes books with detailed discussions of induced drag.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Total drag, D&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, can be defined as&lt;br /&gt;
&lt;br /&gt;
or, in the coefficient form&lt;br /&gt;
&lt;br /&gt;
The parasite drag, D&amp;lt;sub&amp;gt;p&amp;lt;/sub&amp;gt;, and the coefficient, C&amp;lt;sub&amp;gt;DP&amp;lt;/sub&amp;gt;, can be determined in wind-tunnel tests or calculated as the sum of the individual component drags.&lt;br /&gt;
&lt;br /&gt;
The induced drag coefficient, C&amp;lt;sub&amp;gt;Di&amp;lt;/sub&amp;gt; , of a gliding parachute canopy or a wing profile can be calculated&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
C = coefficient of induced drag, dimensionless&lt;br /&gt;
&lt;br /&gt;
The expression b&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;/S is defined as the aspect ratio of a wing or parachute with the notation AR b&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;/S. Therefore&lt;br /&gt;
&lt;br /&gt;
The equation for induced drag indicates that increasing the aspect ratio, AR, reduces the induced drag coefficient,  , and therefore reduces the drag, D. ms, in turn, increases the glide ratio, L/D. Increasing the glide ratio by increasing the aspect ratio is optimized on high-performance sailplanes with aspect ratios higher than 20. Increasing the glide ratio of gliding parachutes by increasing the aspect ratio has limitations, which are discussed in section 5.9.&lt;br /&gt;
&lt;br /&gt;
=== 4.5.4 Aircraft in Horizontal Flight ===&lt;br /&gt;
Figure 4-13 shows forces and moments on an aircraft in steady, horizontal flight. In steady, horizontal flight, an equilibrium exists between all forces and moments acting on the aircraft. Lift on the wing and tail, L&amp;lt;sub&amp;gt;W&amp;lt;/sub&amp;gt; and L&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;. and the weight of the aircraft, W&amp;lt;sub&amp;gt;A&amp;lt;/sub&amp;gt;, balance in the vertical plane. Thrust, T and drag. D, balance each other in the horizontal plane, and the positive or negative moment, M, is balanced by the positive or negative lift of the tail multiplied by the moment arm, L&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
FIGURE 4-13. Forces and Moments Acting on an Aircraft in Steady night,&lt;br /&gt;
&lt;br /&gt;
Any imbalance in these forces results in descent or climb in the vertical plane or faster or slower speed in the horizontal plane. A change in the lift of the elevator initiates climb or descent. Thrust, T, is the prime contributor for climb or descent and faster or slower speed, However, a balance of forces must always be maintained for horizontal flight or steady rate oi climb or descent.&lt;br /&gt;
&lt;br /&gt;
== 4.6 WIND-TUNNEL TESTING OF PARACHUTES ==&lt;br /&gt;
Wind tunnels are an effective tool for testing air vehicles and air-vehicle components and have been used successfully for testing parachutes and parachute systems. Experience has shown that certain rules apply for the wind-tunnel testing of parachutes. Small parachutes manufactured from textiles cannot be made sufficiently similar to large parachutes in geometric design and flexibility, Lightweight material. required to obtain design similarity, is difficult to manufacture or is unobtainable.&lt;br /&gt;
&lt;br /&gt;
One cardinal rule has been established through many years of parachute wind-tunnel testing: A modification that changes the performance of a model parachute in wind-tunnel testing produces the same type and percentage of performance change in a large parachute. This rule is true for drag. stability, and opening-force characteristics.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
=== 4.6.1 Blowers ===&lt;br /&gt;
The simple air blower (Figure 4-14) is a proven tool for preliminary parachute testing of a chiefly qualitative nature. Unless special test conditions prevail, parachutes tested should be a minimum of 1.5 to 2 feet in diameter to obtain meaningful results.&lt;br /&gt;
&lt;br /&gt;
                                                                    &lt;br /&gt;
&lt;br /&gt;
 FIGURE 4-14. Typical Air Blower.&lt;br /&gt;
&lt;br /&gt;
An air blower is a preliminary test too! because it permits quick parachute• configuration changes and excellent visual observation.&lt;br /&gt;
&lt;br /&gt;
=== 4.6.2 Open-Throat, No-Return Wind Tunnels ===&lt;br /&gt;
The open-throat, no-return wind tunnel shown in Figure 4-15 permits exact measurements if parachutes of sufficient size are used. Parachutes 3 feet or more in diameter are well suited for obtaining good, quantitative test results.&lt;br /&gt;
&lt;br /&gt;
              FIGURE 4-15. Open-Throat, No-Return Wind Tunnel&lt;br /&gt;
&lt;br /&gt;
In air blowers and open-throat wind tunnels, the velocity at the skirt of the parachute (Section a-a of Figures 4-14 and 4-15) is lower than the velocity at the nozzle exit of the wind tunnel (Section b&amp;lt;sup&amp;gt;-&amp;lt;/sup&amp;gt;b of Figures 4-14 and 4-15), Care must be taken to measure the parachute test&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
velocity at Section a-a and not at Section b-b, the customary attachment point for airfoils and models.&lt;br /&gt;
&lt;br /&gt;
Wind tunnels frequently cannot test at the descent velocity of most main parachutes of 20 to 30 feet per second. Obtaining proper test results at this low is hampered by a poor velocity distribution in the wind-tunnel-test section, and by the weight of the test parachute. The latter has a tendency to pull the parachute downward, thereby providing a negative angle of attack, lusting unstable parachutes at higher presents the problem that the drag coefficient C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, of unstable parachutes is sensitive. The drag coefficient of unstable parachutes is described in section 5.2.&lt;br /&gt;
&lt;br /&gt;
An open-throat wind tunnel permits quick changes in parachute configuration, such as changing the suspension and reefing line lengths. Large open-throat wind tunnels that are not sealed against outside elements suffer atmospheric problems such as fog formation in the test section.&lt;br /&gt;
&lt;br /&gt;
=== 4.6.3 Closed-Throat, Full-Return Wind Tunnel ===&lt;br /&gt;
Figure 4-16 is a drawing of a full-return, closed-throat wind tunnel. fic full-return, closed-throat wind tunnel is generally considered best suited for obtaining good. qualitative, aerodynamic data, since it has a uniform distribution in the test section. A disadvantage is the difficulty in gaining access to the test section for changing the parachute configuration.&lt;br /&gt;
&lt;br /&gt;
FIGURE 4-16. Closed-Throat, Full-Reuurn Wind Tunnel.&lt;br /&gt;
&lt;br /&gt;
=== 4.6.4 General Comments for Wind-Tunnel Testing of Parachutes ===&lt;br /&gt;
1. Parachute models for wind-tunnel testing should be as large and as similar as possible in geometry and flexibility to full-scale parachutes. Parachutes of less than 1.5 feet in diameter usually lack geometric similarity and material flexibility, which results in inflation characteristics and dissimilar inflated shapes.&lt;br /&gt;
&lt;br /&gt;
2.  The finished dimensions of model parachutes must be measured as accurately as possible to determine the nominal diameter, Do, and the surface area, So. Model parachutes will shrink from 5 to 10% during manufacture because of sewing take-up, which results in a notable difference in the dimensions between the drawing and the completed parachute.&lt;br /&gt;
&lt;br /&gt;
3.  Wind&amp;lt;sup&amp;gt;-&amp;lt;/sup&amp;gt;tunnel tests of parachutes are excellent for comparing different models and modifications: also, they are the most effective means for measuring coefficients of lift, drag. and normal and tangential forces, as well as for determining the load coefficient, for infinite load.&lt;br /&gt;
&lt;br /&gt;
4.  In wind-tunnel tests, velocity decay does not occur during parachute inflation and operation; this is defined as testing under &amp;quot;infinite mass condition. &amp;quot; First-stage drogue chutes and parachutes with a canopy loading, W/C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;S. in excess of 100 lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; approach this condition. Low-canopy-loading main parachutes with rates of descent of 20 to 30 ft/s have a large velocity decay during opening, which requires careful interpretation of the opening-force data obtained in wind-tunnel tests.&lt;br /&gt;
&lt;br /&gt;
5.  In the past, to avoid wind-tunnel blockage and questionable test data. the diameter of a test parachute could not exceed about 5 to 6% of the wind-tunnel test section area. Recent Sandia investigations of single and clustered ribbon parachutes with wind-tunnel blockage ratios of up to 30% have resulted in correction methods that make it possible to test much larger parachutes (Reference 4.2).&lt;br /&gt;
&lt;br /&gt;
= 4.7 REFERENCE MATERIAL =&lt;br /&gt;
4.1 H. H. Hurt. Aerodynamics for Naval Aviators Navy Manual NAVWEPS 00 80T 80. Chief of Naval Operations, Aviation Training Division.&lt;br /&gt;
&lt;br /&gt;
4.2 J, M. Macha and R J. Buffington. &amp;quot;Wall-Interference Corrections for Parachutes in a Closed Wind Tunnel.&amp;quot; AIM Paper, April 1989. (AIM 89-0900-cp.)&lt;br /&gt;
&lt;br /&gt;
For readers interested in a more detailed study of aerodynamics, the following books are recommended.&lt;br /&gt;
&lt;br /&gt;
4.3 J, H, Dwinnel, Principle of Aerodynamics. McGraw-Hill     	Co., New York, 1949.&lt;br /&gt;
&lt;br /&gt;
4.4 J. Morane. Introduction to Theoretical and Computational Aerodynamics. John Wiley &amp;amp; Sons.&lt;br /&gt;
&lt;br /&gt;
4.5 R.S. Shevell. Fundamentals of Flight. Prentice-Hall. 1983.&lt;br /&gt;
&lt;br /&gt;
4.6 J. D. Anderson, Jr. Introduction to Flights, ILS Engineering and History. McGraw-Hill Book co., New York 1978.&lt;br /&gt;
&lt;br /&gt;
4.7 D. J. Cockrell. The Aerodynamics of Parachutes.&amp;quot; AGARDograph No. 6295, available from NASA Langley Research Center, M/S 1M), Hampton, Va., 236.&lt;/div&gt;</summary>
		<author><name>TuanHTruong</name></author>
	</entry>
	<entry>
		<id>https://mediawiki.aerodecelerator.org/index.php?title=Parachute_Aerodynamics&amp;diff=34</id>
		<title>Parachute Aerodynamics</title>
		<link rel="alternate" type="text/html" href="https://mediawiki.aerodecelerator.org/index.php?title=Parachute_Aerodynamics&amp;diff=34"/>
		<updated>2024-05-07T17:35:48Z</updated>

		<summary type="html">&lt;p&gt;TuanHTruong: Formatting&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&lt;br /&gt;
= CHAPTER 4: AERODYNAMICS AS RELATED TO PARACHUTES =&lt;br /&gt;
== 4.1 PROPERTIES OF THE ATMOSPHERE ==&lt;br /&gt;
All forces acting on parachutes and all movements of parachutes are affected by the atmosphere, or air, surrounding the Earth. The air at the Earth's surface is approximately 78% nitrogen; 21% oxygen; and 1% a mixture of gases such as argon, neon, helium, water vapor, and carbon dioxide. This chemical composition remains relatively constant to an altitude of about 160,000 feet (50 kilometers). The following air qualities are of major significance in the dynamics of bodies moving in the atmosphere:&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
!Air quality&lt;br /&gt;
!Symbol&lt;br /&gt;
!Dimension&lt;br /&gt;
|-&lt;br /&gt;
|Specific weight of air&lt;br /&gt;
|w&lt;br /&gt;
|lb/ft&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;, kg/m&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;&lt;br /&gt;
|-&lt;br /&gt;
|Static pressure&lt;br /&gt;
|p&lt;br /&gt;
|atm, lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;, Pa, bar, torr&lt;br /&gt;
|-&lt;br /&gt;
|Temperature&lt;br /&gt;
|T&lt;br /&gt;
|&amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F, &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;C&lt;br /&gt;
|-&lt;br /&gt;
|Mass density&lt;br /&gt;
|&amp;lt;math&amp;gt;\rho&amp;lt;/math&amp;gt;&lt;br /&gt;
|slugs/ft&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;, kg s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;/m&amp;lt;sup&amp;gt;4&amp;lt;/sup&amp;gt;&lt;br /&gt;
|-&lt;br /&gt;
|Gravity&lt;br /&gt;
|''g''&lt;br /&gt;
|ft/s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;, m/s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
|-&lt;br /&gt;
|Speed of sound&lt;br /&gt;
|C&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt;&lt;br /&gt;
|ft/s, m/s&lt;br /&gt;
|}&lt;br /&gt;
All of these qualities are altitude-dependent and may vary slightly on the Earth's surface with geographic latitude because of variations of the Earth's radius caused by the centrifugal forces of the rotation of the Earth. All standard data used herein refer to a latitude of 45 degrees. Sea level is defined as mean sea level (MSL). To compare performance data on an equal basis, the United States Bureau of Standards has defined standard day conditions as follows:&lt;br /&gt;
&lt;br /&gt;
* Temperature = 15 degrees Celsius (&amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;C) or 59 degrees Fahrenheit (&amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F)&lt;br /&gt;
* Pressure = 760 millimeters (mm) of mercury (Hg) or 29.9213 inches (in.) Hg&lt;br /&gt;
&lt;br /&gt;
=== 4.1.1 Specific Weight of Air ===&lt;br /&gt;
For standard day conditions of 59 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F temperature and a pressure of 29.9213 in. Hg, the specific weight of air, w, is 0.07648 lb/ft&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt; or 1.2250 kg/m&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;. The specific weight of air changes with pressure, temperature, and humidity. Further data can be found in References 3.4 and 4.1, and in technical handbooks.&lt;br /&gt;
&lt;br /&gt;
=== 4.1.2 Static Pressure ===&lt;br /&gt;
Static pressure depends on geographic latitude, weather conditions, and altitude. The static pressure at any altitude results from the weight of the air above that altitude. For MSL and standard day conditions, the pressure, p&amp;lt;sub&amp;gt;o&amp;lt;/sub&amp;gt;, is 29.9213 in. Hg = 760 mm Hg = 1.0 atmosphere (atm). For conversion to Pascal, torr, or bar, see the conversion tables in section 3.2.&lt;br /&gt;
&lt;br /&gt;
=== 4.1.3 Temperature ===&lt;br /&gt;
Temperatures are defined in the English and metric systems in the so-called absolute and engineering scales. The absolute temperature minimum at 0 degrees, pressure is 0 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;K = -273.16 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;C, and 0 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;R = -459.69 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F. This is also written&lt;br /&gt;
&lt;br /&gt;
* Degrees Kelvin = degrees Celsius + 273.16&lt;br /&gt;
* Degrees Rankine = degrees Fahrenheit + 459.69&lt;br /&gt;
&lt;br /&gt;
The freezing point of water is 32 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F or 0 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;C. The boiling point of water is 212 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F or 100 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;C.&lt;br /&gt;
&lt;br /&gt;
=== 4.1.4 Mass Density of Air ===&lt;br /&gt;
Mass density defines the amount of mass contained in a unit volume of air. The mass density, &amp;lt;math&amp;gt;\rho&amp;lt;/math&amp;gt;, of air is of special importance in aerodynamic calculations.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\rho = \frac{specific\ weight\ of\ air,\ w}{acceleration\ of\ gravity,\ g} = \frac{lb/ft^3}{ft/s^2} = \frac{kg\ s^2}{m^4}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;slug = \frac{weight}{acceleration\ of\ gravity} = \frac{lb}{ft/s^2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Frequently the density ratio, &amp;lt;math&amp;gt;\sigma&amp;lt;/math&amp;gt;, is used&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\sigma = \frac{ambient\ air\ density,\ \rho}{standard\ sea-level\ density, \rho_o}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The factor, &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;1/\sqrt{\rho/\rho_o}&amp;lt;/math&amp;gt;, determines the increase in parachute rate of descent with altitude. The density at 40,000 feet is ¼ of the MSL density, and the density at 100,000 feet is 1/75 of the MSL density. Therefore, the parachute rate of descent is about twice as high at 40,000 feet and about nine times as high at 100,000 feet. MSL density is 0.00237689 slugs/ft&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;, or 0.1249 kg s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;/m&amp;lt;sup&amp;gt;4&amp;lt;/sup&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
=== 4.1.5 Gravity ===&lt;br /&gt;
Any mass attracts another mass with a force called gravity. If the Earth were surrounded by a vacuum, a body suspended above the Earth and released would fall toward the center of the Earth with increasing velocity caused by the acceleration of gravity, ''g''. In reality, the falling body is decelerated by its air drag until the air drag, D, equals the weight of the body, W, and an equilibrium velocity is reached; for parachutes, this is called the steady-state rate of descent.&lt;br /&gt;
&lt;br /&gt;
The acceleration of gravity, ''g'', at sea lavel is&lt;br /&gt;
&lt;br /&gt;
* ''g'' = 32.174 ft/s2 or 9.80665 m/s2.&lt;br /&gt;
&lt;br /&gt;
The value g = 9.08665 m/s is standardized internationally but is accurate only for a latitude of 45 degrees.&lt;br /&gt;
&lt;br /&gt;
With increasing altitude above the Earth's surface, the acceleration of gravity decreases in accordance with the equation&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;g = g_o(\frac{r}{r+h})^2&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
* ''g'' = acceleration of gravity at any altitude, ft/s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
* g&amp;lt;sub&amp;gt;o&amp;lt;/sub&amp;gt; = acceleration of gravity at sea level, ft/s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
* r = average Earth radius = 2.08556 x 10&amp;lt;sup&amp;gt;7&amp;lt;/sup&amp;gt; ft&lt;br /&gt;
* h = altitude above sea level, ft&lt;br /&gt;
&lt;br /&gt;
For other planets and heavenly bodies, the acceleration of gravity varies with the mass of the body. For example, the acceleration of gravity on Mars is about 1/3 of the acceleration of gravity on Earth. For more details on planets and heavenly bodies, see page XII of Reference 2.1.&lt;br /&gt;
&lt;br /&gt;
=== 4.1.6 Kinematic Viscosity ===&lt;br /&gt;
The coefficient of viscosity, &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt;, defines the shearing stresses in a gas or liquid and is sometimes called the resistance to continuous deformation. In aerodynamics, the coefficient of viscosity is combined with the mass density to form the kinematic viscosity, &amp;lt;math&amp;gt;\nu&amp;lt;/math&amp;gt;, where&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\nu = \frac{coefficient\ of\ viscosity,\ \mu}{mass\ density,\ \rho} = 0.0001576\ ft^2/s\ at\ sea\ level&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The kinematic viscosity, &amp;lt;math&amp;gt;\nu&amp;lt;/math&amp;gt;, is altitude dependent and is used to calculate the Reynolds number, Re.&lt;br /&gt;
&lt;br /&gt;
=== 4.1.7 Reynolds Number ===&lt;br /&gt;
The Reynolds number, Re, defines the relationship of mass forces to viscous friction forces in liquids and gases. It is calculated as&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Re = \frac{v\cdot l}{\nu} = \frac{velocity\ (ft/s)\cdot characteristic\ length\ (ft)}{kinematic\ viscosity\ (ft^2/s)}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Reynolds number is an important criterion in subsonic, noncompressible flow, and allows comparison of model tests with full-scale flight tests. A Reynolds number effect on parachutes working in separated, turbulent flow has not yet been established, as shown in section 5.2. The following chart shows the Reynolds numbers for various air vehicles.&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
!Subject&lt;br /&gt;
!Insect&lt;br /&gt;
!Glider&lt;br /&gt;
!DC-3&lt;br /&gt;
!B-747&lt;br /&gt;
!Drogue&lt;br /&gt;
Chute&lt;br /&gt;
!Main &lt;br /&gt;
Parachute&lt;br /&gt;
!WTT&lt;br /&gt;
Model&lt;br /&gt;
|-&lt;br /&gt;
|Re&lt;br /&gt;
|6 • 10&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;&lt;br /&gt;
|2.5 • 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&lt;br /&gt;
|24 • 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&lt;br /&gt;
|100 • 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&lt;br /&gt;
|50 • 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&lt;br /&gt;
|20 • 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&lt;br /&gt;
|2 • 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
=== 4.1.8 Mach Number ===&lt;br /&gt;
Mach number is an important parameter of supersonic flight; it states how much faster than the speed of sound the air vehicle travels.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Mach\ number,\ M = \frac{flight\ velocity,\ v}{speed\ of\ sound, c_s}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The speed of sound is the velocity at which a pressure disturbance, such as the sound of the human voice, travels in any medium. The speed of sound varies considerably in different gases, liquids, and metals.&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|Speed of sound in air in MSL&lt;br /&gt;
|C&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt; = 1116.46 ft/s = 340.38 m/s&lt;br /&gt;
|-&lt;br /&gt;
|Speed of sound in water&lt;br /&gt;
|C&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt; = 4749 ft/s = 1461.21 m/s&lt;br /&gt;
|-&lt;br /&gt;
|Speed of sound in iron&lt;br /&gt;
|C&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt; = 16,410 ft/s = 5710.7 m/s&lt;br /&gt;
|}&lt;br /&gt;
The speed of sound depends on temperature and the chemical composition of the medium, A widely used equation for speed of sound in air is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;C_s = 41.4\sqrt{\gamma\cdot T}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
* &amp;lt;math&amp;gt;C_s&amp;lt;/math&amp;gt; = speed of sound in dry air, ft/s&lt;br /&gt;
* &amp;lt;math&amp;gt;\gamma&amp;lt;/math&amp;gt; = ratio of specific heat, equal to 1.4 for dry air, dimensionless&lt;br /&gt;
* &amp;lt;math&amp;gt;T&amp;lt;/math&amp;gt; = temperature in Fahrenheit absolute, equal to 459.67 + &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F&lt;br /&gt;
&lt;br /&gt;
The speed of sound changes with altitude, as temperature (see Figure 3-1). The drag of streamlined bodies such as missiles, airfoils, and airplanes increases considerably as their velocities approach Mach 1. Depending on the configuration of the body, supersonic compressibility effects may occur in the 0.75 to 0.85 Mach range, causing local supersonic flow, shock waves, flow separation, and concomitant increases in drag and changes in stability.&lt;br /&gt;
&lt;br /&gt;
Parachutes that operate in separated flow over the entire velocity range do not show the typical drag increase when operating close to or beyond Mach 1. Supersonic parachute behavior is discussed in detail in section 5.8.&lt;br /&gt;
&lt;br /&gt;
== '''4.2 CONTINUITY LAW AND BERNOULLI EQUATION''' ==&lt;br /&gt;
&lt;br /&gt;
=== 4.2.1 Continuity L.aw ===&lt;br /&gt;
Air is thought to flow in layers called streamlines. Figure 4-1 shows streamlines as layers of air without air transfer between individual layers. ne air is shown as being incompressible, a valid assumption for subsonic flow.&lt;br /&gt;
&lt;br /&gt;
[Insert Figure 4-1] 	&lt;br /&gt;
&lt;br /&gt;
If exchange of air does not occur across the streamline boundaries, the amount of air entering the streamline at point 1 must also exit at point 2, as shown in Figure 4-1. Because the cross section at point 2 is smaller than the cross section at point 1, the air must exit at a higher velocity. The following equation defines this condition:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;v_1\cdot S_1\cdot \rho_1 = v_2\cdot S_2\cdot \rho_2&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S&amp;lt;/math&amp;gt; = cross section of the streamline&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;v&amp;lt;/math&amp;gt; = velocity in the streamline&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\rho&amp;lt;/math&amp;gt; = density of the air flowing in the streamline&lt;br /&gt;
&lt;br /&gt;
This equation, which governs the flow in and around a body in gases and liquids, is important in aerodynamics and is called the Continuity Law. For incompressible subsonic flow, it can be simplified to &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;v_1\cdot S_1 = v_2\cdot S_2&amp;lt;/math&amp;gt; &lt;br /&gt;
&lt;br /&gt;
Whenever the cross section narrows, the velocity increases; when the cross section widens, the velocity decreases.&lt;br /&gt;
&lt;br /&gt;
=== 4.2.2 Bernoulli Equation ===&lt;br /&gt;
Figure 4-2 illustrates a streamline with the cross section, S, the velocity, v, and the pressure, p. If the air is incompressible, the downstream is v + Av. and the pressure is p + AP. If the air is inviscid, the inertia forces caused by the acceleration of air from v to v + Av must be balanced by differential pressure forces.&lt;br /&gt;
&lt;br /&gt;
[Insert Figure 4-2]FIGURE 4-2 Pressure and Velocity Distribution in a Streamline Element. 	&lt;br /&gt;
&lt;br /&gt;
The following equation can be written&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;p\cdot S-(p+\Delta p)S = m\cdot \frac{dv}{dt}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Simplified, the above equation yields&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;dp = - \rho vdv&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
and&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;p = - \frac{1}{2}\rho v^2 + C&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The above equation allows the following consideration: If p is pressure, then &amp;lt;math&amp;gt;1/2\ \rho v^2&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;C&amp;lt;/math&amp;gt; must also be pressure. The equation &amp;lt;math&amp;gt;1/2\ \rho v^2&amp;lt;/math&amp;gt; includes a velocity and is referred to as the dynamic pressure, or sometimes as velocity or impact pressure.&lt;br /&gt;
&lt;br /&gt;
Pressure, &amp;lt;math&amp;gt;p&amp;lt;/math&amp;gt;, is defined as static pressure; &amp;lt;math&amp;gt;1/2\ \rho v^2&amp;lt;/math&amp;gt; as dynamic pressure; and the sum of both, &amp;lt;math&amp;gt;C&amp;lt;/math&amp;gt;, as the total pressure or&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;p+\frac{1}{2} \rho v^2 = H&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
and&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;p_1 + \frac{1}{2} \rho {v_1}^2 = p_2 + \frac{1}{2} \rho {v_2}^2&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;H&amp;lt;/math&amp;gt; is the total pressure of the system, lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Dynamic pressure, &amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt;, is a frequently used quantity in aerodynamics:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;q = \frac{1}{2} \rho v^2&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
* &amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt; = dynamic pressure, lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
* &amp;lt;math&amp;gt;\rho&amp;lt;/math&amp;gt; =  air density, slugs/ft&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;&lt;br /&gt;
* &amp;lt;math&amp;gt;v&amp;lt;/math&amp;gt; =  velocity at a point of undisturbed flow, ft/s&lt;br /&gt;
&lt;br /&gt;
The following formulas are used for calculating the sea-level dynamic pressure if the velocity is given in ft/s, knots, mph, or km/h, respectively:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;q=\frac{v^2}{841.4}(ft/s), q=\frac{v^2}{295}(knots), q=\frac{v^2}{391.2}(mph), q=\frac{v^2}{1013.1}(km/h)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
                                              &lt;br /&gt;
&lt;br /&gt;
== '''4.3 NEWTON'S THREE OF MOTION''' ==&lt;br /&gt;
Engineering mechanics are governed by the following three laws of Isaac Newton:&lt;br /&gt;
&lt;br /&gt;
1.  A body remains at rest or in an unaccelerated state of motion unless acted upon.&lt;br /&gt;
&lt;br /&gt;
2.  A force acting upon a body will produce an acceleration in the direction of the force.&lt;br /&gt;
&lt;br /&gt;
3.  An action in one direction will produce an equal reaction in the opposite direction.&lt;br /&gt;
&lt;br /&gt;
The first law is self-explanatory. The second law may be expressed by the equation&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;F=m\cdot a&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;F&amp;lt;/math&amp;gt; = force in pounds acting on the mass, lb&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;m&amp;lt;/math&amp;gt; = mass of body that the force is acting upon, slugs&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; = acceleration in ft/s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; resulting from the force, F&lt;br /&gt;
&lt;br /&gt;
The mass, m, of a body is obtained by&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;m=\frac{W}{g}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;W&amp;lt;/math&amp;gt; = weight of the body, lb&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;g&amp;lt;/math&amp;gt; = acceleration of gravity, ft/s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The mass, therefore, has the dimension of&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;m = \frac{W}{g}=\frac{lb}{ft/s^2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
This unit of mass is the slug.&lt;br /&gt;
&lt;br /&gt;
The equation of Newton's second law can now be written&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;F=\frac{W}{g}\cdot a,\ or\ F=W\frac{a}{g}&amp;lt;/math&amp;gt; 	&lt;br /&gt;
&lt;br /&gt;
The factor a/g is frequently called the load factor, G, and tells how much larger a force is than a force equivalent to the weight of the body. It is customary in parachute work to state that the maximum parachute force allowed is G • W or (a/g) • W. It is appropriate to write&lt;br /&gt;
&lt;br /&gt;
Maximum allowable parachute force, &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;F=W\frac{a}{g},\ or\ W\cdot G&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Figure 4-3 illustrates Newton's third law, explaining the principle of the rocket that can produce thrust in a perfect vacuum.&lt;br /&gt;
&lt;br /&gt;
A mass, m, ejected from a rocket at the velocity, v, per unit time, t, will produce a force, F, which in turn will create a reaction force, R, of equal magnitude but acting in the opposite direction.&lt;br /&gt;
&lt;br /&gt;
== 4.4 FORCES ACTING ON A BODY MOVING THROUGH AIR ==&lt;br /&gt;
&lt;br /&gt;
=== 4.4.1 Symmetrical Body ===&lt;br /&gt;
A body moving through air experiences forces caused by air pressure acting on the body. The same forces if the body moves through air, such as a descending parachute, or if the body is fixed and the air moves against the body, such as a parachute or an airfoil in a wind tunnel (Figure 44).&lt;br /&gt;
&lt;br /&gt;
         	 &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
A stable parachute in a wind tunnel experiences only the force called &amp;quot;drag&amp;quot; in the direction of the airflow. drag force, D, is calculated to&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;D=q\cdot S\cdot C_D&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;D&amp;lt;/math&amp;gt; = drag, lb&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt; = dynamic pressure, lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S&amp;lt;/math&amp;gt; = total surface area of the parachute canopy, ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;C_D&amp;lt;/math&amp;gt; = coefficient of drag,  dimensionless&lt;br /&gt;
&lt;br /&gt;
The dynamic pressure, q, can be calculated from section 4.2.2. The surface area of the canopy, S, is selected as a reference area. The drag coefficient, C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, is a form factor that indicates the drag characteristic of a specific shape. Most aerodynamic bodies are designed for low drag or a low drag coefficient. Parachutes, generally, are designed for high drag; therefore, a high drag coefficient is desirable. this difference in drag is demonstrated by the two bodies shown in Figure 4-5.&lt;br /&gt;
&lt;br /&gt;
            	&lt;br /&gt;
&lt;br /&gt;
Both bodies have the same cross section perpendicular to the airflow. The cylindrical. streamlined body has a smooth airflow over its total body length, resulting in a drag coefficient. C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, of 0.05 to 0.1, depending on slenderness ratio, surface roughness, and shape. The drag coefficient of all streamlined bodies is much affected by Reynolds number and Mach number. The open hemisphere, which is similar to a parachute canopy, has a drag coefficient, C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, of 1.3 to 1.4 for the same body cross section. The difference in drag is explained by the smooth airflow around the streamlined body and a separated, turbulent flow around the open hemisphere. The drag of bodies with separated flow, like parachute canopies, is little affected by Reynolds number.&lt;br /&gt;
&lt;br /&gt;
=== 4.4.2 Airflow Around an Asymmetrical Body (Airfoil) ===&lt;br /&gt;
Figure 4-6 shows an airfoil fixed at an angle of attack, a. against the airflow in a wind tunnel. This airfoil creates a drag force, D, in the direction of the flow; a lift force L perpendicular to the direction of the flow; and a moment, M. around the attachment point of the airfoil. fie sign convention of moments and forces shown are positive. Lift and drag can be combined for the resultant force, R.&lt;br /&gt;
&lt;br /&gt;
FIGURE. 4-6, Wind-Tunnel Forces Acting on an Airfoil.&lt;br /&gt;
&lt;br /&gt;
The lift, L is calculated&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;L = q\cdot S\cdot C_L&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; = measured lift, lb&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt; = dynamic pressure, lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S&amp;lt;/math&amp;gt; = reference area, ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;C_L&amp;lt;/math&amp;gt; = lift coefficient, dimensionless&lt;br /&gt;
&lt;br /&gt;
The moment is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;M=q\cdot S\cdot c_m\cdot c&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Where&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;M&amp;lt;/math&amp;gt; = measured lift, lb&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt; = dynamic pressure, lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S&amp;lt;/math&amp;gt; = reference area, ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;c_m&amp;lt;/math&amp;gt; = moment coefficient, dimensionless&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;c&amp;lt;/math&amp;gt; = average chord width of the wing, ft&lt;br /&gt;
&lt;br /&gt;
The reference area, S, is defined by agreement. For streamlined bodies, the maximum body cross section is used. Airfoils use the planform of the wing, and parachutes use the canopy surface area. The selection of the wing planform and the parachute surface area as references was made for practical reasons. The wing planform for a specific wing is fixed, whereas the cross section of the wing in the direction of the flow changes with the angle of attack. Similarly, the surface area of the parachute canopy is fixed; however, the frontal projected area of the inflated parachute canopy changes with airspeed, porosity, line length, and type of parachute.&lt;br /&gt;
&lt;br /&gt;
Forces and moments acting on an airfoil or a parachute canopy may be presented in several ways. The two most frequently used methods, as shown in Figure 4-7, are with forces oriented to the axis of flight and with forces oriented to the axis of the airfoil.&lt;br /&gt;
&lt;br /&gt;
The tangential force, and the normal force, N, are calculated&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;T = C_T\cdot S\cdot q&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
and 	&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;N = C_N\cdot S\cdot q&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
C&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; = tangential force coefficient, dimensionless&lt;br /&gt;
&lt;br /&gt;
C&amp;lt;sub&amp;gt;N&amp;lt;/sub&amp;gt; = normal force coefficient, dimensionless&lt;br /&gt;
&lt;br /&gt;
The resultant force, R, and the moment, M, in both presentations have the same direction and the same magnitude. The airflow fixed system is preferred for aerodynamic performance calculations, and the airfoil fixed system for wing stress calculations. me aerodynamic coefficients C&amp;lt;sub&amp;gt;L&amp;lt;/sub&amp;gt;, C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, C&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, C&amp;lt;sub&amp;gt;N&amp;lt;/sub&amp;gt;, and C&amp;lt;sub&amp;gt;m&amp;lt;/sub&amp;gt; can easily be determined in wind•tunnel measurements.&lt;br /&gt;
&lt;br /&gt;
Figure 4-8 shows the relationship of both force systems on a parachute. By definition, a negative moment is stabilizing, as illustrated in Figure 4-8. It is interesting to note that in Europe the stabilizing moment is defined as positive. Wind-tunnel installations frequently measure normal and tangential force instead of lift and drag. If α, T, and N are known, the drag D, can be calculated&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;D=T\cdot cos(\alpha)+N\cdot sin(\alpha)&amp;lt;/math&amp;gt;For a parachute with an angle of attack, &amp;lt;math&amp;gt;\alpha&amp;lt;/math&amp;gt;, equal to zero, the drag force and the tangential force are synonymous.&lt;br /&gt;
&lt;br /&gt;
Figure 4-9 shows the coefficients C&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, and C&amp;lt;sub&amp;gt;m&amp;lt;/sub&amp;gt; versus angle of attack for stable and unstable parachutes.&lt;br /&gt;
&lt;br /&gt;
The coefficient presentation shows two interesting facts. The slope of the moment coefficient curve, dC&amp;lt;sub&amp;gt;m&amp;lt;/sub&amp;gt;/dα, for the unstable parachute is positive between -25 degrees and + 25 degrees; this is, by definition, destabilizing. This parachute will oscillate approximately ± 25&lt;br /&gt;
&lt;br /&gt;
FIGURE 4-9. Coefficients C&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, and C&amp;lt;sub&amp;gt;M&amp;lt;/sub&amp;gt; Versus Angle of Attack, α, for a Stable and Unstable Parachute.&lt;br /&gt;
&lt;br /&gt;
degrees. The slope of the moment, dC&amp;lt;sub&amp;gt;m&amp;lt;/sub&amp;gt;/dα, for the stable parachute is negative over the total angle of attack; this is, by definition, stabilizing. The steeper the negative dC&amp;lt;sub&amp;gt;m&amp;lt;/sub&amp;gt;/dα slope, the greater is the stabilizing tendency of the parachute, and the better is its damping capability against unstabilizing forces such as sudden gusts of wind.&lt;br /&gt;
&lt;br /&gt;
Figure 4-10, from Reference 4.1, demonstrates the effect of airflow around a cylinder and an airfoil. The circulation around a rotating cylinder creates lift caused by the increase in velocity on one side of the cylinder and a decrease on the opposite side. This is called the Magnus effect.&lt;br /&gt;
&lt;br /&gt;
= 4.5 EQUILIBRIUM OF FORCES IN STUDY DESCENT OR FLIGHT =&lt;br /&gt;
&lt;br /&gt;
=== 4.5.1 Parachute in Steady Descent ===&lt;br /&gt;
A stable parachute in unaccelerated descent has an equilibrium between the total drag of the parachute and the load, Dr, and the weight of the load and the parachute assembly, WT (Figure 4-11). For steady descent&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
D&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; = total drag, 1b&lt;br /&gt;
&lt;br /&gt;
D&amp;lt;sub&amp;gt;P&amp;lt;/sub&amp;gt; = drag of parachute, 1b&lt;br /&gt;
&lt;br /&gt;
W&amp;lt;sub&amp;gt;C&amp;lt;/sub&amp;gt; = weight of load. 1b&lt;br /&gt;
&lt;br /&gt;
In most cases, the drag of the load can be neglected in relation to the large drag of the parachute, With drag, D — (C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;S)&amp;lt;sub&amp;gt;p&amp;lt;/sub&amp;gt; • p/2• v&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; and D&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; = W&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;. and solving for v, the important equation for rate of descent, v&amp;lt;sub&amp;gt;e&amp;lt;/sub&amp;gt;, is obtained,&lt;br /&gt;
&lt;br /&gt;
Rate of descent,&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
FIGURE 4-11. Forces Acting on a Parachute in Steady Descent.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
or in parachute terminology for rate of descent at sea level&lt;br /&gt;
&lt;br /&gt;
and rate of descent at any altitude&lt;br /&gt;
&lt;br /&gt;
For 1/, see column 4 in Table 3-3,&lt;br /&gt;
&lt;br /&gt;
In the equation for rate of descent. V&amp;lt;sub&amp;gt;e&amp;lt;/sub&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
W&amp;lt;sub&amp;gt;T =&amp;lt;/sub&amp;gt; weight of load and parachute assembly, 1b&lt;br /&gt;
&lt;br /&gt;
S&amp;lt;sub&amp;gt;o&amp;lt;/sub&amp;gt; = canopy surface area, ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
C&amp;lt;sub&amp;gt;Do&amp;lt;/sub&amp;gt; = parachute drag coefficient related to S&amp;lt;sub&amp;gt;o&amp;lt;/sub&amp;gt;&lt;br /&gt;
&lt;br /&gt;
p = air density at a specific altitude in slugs/ft&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;, as shown in Table 3-3&lt;br /&gt;
&lt;br /&gt;
During descent from altitude, the parachute system is constantly decelerated because of the increasing air density. This can be ignored for slowly descending main parachutes. However, for drogue chute systems that descend at 200 ft/s or faster, the constant deceleration may result in velocities 3 to 5% higher than the steady rate of descent.&lt;br /&gt;
&lt;br /&gt;
=== 4.5.2 Gliding Parachutes ===&lt;br /&gt;
Figure 4-12 shows the balance of forces on a gliding parachute. The total weight of the system, W&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; . must be balanced by the resultant force. R. However, a lifting force is required for glide. To satisfy the force balance&lt;br /&gt;
&lt;br /&gt;
R = C&amp;lt;sub&amp;gt;R&amp;lt;/sub&amp;gt; * S * p/2 * v&lt;br /&gt;
&lt;br /&gt;
Trajectory velocity, V&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, is calculated&lt;br /&gt;
&lt;br /&gt;
Horizontal velocity is calculated&lt;br /&gt;
&lt;br /&gt;
V&amp;lt;sub&amp;gt;H&amp;lt;/sub&amp;gt; = V&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; • cosø, and vertical velocity, v&amp;lt;sub&amp;gt;v&amp;lt;/sub&amp;gt; = V&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; • sinø&lt;br /&gt;
&lt;br /&gt;
The glide ratio is obtained from&lt;br /&gt;
&lt;br /&gt;
Analysis of Figure 4-12 indicates that the larger the ratio of lift to drag, the better the glide ratio, I./D A high resultant coefficient, C&amp;lt;sub&amp;gt;R&amp;lt;/sub&amp;gt;, results in a low glide or trajectory V&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, desirable for landing. A small C&amp;lt;sub&amp;gt;R&amp;lt;/sub&amp;gt; results in a high glide velocity, V&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, which is desirable for flying toward a target, compensating for head winds, or covering a distance quickly. Generally, gliding parachutes follow the same aerodynamic rules as low-aspect-ratio wings.&lt;br /&gt;
&lt;br /&gt;
           	   	&lt;br /&gt;
&lt;br /&gt;
FIGUR E 4-12, Forces Acting on a Gliding Parachute&lt;br /&gt;
&lt;br /&gt;
=== 4.5.3 Parasite Drag and Induced Drag ===&lt;br /&gt;
The drag acting on a lift-producing air vehicle, such as a gliding parachute or an aircraft, has two primary components: the parasite drag, D&amp;lt;sub&amp;gt;P&amp;lt;/sub&amp;gt; , and the induced drag. D&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Parasite drag is produced by the form drag from individual components such as the suspension lines, canopy, and the jumper of a gliding parachute, and the fuselage, tail sectiora, and control surfaces of an airplane. Large surfaces produce surface friction drag as part of the parasite drag.&lt;br /&gt;
&lt;br /&gt;
Induced drag is caused by the lifting action of the parachute canopy or the aircraft wing. Section 4.7 includes books with detailed discussions of induced drag.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Total drag, D&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, can be defined as&lt;br /&gt;
&lt;br /&gt;
or, in the coefficient form&lt;br /&gt;
&lt;br /&gt;
The parasite drag, D&amp;lt;sub&amp;gt;p&amp;lt;/sub&amp;gt;, and the coefficient, C&amp;lt;sub&amp;gt;DP&amp;lt;/sub&amp;gt;, can be determined in wind-tunnel tests or calculated as the sum of the individual component drags.&lt;br /&gt;
&lt;br /&gt;
The induced drag coefficient, C&amp;lt;sub&amp;gt;Di&amp;lt;/sub&amp;gt; , of a gliding parachute canopy or a wing profile can be calculated&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
C = coefficient of induced drag, dimensionless&lt;br /&gt;
&lt;br /&gt;
The expression b&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;/S is defined as the aspect ratio of a wing or parachute with the notation AR b&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;/S. Therefore&lt;br /&gt;
&lt;br /&gt;
The equation for induced drag indicates that increasing the aspect ratio, AR, reduces the induced drag coefficient,  , and therefore reduces the drag, D. ms, in turn, increases the glide ratio, L/D. Increasing the glide ratio by increasing the aspect ratio is optimized on high-performance sailplanes with aspect ratios higher than 20. Increasing the glide ratio of gliding parachutes by increasing the aspect ratio has limitations, which are discussed in section 5.9.&lt;br /&gt;
&lt;br /&gt;
=== 4.5.4 Aircraft in Horizontal Flight ===&lt;br /&gt;
Figure 4-13 shows forces and moments on an aircraft in steady, horizontal flight. In steady, horizontal flight, an equilibrium exists between all forces and moments acting on the aircraft. Lift on the wing and tail, L&amp;lt;sub&amp;gt;W&amp;lt;/sub&amp;gt; and L&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;. and the weight of the aircraft, W&amp;lt;sub&amp;gt;A&amp;lt;/sub&amp;gt;, balance in the vertical plane. Thrust, T and drag. D, balance each other in the horizontal plane, and the positive or negative moment, M, is balanced by the positive or negative lift of the tail multiplied by the moment arm, L&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
FIGURE 4-13. Forces and Moments Acting on an Aircraft in Steady night,&lt;br /&gt;
&lt;br /&gt;
Any imbalance in these forces results in descent or climb in the vertical plane or faster or slower speed in the horizontal plane. A change in the lift of the elevator initiates climb or descent. Thrust, T, is the prime contributor for climb or descent and faster or slower speed, However, a balance of forces must always be maintained for horizontal flight or steady rate oi climb or descent.&lt;br /&gt;
&lt;br /&gt;
== 4.6 WIND-TUNNEL TESTING OF PARACHUTES ==&lt;br /&gt;
Wind tunnels are an effective tool for testing air vehicles and air-vehicle components and have been used successfully for testing parachutes and parachute systems. Experience has shown that certain rules apply for the wind-tunnel testing of parachutes. Small parachutes manufactured from textiles cannot be made sufficiently similar to large parachutes in geometric design and flexibility, Lightweight material. required to obtain design similarity, is difficult to manufacture or is unobtainable.&lt;br /&gt;
&lt;br /&gt;
One cardinal rule has been established through many years of parachute wind-tunnel testing: A modification that changes the performance of a model parachute in wind-tunnel testing produces the same type and percentage of performance change in a large parachute. This rule is true for drag. stability, and opening-force characteristics.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
=== 4.6.1 Blowers ===&lt;br /&gt;
The simple air blower (Figure 4-14) is a proven tool for preliminary parachute testing of a chiefly qualitative nature. Unless special test conditions prevail, parachutes tested should be a minimum of 1.5 to 2 feet in diameter to obtain meaningful results.&lt;br /&gt;
&lt;br /&gt;
                                                                    &lt;br /&gt;
&lt;br /&gt;
 FIGURE 4-14. Typical Air Blower.&lt;br /&gt;
&lt;br /&gt;
An air blower is a preliminary test too! because it permits quick parachute• configuration changes and excellent visual observation.&lt;br /&gt;
&lt;br /&gt;
=== 4.6.2 Open-Throat, No-Return Wind Tunnels ===&lt;br /&gt;
The open-throat, no-return wind tunnel shown in Figure 4-15 permits exact measurements if parachutes of sufficient size are used. Parachutes 3 feet or more in diameter are well suited for obtaining good, quantitative test results.&lt;br /&gt;
&lt;br /&gt;
              FIGURE 4-15. Open-Throat, No-Return Wind Tunnel&lt;br /&gt;
&lt;br /&gt;
In air blowers and open-throat wind tunnels, the velocity at the skirt of the parachute (Section a-a of Figures 4-14 and 4-15) is lower than the velocity at the nozzle exit of the wind tunnel (Section b&amp;lt;sup&amp;gt;-&amp;lt;/sup&amp;gt;b of Figures 4-14 and 4-15), Care must be taken to measure the parachute test&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
velocity at Section a-a and not at Section b-b, the customary attachment point for airfoils and models.&lt;br /&gt;
&lt;br /&gt;
Wind tunnels frequently cannot test at the descent velocity of most main parachutes of 20 to 30 feet per second. Obtaining proper test results at this low is hampered by a poor velocity distribution in the wind-tunnel-test section, and by the weight of the test parachute. The latter has a tendency to pull the parachute downward, thereby providing a negative angle of attack, lusting unstable parachutes at higher presents the problem that the drag coefficient C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, of unstable parachutes is sensitive. The drag coefficient of unstable parachutes is described in section 5.2.&lt;br /&gt;
&lt;br /&gt;
An open-throat wind tunnel permits quick changes in parachute configuration, such as changing the suspension and reefing line lengths. Large open-throat wind tunnels that are not sealed against outside elements suffer atmospheric problems such as fog formation in the test section.&lt;br /&gt;
&lt;br /&gt;
=== 4.6.3 Closed-Throat, Full-Return Wind Tunnel ===&lt;br /&gt;
Figure 4-16 is a drawing of a full-return, closed-throat wind tunnel. fic full-return, closed-throat wind tunnel is generally considered best suited for obtaining good. qualitative, aerodynamic data, since it has a uniform distribution in the test section. A disadvantage is the difficulty in gaining access to the test section for changing the parachute configuration.&lt;br /&gt;
&lt;br /&gt;
FIGURE 4-16. Closed-Throat, Full-Reuurn Wind Tunnel.&lt;br /&gt;
&lt;br /&gt;
=== 4.6.4 General Comments for Wind-Tunnel Testing of Parachutes ===&lt;br /&gt;
1. Parachute models for wind-tunnel testing should be as large and as similar as possible in geometry and flexibility to full-scale parachutes. Parachutes of less than 1.5 feet in diameter usually lack geometric similarity and material flexibility, which results in inflation characteristics and dissimilar inflated shapes.&lt;br /&gt;
&lt;br /&gt;
2.  The finished dimensions of model parachutes must be measured as accurately as possible to determine the nominal diameter, Do, and the surface area, So. Model parachutes will shrink from 5 to 10% during manufacture because of sewing take-up, which results in a notable difference in the dimensions between the drawing and the completed parachute.&lt;br /&gt;
&lt;br /&gt;
3.  Wind&amp;lt;sup&amp;gt;-&amp;lt;/sup&amp;gt;tunnel tests of parachutes are excellent for comparing different models and modifications: also, they are the most effective means for measuring coefficients of lift, drag. and normal and tangential forces, as well as for determining the load coefficient, for infinite load.&lt;br /&gt;
&lt;br /&gt;
4.  In wind-tunnel tests, velocity decay does not occur during parachute inflation and operation; this is defined as testing under &amp;quot;infinite mass condition. &amp;quot; First-stage drogue chutes and parachutes with a canopy loading, W/C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;S. in excess of 100 lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; approach this condition. Low-canopy-loading main parachutes with rates of descent of 20 to 30 ft/s have a large velocity decay during opening, which requires careful interpretation of the opening-force data obtained in wind-tunnel tests.&lt;br /&gt;
&lt;br /&gt;
5.  In the past, to avoid wind-tunnel blockage and questionable test data. the diameter of a test parachute could not exceed about 5 to 6% of the wind-tunnel test section area. Recent Sandia investigations of single and clustered ribbon parachutes with wind-tunnel blockage ratios of up to 30% have resulted in correction methods that make it possible to test much larger parachutes (Reference 4.2).&lt;br /&gt;
&lt;br /&gt;
= 4.7 REFERENCE MATERIAL =&lt;br /&gt;
4.1 H. H. Hurt. Aerodynamics for Naval Aviators Navy Manual NAVWEPS 00 80T 80. Chief of Naval Operations, Aviation Training Division.&lt;br /&gt;
&lt;br /&gt;
4.2 J, M. Macha and R J. Buffington. &amp;quot;Wall-Interference Corrections for Parachutes in a Closed Wind Tunnel.&amp;quot; AIM Paper, April 1989. (AIM 89-0900-cp.)&lt;br /&gt;
&lt;br /&gt;
For readers interested in a more detailed study of aerodynamics, the following books are recommended.&lt;br /&gt;
&lt;br /&gt;
4.3 J, H, Dwinnel, Principle of Aerodynamics. McGraw-Hill     	Co., New York, 1949.&lt;br /&gt;
&lt;br /&gt;
4.4 J. Morane. Introduction to Theoretical and Computational Aerodynamics. John Wiley &amp;amp; Sons.&lt;br /&gt;
&lt;br /&gt;
4.5 R.S. Shevell. Fundamentals of Flight. Prentice-Hall. 1983.&lt;br /&gt;
&lt;br /&gt;
4.6 J. D. Anderson, Jr. Introduction to Flights, ILS Engineering and History. McGraw-Hill Book co., New York 1978.&lt;br /&gt;
&lt;br /&gt;
4.7 D. J. Cockrell. The Aerodynamics of Parachutes.&amp;quot; AGARDograph No. 6295, available from NASA Langley Research Center, M/S 1M), Hampton, Va., 236.&lt;/div&gt;</summary>
		<author><name>TuanHTruong</name></author>
	</entry>
	<entry>
		<id>https://mediawiki.aerodecelerator.org/index.php?title=Parachute_Aerodynamics&amp;diff=33</id>
		<title>Parachute Aerodynamics</title>
		<link rel="alternate" type="text/html" href="https://mediawiki.aerodecelerator.org/index.php?title=Parachute_Aerodynamics&amp;diff=33"/>
		<updated>2024-05-07T17:32:36Z</updated>

		<summary type="html">&lt;p&gt;TuanHTruong: Formatting&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&lt;br /&gt;
= CHAPTER 4: AERODYNAMICS AS RELATED TO PARACHUTES =&lt;br /&gt;
== 4.1 PROPERTIES OF THE ATMOSPHERE ==&lt;br /&gt;
All forces acting on parachutes and all movements of parachutes are affected by the atmosphere, or air, surrounding the Earth. The air at the Earth's surface is approximately 78% nitrogen; 21% oxygen; and 1% a mixture of gases such as argon, neon, helium, water vapor, and carbon dioxide. This chemical composition remains relatively constant to an altitude of about 160,000 feet (50 kilometers). The following air qualities are of major significance in the dynamics of bodies moving in the atmosphere:&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
!Air quality&lt;br /&gt;
!Symbol&lt;br /&gt;
!Dimension&lt;br /&gt;
|-&lt;br /&gt;
|Specific weight of air&lt;br /&gt;
|w&lt;br /&gt;
|lb/ft&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;, kg/m&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;&lt;br /&gt;
|-&lt;br /&gt;
|Static pressure&lt;br /&gt;
|p&lt;br /&gt;
|atm, lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;, Pa, bar, torr&lt;br /&gt;
|-&lt;br /&gt;
|Temperature&lt;br /&gt;
|T&lt;br /&gt;
|&amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F, &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;C&lt;br /&gt;
|-&lt;br /&gt;
|Mass density&lt;br /&gt;
|&amp;lt;math&amp;gt;\rho&amp;lt;/math&amp;gt;&lt;br /&gt;
|slugs/ft&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;, kg s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;/m&amp;lt;sup&amp;gt;4&amp;lt;/sup&amp;gt;&lt;br /&gt;
|-&lt;br /&gt;
|Gravity&lt;br /&gt;
|''g''&lt;br /&gt;
|ft/s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;, m/s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
|-&lt;br /&gt;
|Speed of sound&lt;br /&gt;
|C&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt;&lt;br /&gt;
|ft/s, m/s&lt;br /&gt;
|}&lt;br /&gt;
All of these qualities are altitude-dependent and may vary slightly on the Earth's surface with geographic latitude because of variations of the Earth's radius caused by the centrifugal forces of the rotation of the Earth. All standard data used herein refer to a latitude of 45 degrees. Sea level is defined as mean sea level (MSL). To compare performance data on an equal basis, the United States Bureau of Standards has defined standard day conditions as follows:&lt;br /&gt;
&lt;br /&gt;
* Temperature = 15 degrees Celsius (&amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;C) or 59 degrees Fahrenheit (&amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F)&lt;br /&gt;
* Pressure = 760 millimeters (mm) of mercury (Hg) or 29.9213 inches (in.) Hg&lt;br /&gt;
&lt;br /&gt;
=== 4.1.1 Specific Weight of Air ===&lt;br /&gt;
For standard day conditions of 59 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F temperature and a pressure of 29.9213 in. Hg, the specific weight of air, w, is 0.07648 lb/ft&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt; or 1.2250 kg/m&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;. The specific weight of air changes with pressure, temperature, and humidity. Further data can be found in References 3.4 and 4.1, and in technical handbooks.&lt;br /&gt;
&lt;br /&gt;
=== 4.1.2 Static Pressure ===&lt;br /&gt;
Static pressure depends on geographic latitude, weather conditions, and altitude. The static pressure at any altitude results from the weight of the air above that altitude. For MSL and standard day conditions, the pressure, p&amp;lt;sub&amp;gt;o&amp;lt;/sub&amp;gt;, is 29.9213 in. Hg = 760 mm Hg = 1.0 atmosphere (atm). For conversion to Pascal, torr, or bar, see the conversion tables in section 3.2.&lt;br /&gt;
&lt;br /&gt;
=== 4.1.3 Temperature ===&lt;br /&gt;
Temperatures are defined in the English and metric systems in the so-called absolute and engineering scales. The absolute temperature minimum at 0 degrees, pressure is 0 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;K = -273.16 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;C, and 0 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;R = -459.69 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F. This is also written&lt;br /&gt;
&lt;br /&gt;
* Degrees Kelvin = degrees Celsius + 273.16&lt;br /&gt;
* Degrees Rankine = degrees Fahrenheit + 459.69&lt;br /&gt;
&lt;br /&gt;
The freezing point of water is 32 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F or 0 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;C. The boiling point of water is 212 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F or 100 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;C.&lt;br /&gt;
&lt;br /&gt;
=== 4.1.4 Mass Density of Air ===&lt;br /&gt;
Mass density defines the amount of mass contained in a unit volume of air. The mass density, &amp;lt;math&amp;gt;\rho&amp;lt;/math&amp;gt;, of air is of special importance in aerodynamic calculations.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\rho = \frac{specific\ weight\ of\ air,\ w}{acceleration\ of\ gravity,\ g} = \frac{lb/ft^3}{ft/s^2} = \frac{kg\ s^2}{m^4}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;slug = \frac{weight}{acceleration\ of\ gravity} = \frac{lb}{ft/s^2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Frequently the density ratio, &amp;lt;math&amp;gt;\sigma&amp;lt;/math&amp;gt;, is used&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\sigma = \frac{ambient\ air\ density,\ \rho}{standard\ sea-level\ density, \rho_o}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The factor, &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;1/\sqrt{\rho/\rho_o}&amp;lt;/math&amp;gt;, determines the increase in parachute rate of descent with altitude. The density at 40,000 feet is ¼ of the MSL density, and the density at 100,000 feet is 1/75 of the MSL density. Therefore, the parachute rate of descent is about twice as high at 40,000 feet and about nine times as high at 100,000 feet. MSL density is 0.00237689 slugs/ft&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;, or 0.1249 kg s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;/m&amp;lt;sup&amp;gt;4&amp;lt;/sup&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
=== 4.1.5 Gravity ===&lt;br /&gt;
Any mass attracts another mass with a force called gravity. If the Earth were surrounded by a vacuum, a body suspended above the Earth and released would fall toward the center of the Earth with increasing velocity caused by the acceleration of gravity, ''g''. In reality, the falling body is decelerated by its air drag until the air drag, D, equals the weight of the body, W, and an equilibrium velocity is reached; for parachutes, this is called the steady-state rate of descent.&lt;br /&gt;
&lt;br /&gt;
The acceleration of gravity, ''g'', at sea lavel is&lt;br /&gt;
&lt;br /&gt;
* ''g'' = 32.174 ft/s2 or 9.80665 m/s2.&lt;br /&gt;
&lt;br /&gt;
The value g = 9.08665 m/s is standardized internationally but is accurate only for a latitude of 45 degrees.&lt;br /&gt;
&lt;br /&gt;
With increasing altitude above the Earth's surface, the acceleration of gravity decreases in accordance with the equation&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;g = g_o(\frac{r}{r+h})^2&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
* ''g'' = acceleration of gravity at any altitude, ft/s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
* g&amp;lt;sub&amp;gt;o&amp;lt;/sub&amp;gt; = acceleration of gravity at sea level, ft/s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
* r = average Earth radius = 2.08556 x 10&amp;lt;sup&amp;gt;7&amp;lt;/sup&amp;gt; ft&lt;br /&gt;
* h = altitude above sea level, ft&lt;br /&gt;
&lt;br /&gt;
For other planets and heavenly bodies, the acceleration of gravity varies with the mass of the body. For example, the acceleration of gravity on Mars is about 1/3 of the acceleration of gravity on Earth. For more details on planets and heavenly bodies, see page XII of Reference 2.1.&lt;br /&gt;
&lt;br /&gt;
=== 4.1.6 Kinematic Viscosity ===&lt;br /&gt;
The coefficient of viscosity, &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt;, defines the shearing stresses in a gas or liquid and is sometimes called the resistance to continuous deformation. In aerodynamics, the coefficient of viscosity is combined with the mass density to form the kinematic viscosity, &amp;lt;math&amp;gt;\nu&amp;lt;/math&amp;gt;, where&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\nu = \frac{coefficient\ of\ viscosity,\ \mu}{mass\ density,\ \rho} = 0.0001576\ ft^2/s\ at\ sea\ level&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The kinematic viscosity, &amp;lt;math&amp;gt;\nu&amp;lt;/math&amp;gt;, is altitude dependent and is used to calculate the Reynolds number, Re.&lt;br /&gt;
&lt;br /&gt;
=== 4.1.7 Reynolds Number ===&lt;br /&gt;
The Reynolds number, Re, defines the relationship of mass forces to viscous friction forces in liquids and gases. It is calculated as&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Re = \frac{v\cdot l}{\nu} = \frac{velocity\ (ft/s)\cdot characteristic\ length\ (ft)}{kinematic\ viscosity\ (ft^2/s)}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Reynolds number is an important criterion in subsonic, noncompressible flow, and allows comparison of model tests with full-scale flight tests. A Reynolds number effect on parachutes working in separated, turbulent flow has not yet been established, as shown in section 5.2. The following chart shows the Reynolds numbers for various air vehicles.&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
!Subject&lt;br /&gt;
!Insect&lt;br /&gt;
!Glider&lt;br /&gt;
!DC-3&lt;br /&gt;
!B-747&lt;br /&gt;
!Drogue&lt;br /&gt;
Chute&lt;br /&gt;
!Main &lt;br /&gt;
Parachute&lt;br /&gt;
!WTT&lt;br /&gt;
Model&lt;br /&gt;
|-&lt;br /&gt;
|Re&lt;br /&gt;
|6 • 10&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;&lt;br /&gt;
|2.5 • 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&lt;br /&gt;
|24 • 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&lt;br /&gt;
|100 • 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&lt;br /&gt;
|50 • 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&lt;br /&gt;
|20 • 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&lt;br /&gt;
|2 • 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
=== 4.1.8 Mach Number ===&lt;br /&gt;
Mach number is an important parameter of supersonic flight; it states how much faster than the speed of sound the air vehicle travels.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Mach\ number,\ M = \frac{flight\ velocity,\ v}{speed\ of\ sound, c_s}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The speed of sound is the velocity at which a pressure disturbance, such as the sound of the human voice, travels in any medium. The speed of sound varies considerably in different gases, liquids, and metals.&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|Speed of sound in air in MSL&lt;br /&gt;
|C&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt; = 1116.46 ft/s = 340.38 m/s&lt;br /&gt;
|-&lt;br /&gt;
|Speed of sound in water&lt;br /&gt;
|C&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt; = 4749 ft/s = 1461.21 m/s&lt;br /&gt;
|-&lt;br /&gt;
|Speed of sound in iron&lt;br /&gt;
|C&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt; = 16,410 ft/s = 5710.7 m/s&lt;br /&gt;
|}&lt;br /&gt;
The speed of sound depends on temperature and the chemical composition of the medium, A widely used equation for speed of sound in air is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;C_s = 41.4\sqrt{\gamma\cdot T}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
* &amp;lt;math&amp;gt;C_s&amp;lt;/math&amp;gt; = speed of sound in dry air, ft/s&lt;br /&gt;
* &amp;lt;math&amp;gt;\gamma&amp;lt;/math&amp;gt; = ratio of specific heat, equal to 1.4 for dry air, dimensionless&lt;br /&gt;
* &amp;lt;math&amp;gt;T&amp;lt;/math&amp;gt; = temperature in Fahrenheit absolute, equal to 459.67 + &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F&lt;br /&gt;
&lt;br /&gt;
The speed of sound changes with altitude, as temperature (see Figure 3-1). The drag of streamlined bodies such as missiles, airfoils, and airplanes increases considerably as their velocities approach Mach 1. Depending on the configuration of the body, supersonic compressibility effects may occur in the 0.75 to 0.85 Mach range, causing local supersonic flow, shock waves, flow separation, and concomitant increases in drag and changes in stability.&lt;br /&gt;
&lt;br /&gt;
Parachutes that operate in separated flow over the entire velocity range do not show the typical drag increase when operating close to or beyond Mach 1. Supersonic parachute behavior is discussed in detail in section 5.8.&lt;br /&gt;
&lt;br /&gt;
== 4.2 CONTINUITY LAW AND BERNOULLI EQUATION ==&lt;br /&gt;
&lt;br /&gt;
=== 4.2.1 Continuity Law ===&lt;br /&gt;
Air is thought to flow in layers called streamlines. Figure 4-1 shows streamlines as layers of air without air transfer between individual layers. ne air is shown as being incompressible, a valid assumption for subsonic flow.&lt;br /&gt;
&lt;br /&gt;
[Insert Figure 4-1] 	&lt;br /&gt;
&lt;br /&gt;
If exchange of air does not occur across the streamline boundaries, the amount of air entering the streamline at point 1 must also exit at point 2, as shown in Figure 4-1. Because the cross section at point 2 is smaller than the cross section at point 1, the air must exit at a higher velocity. The following equation defines this condition:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;v_1\cdot S_1\cdot \rho_1 = v_2\cdot S_2\cdot \rho_2&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S&amp;lt;/math&amp;gt; = cross section of the streamline&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;v&amp;lt;/math&amp;gt; = velocity in the streamline&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\rho&amp;lt;/math&amp;gt; = density of the air flowing in the streamline&lt;br /&gt;
&lt;br /&gt;
This equation, which governs the flow in and around a body in gases and liquids, is important in aerodynamics and is called the Continuity Law. For incompressible subsonic flow, it can be simplified to &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;v_1\cdot S_1 = v_2\cdot S_2&amp;lt;/math&amp;gt; &lt;br /&gt;
&lt;br /&gt;
Whenever the cross section narrows, the velocity increases; when the cross section widens, the velocity decreases.&lt;br /&gt;
&lt;br /&gt;
=== 4.2.2 Bernoulli Equation ===&lt;br /&gt;
Figure 4-2 illustrates a streamline with the cross section, S, the velocity, v, and the pressure, p. If the air is incompressible, the downstream is v + Av. and the pressure is p + AP. If the air is inviscid, the inertia forces caused by the acceleration of air from v to v + Av must be balanced by differential pressure forces.&lt;br /&gt;
&lt;br /&gt;
[Insert Figure 4-2]FIGURE 4-2 Pressure and Velocity Distribution in a Streamline Element. 	&lt;br /&gt;
&lt;br /&gt;
The following equation can be written&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;p\cdot S-(p+\Delta p)S = m\cdot \frac{dv}{dt}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Simplified, the above equation yields&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;dp = - \rho vdv&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
and&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;p = - \frac{1}{2}\rho v^2 + C&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The above equation allows the following consideration: If p is pressure, then &amp;lt;math&amp;gt;1/2\ \rho v^2&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;C&amp;lt;/math&amp;gt; must also be pressure. The equation &amp;lt;math&amp;gt;1/2\ \rho v^2&amp;lt;/math&amp;gt; includes a velocity and is referred to as the dynamic pressure, or sometimes as velocity or impact pressure.&lt;br /&gt;
&lt;br /&gt;
Pressure, &amp;lt;math&amp;gt;p&amp;lt;/math&amp;gt;, is defined as static pressure; &amp;lt;math&amp;gt;1/2\ \rho v^2&amp;lt;/math&amp;gt; as dynamic pressure; and the sum of both, &amp;lt;math&amp;gt;C&amp;lt;/math&amp;gt;, as the total pressure or&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;p+\frac{1}{2} \rho v^2 = H&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
and&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;p_1 + \frac{1}{2} \rho {v_1}^2 = p_2 + \frac{1}{2} \rho {v_2}^2&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;H&amp;lt;/math&amp;gt; is the total pressure of the system, lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Dynamic pressure, &amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt;, is a frequently used quantity in aerodynamics:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;q = \frac{1}{2} \rho v^2&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
* &amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt; = dynamic pressure, lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
* &amp;lt;math&amp;gt;\rho&amp;lt;/math&amp;gt; =  air density, slugs/ft&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;&lt;br /&gt;
* &amp;lt;math&amp;gt;v&amp;lt;/math&amp;gt; =  velocity at a point of undisturbed flow, ft/s&lt;br /&gt;
&lt;br /&gt;
The following formulas are used for calculating the sea-level dynamic pressure if the velocity is given in ft/s, knots, mph, or km/h, respectively:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;q=\frac{v^2}{841.4}(ft/s), q=\frac{v^2}{295}(knots), q=\frac{v^2}{391.2}(mph), q=\frac{v^2}{1013.1}(km/h)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
                                              &lt;br /&gt;
&lt;br /&gt;
== 4.3 NEWTON'S THREE OF MOTION ==&lt;br /&gt;
Engineering mechanics are governed by the following three laws of Isaac Newton:&lt;br /&gt;
&lt;br /&gt;
1.  A body remains at rest or in an unaccelerated state of motion unless acted upon.&lt;br /&gt;
&lt;br /&gt;
2.  A force acting upon a body will produce an acceleration in the direction of the force.&lt;br /&gt;
&lt;br /&gt;
3.  An action in one direction will produce an equal reaction in the opposite direction.&lt;br /&gt;
&lt;br /&gt;
The first law is self-explanatory. The second law may be expressed by the equation&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;F=m\cdot a&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;F&amp;lt;/math&amp;gt; = force in pounds acting on the mass, lb&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;m&amp;lt;/math&amp;gt; = mass of body that the force is acting upon, slugs&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; = acceleration in ft/s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; resulting from the force, F&lt;br /&gt;
&lt;br /&gt;
The mass, m, of a body is obtained by&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;m=\frac{W}{g}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;W&amp;lt;/math&amp;gt; = weight of the body, lb&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;g&amp;lt;/math&amp;gt; = acceleration of gravity, ft/s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The mass, therefore, has the dimension of&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;m = \frac{W}{g}=\frac{lb}{ft/s^2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
This unit of mass is the slug.&lt;br /&gt;
&lt;br /&gt;
The equation of Newton's second law can now be written&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;F=\frac{W}{g}\cdot a,\ or\ F=W\frac{a}{g}&amp;lt;/math&amp;gt; 	&lt;br /&gt;
&lt;br /&gt;
The factor a/g is frequently called the load factor, G, and tells how much larger a force is than a force equivalent to the weight of the body. It is customary in parachute work to state that the maximum parachute force allowed is G • W or (a/g) • W. It is appropriate to write&lt;br /&gt;
&lt;br /&gt;
Maximum allowable parachute force, &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;F=W\frac{a}{g},\ or\ W\cdot G&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Figure 4-3 illustrates Newton's third law, explaining the principle of the rocket that can produce thrust in a perfect vacuum.&lt;br /&gt;
&lt;br /&gt;
A mass, m, ejected from a rocket at the velocity, v, per unit time, t, will produce a force, F, which in turn will create a reaction force, R, of equal magnitude but acting in the opposite direction.&lt;br /&gt;
&lt;br /&gt;
== 4.4 FORCES ACTING ON A BODY MOVING THROUGH AIR ==&lt;br /&gt;
&lt;br /&gt;
=== 4.4.1 Symmetrical Body ===&lt;br /&gt;
A body moving through air experiences forces caused by air pressure acting on the body. The same forces if the body moves through air, such as a descending parachute, or if the body is fixed and the air moves against the body, such as a parachute or an airfoil in a wind tunnel (Figure 44).&lt;br /&gt;
&lt;br /&gt;
         	 &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
A stable parachute in a wind tunnel experiences only the force called &amp;quot;drag&amp;quot; in the direction of the airflow. drag force, D, is calculated to&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;D=q\cdot S\cdot C_D&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;D&amp;lt;/math&amp;gt; = drag, lb&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt; = dynamic pressure, lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S&amp;lt;/math&amp;gt; = total surface area of the parachute canopy, ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;C_D&amp;lt;/math&amp;gt; = coefficient of drag,  dimensionless&lt;br /&gt;
&lt;br /&gt;
The dynamic pressure, q, can be calculated from section 4.2.2. The surface area of the canopy, S, is selected as a reference area. The drag coefficient, C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, is a form factor that indicates the drag characteristic of a specific shape. Most aerodynamic bodies are designed for low drag or a low drag coefficient. Parachutes, generally, are designed for high drag; therefore, a high drag coefficient is desirable. this difference in drag is demonstrated by the two bodies shown in Figure 4-5.&lt;br /&gt;
&lt;br /&gt;
            	&lt;br /&gt;
&lt;br /&gt;
Both bodies have the same cross section perpendicular to the airflow. The cylindrical. streamlined body has a smooth airflow over its total body length, resulting in a drag coefficient. C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, of 0.05 to 0.1, depending on slenderness ratio, surface roughness, and shape. The drag coefficient of all streamlined bodies is much affected by Reynolds number and Mach number. The open hemisphere, which is similar to a parachute canopy, has a drag coefficient, C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, of 1.3 to 1.4 for the same body cross section. The difference in drag is explained by the smooth airflow around the streamlined body and a separated, turbulent flow around the open hemisphere. The drag of bodies with separated flow, like parachute canopies, is little affected by Reynolds number.&lt;br /&gt;
&lt;br /&gt;
=== 4.4.2 Airflow Around an Asymmetrical Body (Airfoil) ===&lt;br /&gt;
Figure 4-6 shows an airfoil fixed at an angle of attack, a. against the airflow in a wind tunnel. This airfoil creates a drag force, D, in the direction of the flow; a lift force L perpendicular to the direction of the flow; and a moment, M. around the attachment point of the airfoil. fie sign convention of moments and forces shown are positive. Lift and drag can be combined for the resultant force, R.&lt;br /&gt;
&lt;br /&gt;
FIGURE. 4-6, Wind-Tunnel Forces Acting on an Airfoil.&lt;br /&gt;
&lt;br /&gt;
The lift, L is calculated&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;L = q\cdot S\cdot C_L&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; = measured lift, lb&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt; = dynamic pressure, lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S&amp;lt;/math&amp;gt; = reference area, ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;C_L&amp;lt;/math&amp;gt; = lift coefficient, dimensionless&lt;br /&gt;
&lt;br /&gt;
The moment is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;M=q\cdot S\cdot c_m\cdot c&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Where&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;M&amp;lt;/math&amp;gt; = measured lift, lb&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt; = dynamic pressure, lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S&amp;lt;/math&amp;gt; = reference area, ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;c_m&amp;lt;/math&amp;gt; = moment coefficient, dimensionless&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;c&amp;lt;/math&amp;gt; = average chord width of the wing, ft&lt;br /&gt;
&lt;br /&gt;
The reference area, S, is defined by agreement. For streamlined bodies, the maximum body cross section is used. Airfoils use the planform of the wing, and parachutes use the canopy surface area. The selection of the wing planform and the parachute surface area as references was made for practical reasons. The wing planform for a specific wing is fixed, whereas the cross section of the wing in the direction of the flow changes with the angle of attack. Similarly, the surface area of the parachute canopy is fixed; however, the frontal projected area of the inflated parachute canopy changes with airspeed, porosity, line length, and type of parachute.&lt;br /&gt;
&lt;br /&gt;
Forces and moments acting on an airfoil or a parachute canopy may be presented in several ways. The two most frequently used methods, as shown in Figure 4-7, are with forces oriented to the axis of flight and with forces oriented to the axis of the airfoil.&lt;br /&gt;
&lt;br /&gt;
The tangential force, and the normal force, N, are calculated&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;T = C_T\cdot S\cdot q&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
and 	&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;N = C_N\cdot S\cdot q&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
C&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; = tangential force coefficient, dimensionless&lt;br /&gt;
&lt;br /&gt;
C&amp;lt;sub&amp;gt;N&amp;lt;/sub&amp;gt; = normal force coefficient, dimensionless&lt;br /&gt;
&lt;br /&gt;
The resultant force, R, and the moment, M, in both presentations have the same direction and the same magnitude. The airflow fixed system is preferred for aerodynamic performance calculations, and the airfoil fixed system for wing stress calculations. me aerodynamic coefficients C&amp;lt;sub&amp;gt;L&amp;lt;/sub&amp;gt;, C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, C&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, C&amp;lt;sub&amp;gt;N&amp;lt;/sub&amp;gt;, and C&amp;lt;sub&amp;gt;m&amp;lt;/sub&amp;gt; can easily be determined in wind•tunnel measurements.&lt;br /&gt;
&lt;br /&gt;
Figure 4-8 shows the relationship of both force systems on a parachute. By definition, a negative moment is stabilizing, as illustrated in Figure 4-8. It is interesting to note that in Europe the stabilizing moment is defined as positive. Wind-tunnel installations frequently measure normal and tangential force instead of lift and drag. If α, T, and N are known, the drag D, can be calculated&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;D=T\cdot cos(\alpha)+N\cdot sin(\alpha)&amp;lt;/math&amp;gt;For a parachute with an angle of attack, &amp;lt;math&amp;gt;\alpha&amp;lt;/math&amp;gt;, equal to zero, the drag force and the tangential force are synonymous.&lt;br /&gt;
&lt;br /&gt;
Figure 4-9 shows the coefficients C&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, and C&amp;lt;sub&amp;gt;m&amp;lt;/sub&amp;gt; versus angle of attack for stable and unstable parachutes.&lt;br /&gt;
&lt;br /&gt;
The coefficient presentation shows two interesting facts. The slope of the moment coefficient curve, dC&amp;lt;sub&amp;gt;m&amp;lt;/sub&amp;gt;/dα, for the unstable parachute is positive between -25 degrees and + 25 degrees; this is, by definition, destabilizing. This parachute will oscillate approximately ± 25&lt;br /&gt;
&lt;br /&gt;
FIGURE 4-9. Coefficients C&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, and C&amp;lt;sub&amp;gt;M&amp;lt;/sub&amp;gt; Versus Angle of Attack, α, for a Stable and Unstable Parachute.&lt;br /&gt;
&lt;br /&gt;
degrees. The slope of the moment, dC&amp;lt;sub&amp;gt;m&amp;lt;/sub&amp;gt;/dα, for the stable parachute is negative over the total angle of attack; this is, by definition, stabilizing. The steeper the negative dC&amp;lt;sub&amp;gt;m&amp;lt;/sub&amp;gt;/dα slope, the greater is the stabilizing tendency of the parachute, and the better is its damping capability against unstabilizing forces such as sudden gusts of wind.&lt;br /&gt;
&lt;br /&gt;
Figure 4-10, from Reference 4.1, demonstrates the effect of airflow around a cylinder and an airfoil. The circulation around a rotating cylinder creates lift caused by the increase in velocity on one side of the cylinder and a decrease on the opposite side. This is called the Magnus effect.&lt;br /&gt;
&lt;br /&gt;
= 4.5 EQUILIBRIUM OF FORCES IN STUDY DESCENT OR FLIGHT =&lt;br /&gt;
&lt;br /&gt;
=== 4.5.1 Parachute in Steady Descent ===&lt;br /&gt;
A stable parachute in unaccelerated descent has an equilibrium between the total drag of the parachute and the load, Dr, and the weight of the load and the parachute assembly, WT (Figure 4-11). For steady descent&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
D&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; = total drag, 1b&lt;br /&gt;
&lt;br /&gt;
D&amp;lt;sub&amp;gt;P&amp;lt;/sub&amp;gt; = drag of parachute, 1b&lt;br /&gt;
&lt;br /&gt;
W&amp;lt;sub&amp;gt;C&amp;lt;/sub&amp;gt; = weight of load. 1b&lt;br /&gt;
&lt;br /&gt;
In most cases, the drag of the load can be neglected in relation to the large drag of the parachute, With drag, D — (C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;S)&amp;lt;sub&amp;gt;p&amp;lt;/sub&amp;gt; • p/2• v&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; and D&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; = W&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;. and solving for v, the important equation for rate of descent, v&amp;lt;sub&amp;gt;e&amp;lt;/sub&amp;gt;, is obtained,&lt;br /&gt;
&lt;br /&gt;
Rate of descent,&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
FIGURE 4-11. Forces Acting on a Parachute in Steady Descent.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
or in parachute terminology for rate of descent at sea level&lt;br /&gt;
&lt;br /&gt;
and rate of descent at any altitude&lt;br /&gt;
&lt;br /&gt;
For 1/, see column 4 in Table 3-3,&lt;br /&gt;
&lt;br /&gt;
In the equation for rate of descent. V&amp;lt;sub&amp;gt;e&amp;lt;/sub&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
W&amp;lt;sub&amp;gt;T =&amp;lt;/sub&amp;gt; weight of load and parachute assembly, 1b&lt;br /&gt;
&lt;br /&gt;
S&amp;lt;sub&amp;gt;o&amp;lt;/sub&amp;gt; = canopy surface area, ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
C&amp;lt;sub&amp;gt;Do&amp;lt;/sub&amp;gt; = parachute drag coefficient related to S&amp;lt;sub&amp;gt;o&amp;lt;/sub&amp;gt;&lt;br /&gt;
&lt;br /&gt;
p = air density at a specific altitude in slugs/ft&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;, as shown in Table 3-3&lt;br /&gt;
&lt;br /&gt;
During descent from altitude, the parachute system is constantly decelerated because of the increasing air density. This can be ignored for slowly descending main parachutes. However, for drogue chute systems that descend at 200 ft/s or faster, the constant deceleration may result in velocities 3 to 5% higher than the steady rate of descent.&lt;br /&gt;
&lt;br /&gt;
=== 4.5.2 Gliding Parachutes ===&lt;br /&gt;
Figure 4-12 shows the balance of forces on a gliding parachute. The total weight of the system, W&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; . must be balanced by the resultant force. R. However, a lifting force is required for glide. To satisfy the force balance&lt;br /&gt;
&lt;br /&gt;
R = C&amp;lt;sub&amp;gt;R&amp;lt;/sub&amp;gt; * S * p/2 * v&lt;br /&gt;
&lt;br /&gt;
Trajectory velocity, V&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, is calculated&lt;br /&gt;
&lt;br /&gt;
Horizontal velocity is calculated&lt;br /&gt;
&lt;br /&gt;
V&amp;lt;sub&amp;gt;H&amp;lt;/sub&amp;gt; = V&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; • cosø, and vertical velocity, v&amp;lt;sub&amp;gt;v&amp;lt;/sub&amp;gt; = V&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; • sinø&lt;br /&gt;
&lt;br /&gt;
The glide ratio is obtained from&lt;br /&gt;
&lt;br /&gt;
Analysis of Figure 4-12 indicates that the larger the ratio of lift to drag, the better the glide ratio, I./D A high resultant coefficient, C&amp;lt;sub&amp;gt;R&amp;lt;/sub&amp;gt;, results in a low glide or trajectory V&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, desirable for landing. A small C&amp;lt;sub&amp;gt;R&amp;lt;/sub&amp;gt; results in a high glide velocity, V&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, which is desirable for flying toward a target, compensating for head winds, or covering a distance quickly. Generally, gliding parachutes follow the same aerodynamic rules as low-aspect-ratio wings.&lt;br /&gt;
&lt;br /&gt;
           	   	&lt;br /&gt;
&lt;br /&gt;
FIGUR E 4-12, Forces Acting on a Gliding Parachute&lt;br /&gt;
&lt;br /&gt;
=== 4.5.3 Parasite Drag and Induced Drag ===&lt;br /&gt;
The drag acting on a lift-producing air vehicle, such as a gliding parachute or an aircraft, has two primary components: the parasite drag, D&amp;lt;sub&amp;gt;P&amp;lt;/sub&amp;gt; , and the induced drag. D&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Parasite drag is produced by the form drag from individual components such as the suspension lines, canopy, and the jumper of a gliding parachute, and the fuselage, tail sectiora, and control surfaces of an airplane. Large surfaces produce surface friction drag as part of the parasite drag.&lt;br /&gt;
&lt;br /&gt;
Induced drag is caused by the lifting action of the parachute canopy or the aircraft wing. Section 4.7 includes books with detailed discussions of induced drag.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Total drag, D&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, can be defined as&lt;br /&gt;
&lt;br /&gt;
or, in the coefficient form&lt;br /&gt;
&lt;br /&gt;
The parasite drag, D&amp;lt;sub&amp;gt;p&amp;lt;/sub&amp;gt;, and the coefficient, C&amp;lt;sub&amp;gt;DP&amp;lt;/sub&amp;gt;, can be determined in wind-tunnel tests or calculated as the sum of the individual component drags.&lt;br /&gt;
&lt;br /&gt;
The induced drag coefficient, C&amp;lt;sub&amp;gt;Di&amp;lt;/sub&amp;gt; , of a gliding parachute canopy or a wing profile can be calculated&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
C = coefficient of induced drag, dimensionless&lt;br /&gt;
&lt;br /&gt;
The expression b&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;/S is defined as the aspect ratio of a wing or parachute with the notation AR b&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;/S. Therefore&lt;br /&gt;
&lt;br /&gt;
The equation for induced drag indicates that increasing the aspect ratio, AR, reduces the induced drag coefficient,  , and therefore reduces the drag, D. ms, in turn, increases the glide ratio, L/D. Increasing the glide ratio by increasing the aspect ratio is optimized on high-performance sailplanes with aspect ratios higher than 20. Increasing the glide ratio of gliding parachutes by increasing the aspect ratio has limitations, which are discussed in section 5.9.&lt;br /&gt;
&lt;br /&gt;
=== 4.5.4 Aircraft in Horizontal Flight ===&lt;br /&gt;
Figure 4-13 shows forces and moments on an aircraft in steady, horizontal flight. In steady, horizontal flight, an equilibrium exists between all forces and moments acting on the aircraft. Lift on the wing and tail, L&amp;lt;sub&amp;gt;W&amp;lt;/sub&amp;gt; and L&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;. and the weight of the aircraft, W&amp;lt;sub&amp;gt;A&amp;lt;/sub&amp;gt;, balance in the vertical plane. Thrust, T and drag. D, balance each other in the horizontal plane, and the positive or negative moment, M, is balanced by the positive or negative lift of the tail multiplied by the moment arm, L&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
FIGURE 4-13. Forces and Moments Acting on an Aircraft in Steady night,&lt;br /&gt;
&lt;br /&gt;
Any imbalance in these forces results in descent or climb in the vertical plane or faster or slower speed in the horizontal plane. A change in the lift of the elevator initiates climb or descent. Thrust, T, is the prime contributor for climb or descent and faster or slower speed, However, a balance of forces must always be maintained for horizontal flight or steady rate oi climb or descent.&lt;br /&gt;
&lt;br /&gt;
== 4.6 WIND-TUNNEL TESTING OF PARACHUTES ==&lt;br /&gt;
Wind tunnels are an effective tool for testing air vehicles and air-vehicle components and have been used successfully for testing parachutes and parachute systems. Experience has shown that certain rules apply for the wind-tunnel testing of parachutes. Small parachutes manufactured from textiles cannot be made sufficiently similar to large parachutes in geometric design and flexibility, Lightweight material. required to obtain design similarity, is difficult to manufacture or is unobtainable.&lt;br /&gt;
&lt;br /&gt;
One cardinal rule has been established through many years of parachute wind-tunnel testing: A modification that changes the performance of a model parachute in wind-tunnel testing produces the same type and percentage of performance change in a large parachute. This rule is true for drag. stability, and opening-force characteristics.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
=== 4.6.1 Blowers ===&lt;br /&gt;
The simple air blower (Figure 4-14) is a proven tool for preliminary parachute testing of a chiefly qualitative nature. Unless special test conditions prevail, parachutes tested should be a minimum of 1.5 to 2 feet in diameter to obtain meaningful results.&lt;br /&gt;
&lt;br /&gt;
                                                                    &lt;br /&gt;
&lt;br /&gt;
 FIGURE 4-14. Typical Air Blower.&lt;br /&gt;
&lt;br /&gt;
An air blower is a preliminary test too! because it permits quick parachute• configuration changes and excellent visual observation.&lt;br /&gt;
&lt;br /&gt;
=== 4.6.2 Open-Throat, No-Return Wind Tunnels ===&lt;br /&gt;
The open-throat, no-return wind tunnel shown in Figure 4-15 permits exact measurements if parachutes of sufficient size are used. Parachutes 3 feet or more in diameter are well suited for obtaining good, quantitative test results.&lt;br /&gt;
&lt;br /&gt;
              FIGURE 4-15. Open-Throat, No-Return Wind Tunnel&lt;br /&gt;
&lt;br /&gt;
In air blowers and open-throat wind tunnels, the velocity at the skirt of the parachute (Section a-a of Figures 4-14 and 4-15) is lower than the velocity at the nozzle exit of the wind tunnel (Section b&amp;lt;sup&amp;gt;-&amp;lt;/sup&amp;gt;b of Figures 4-14 and 4-15), Care must be taken to measure the parachute test&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
velocity at Section a-a and not at Section b-b, the customary attachment point for airfoils and models.&lt;br /&gt;
&lt;br /&gt;
Wind tunnels frequently cannot test at the descent velocity of most main parachutes of 20 to 30 feet per second. Obtaining proper test results at this low is hampered by a poor velocity distribution in the wind-tunnel-test section, and by the weight of the test parachute. The latter has a tendency to pull the parachute downward, thereby providing a negative angle of attack, lusting unstable parachutes at higher presents the problem that the drag coefficient C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, of unstable parachutes is sensitive. The drag coefficient of unstable parachutes is described in section 5.2.&lt;br /&gt;
&lt;br /&gt;
An open-throat wind tunnel permits quick changes in parachute configuration, such as changing the suspension and reefing line lengths. Large open-throat wind tunnels that are not sealed against outside elements suffer atmospheric problems such as fog formation in the test section.&lt;br /&gt;
&lt;br /&gt;
=== 4.6.3 Closed-Throat, Full-Return Wind Tunnel ===&lt;br /&gt;
Figure 4-16 is a drawing of a full-return, closed-throat wind tunnel. fic full-return, closed-throat wind tunnel is generally considered best suited for obtaining good. qualitative, aerodynamic data, since it has a uniform distribution in the test section. A disadvantage is the difficulty in gaining access to the test section for changing the parachute configuration.&lt;br /&gt;
&lt;br /&gt;
FIGURE 4-16. Closed-Throat, Full-Reuurn Wind Tunnel.&lt;br /&gt;
&lt;br /&gt;
=== 4.6.4 General Comments for Wind-Tunnel Testing of Parachutes ===&lt;br /&gt;
1. Parachute models for wind-tunnel testing should be as large and as similar as possible in geometry and flexibility to full-scale parachutes. Parachutes of less than 1.5 feet in diameter usually lack geometric similarity and material flexibility, which results in inflation characteristics and dissimilar inflated shapes.&lt;br /&gt;
&lt;br /&gt;
2.  The finished dimensions of model parachutes must be measured as accurately as possible to determine the nominal diameter, Do, and the surface area, So. Model parachutes will shrink from 5 to 10% during manufacture because of sewing take-up, which results in a notable difference in the dimensions between the drawing and the completed parachute.&lt;br /&gt;
&lt;br /&gt;
3.  Wind&amp;lt;sup&amp;gt;-&amp;lt;/sup&amp;gt;tunnel tests of parachutes are excellent for comparing different models and modifications: also, they are the most effective means for measuring coefficients of lift, drag. and normal and tangential forces, as well as for determining the load coefficient, for infinite load.&lt;br /&gt;
&lt;br /&gt;
4.  In wind-tunnel tests, velocity decay does not occur during parachute inflation and operation; this is defined as testing under &amp;quot;infinite mass condition. &amp;quot; First-stage drogue chutes and parachutes with a canopy loading, W/C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;S. in excess of 100 lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; approach this condition. Low-canopy-loading main parachutes with rates of descent of 20 to 30 ft/s have a large velocity decay during opening, which requires careful interpretation of the opening-force data obtained in wind-tunnel tests.&lt;br /&gt;
&lt;br /&gt;
5.  In the past, to avoid wind-tunnel blockage and questionable test data. the diameter of a test parachute could not exceed about 5 to 6% of the wind-tunnel test section area. Recent Sandia investigations of single and clustered ribbon parachutes with wind-tunnel blockage ratios of up to 30% have resulted in correction methods that make it possible to test much larger parachutes (Reference 4.2).&lt;br /&gt;
&lt;br /&gt;
= 4.7 REFERENCE MATERIAL =&lt;br /&gt;
4.1 H. H. Hurt. Aerodynamics for Naval Aviators Navy Manual NAVWEPS 00 80T 80. Chief of Naval Operations, Aviation Training Division.&lt;br /&gt;
&lt;br /&gt;
4.2 J, M. Macha and R J. Buffington. &amp;quot;Wall-Interference Corrections for Parachutes in a Closed Wind Tunnel.&amp;quot; AIM Paper, April 1989. (AIM 89-0900-cp.)&lt;br /&gt;
&lt;br /&gt;
For readers interested in a more detailed study of aerodynamics, the following books are recommended.&lt;br /&gt;
&lt;br /&gt;
4.3 J, H, Dwinnel, Principle of Aerodynamics. McGraw-Hill     	Co., New York, 1949.&lt;br /&gt;
&lt;br /&gt;
4.4 J. Morane. Introduction to Theoretical and Computational Aerodynamics. John Wiley &amp;amp; Sons.&lt;br /&gt;
&lt;br /&gt;
4.5 R.S. Shevell. Fundamentals of Flight. Prentice-Hall. 1983.&lt;br /&gt;
&lt;br /&gt;
4.6 J. D. Anderson, Jr. Introduction to Flights, ILS Engineering and History. McGraw-Hill Book co., New York 1978.&lt;br /&gt;
&lt;br /&gt;
4.7 D. J. Cockrell. The Aerodynamics of Parachutes.&amp;quot; AGARDograph No. 6295, available from NASA Langley Research Center, M/S 1M), Hampton, Va., 236.&lt;/div&gt;</summary>
		<author><name>TuanHTruong</name></author>
	</entry>
	<entry>
		<id>https://mediawiki.aerodecelerator.org/index.php?title=Parachute_Aerodynamics&amp;diff=32</id>
		<title>Parachute Aerodynamics</title>
		<link rel="alternate" type="text/html" href="https://mediawiki.aerodecelerator.org/index.php?title=Parachute_Aerodynamics&amp;diff=32"/>
		<updated>2024-05-07T17:28:30Z</updated>

		<summary type="html">&lt;p&gt;TuanHTruong: Fixed the heading and sub-headings in hope that saving changes work better with editing smaller sections&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&lt;br /&gt;
= CHAPTER 4: AERODYNAMICS AS RELATED TO PARACHUTES =&lt;br /&gt;
== 4.1 PROPERTIES OF THE ATMOSPHERE ==&lt;br /&gt;
All forces acting on parachutes and all movements of parachutes are affected by the atmosphere, or air, surrounding the Earth. The air at the Earth's surface is approximately 78% nitrogen; 21% oxygen; and 1% a mixture of gases such as argon, neon, helium, water vapor, and carbon dioxide. This chemical composition remains relatively constant to an altitude of about 160,000 feet (50 kilometers). The following air qualities are of major significance in the dynamics of bodies moving in the atmosphere:&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
!Air quality&lt;br /&gt;
!Symbol&lt;br /&gt;
!Dimension&lt;br /&gt;
|-&lt;br /&gt;
|Specific weight of air&lt;br /&gt;
|w&lt;br /&gt;
|lb/ft&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;, kg/m&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;&lt;br /&gt;
|-&lt;br /&gt;
|Static pressure&lt;br /&gt;
|p&lt;br /&gt;
|atm, lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;, Pa, bar, torr&lt;br /&gt;
|-&lt;br /&gt;
|Temperature&lt;br /&gt;
|T&lt;br /&gt;
|&amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F, &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;C&lt;br /&gt;
|-&lt;br /&gt;
|Mass density&lt;br /&gt;
|&amp;lt;math&amp;gt;\rho&amp;lt;/math&amp;gt;&lt;br /&gt;
|slugs/ft&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;, kg s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;/m&amp;lt;sup&amp;gt;4&amp;lt;/sup&amp;gt;&lt;br /&gt;
|-&lt;br /&gt;
|Gravity&lt;br /&gt;
|''g''&lt;br /&gt;
|ft/s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;, m/s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
|-&lt;br /&gt;
|Speed of sound&lt;br /&gt;
|C&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt;&lt;br /&gt;
|ft/s, m/s&lt;br /&gt;
|}&lt;br /&gt;
All of these qualities are altitude-dependent and may vary slightly on the Earth's surface with geographic latitude because of variations of the Earth's radius caused by the centrifugal forces of the rotation of the Earth. All standard data used herein refer to a latitude of 45 degrees. Sea level is defined as mean sea level (MSL). To compare performance data on an equal basis, the United States Bureau of Standards has defined standard day conditions as follows:&lt;br /&gt;
&lt;br /&gt;
* Temperature = 15 degrees Celsius (&amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;C) or 59 degrees Fahrenheit (&amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F)&lt;br /&gt;
* Pressure = 760 millimeters (mm) of mercury (Hg) or 29.9213 inches (in.) Hg&lt;br /&gt;
&lt;br /&gt;
=== 4.1.1 Specific Weight of Air ===&lt;br /&gt;
For standard day conditions of 59 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F temperature and a pressure of 29.9213 in. Hg, the specific weight of air, w, is 0.07648 lb/ft&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt; or 1.2250 kg/m&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;. The specific weight of air changes with pressure, temperature, and humidity. Further data can be found in References 3.4 and 4.1, and in technical handbooks.&lt;br /&gt;
&lt;br /&gt;
=== 4.1.2 Static Pressure ===&lt;br /&gt;
Static pressure depends on geographic latitude, weather conditions, and altitude. The static pressure at any altitude results from the weight of the air above that altitude. For MSL and standard day conditions, the pressure, p&amp;lt;sub&amp;gt;o&amp;lt;/sub&amp;gt;, is 29.9213 in. Hg = 760 mm Hg = 1.0 atmosphere (atm). For conversion to Pascal, torr, or bar, see the conversion tables in section 3.2.&lt;br /&gt;
&lt;br /&gt;
=== 4.1.3 Temperature ===&lt;br /&gt;
Temperatures are defined in the English and metric systems in the so-called absolute and engineering scales. The absolute temperature minimum at 0 degrees, pressure is 0 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;K = -273.16 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;C, and 0 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;R = -459.69 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F. This is also written&lt;br /&gt;
&lt;br /&gt;
* Degrees Kelvin = degrees Celsius + 273.16&lt;br /&gt;
* Degrees Rankine = degrees Fahrenheit + 459.69&lt;br /&gt;
&lt;br /&gt;
The freezing point of water is 32 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F or 0 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;C. The boiling point of water is 212 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F or 100 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;C.&lt;br /&gt;
&lt;br /&gt;
=== 4.1.4 Mass Density of Air ===&lt;br /&gt;
Mass density defines the amount of mass contained in a unit volume of air. The mass density, &amp;lt;math&amp;gt;\rho&amp;lt;/math&amp;gt;, of air is of special importance in aerodynamic calculations.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\rho = \frac{specific\ weight\ of\ air,\ w}{acceleration\ of\ gravity,\ g} = \frac{lb/ft^3}{ft/s^2} = \frac{kg\ s^2}{m^4}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;slug = \frac{weight}{acceleration\ of\ gravity} = \frac{lb}{ft/s^2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Frequently the density ratio, &amp;lt;math&amp;gt;\sigma&amp;lt;/math&amp;gt;, is used&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\sigma = \frac{ambient\ air\ density,\ \rho}{standard\ sea-level\ density, \rho_o}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The factor, &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;1/\sqrt{\rho/\rho_o}&amp;lt;/math&amp;gt;, determines the increase in parachute rate of descent with altitude. The density at 40,000 feet is ¼ of the MSL density, and the density at 100,000 feet is 1/75 of the MSL density. Therefore, the parachute rate of descent is about twice as high at 40,000 feet and about nine times as high at 100,000 feet. MSL density is 0.00237689 slugs/ft&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;, or 0.1249 kg s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;/m&amp;lt;sup&amp;gt;4&amp;lt;/sup&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
=== 4.1.5 Gravity ===&lt;br /&gt;
Any mass attracts another mass with a force called gravity. If the Earth were surrounded by a vacuum, a body suspended above the Earth and released would fall toward the center of the Earth with increasing velocity caused by the acceleration of gravity, ''g''. In reality, the falling body is decelerated by its air drag until the air drag, D, equals the weight of the body, W, and an equilibrium velocity is reached; for parachutes, this is called the steady-state rate of descent.&lt;br /&gt;
&lt;br /&gt;
The acceleration of gravity, ''g'', at sea lavel is&lt;br /&gt;
&lt;br /&gt;
* ''g'' = 32.174 ft/s2 or 9.80665 m/s2.&lt;br /&gt;
&lt;br /&gt;
The value g = 9.08665 m/s is standardized internationally but is accurate only for a latitude of 45 degrees.&lt;br /&gt;
&lt;br /&gt;
With increasing altitude above the Earth's surface, the acceleration of gravity decreases in accordance with the equation&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;g = g_o(\frac{r}{r+h})^2&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
* ''g'' = acceleration of gravity at any altitude, ft/s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
* g&amp;lt;sub&amp;gt;o&amp;lt;/sub&amp;gt; = acceleration of gravity at sea level, ft/s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
* r = average Earth radius = 2.08556 x 10&amp;lt;sup&amp;gt;7&amp;lt;/sup&amp;gt; ft&lt;br /&gt;
* h = altitude above sea level, ft&lt;br /&gt;
&lt;br /&gt;
For other planets and heavenly bodies, the acceleration of gravity varies with the mass of the body. For example, the acceleration of gravity on Mars is about 1/3 of the acceleration of gravity on Earth. For more details on planets and heavenly bodies, see page XII of Reference 2.1.&lt;br /&gt;
&lt;br /&gt;
=== 4.1.6 Kinematic Viscosity ===&lt;br /&gt;
The coefficient of viscosity, &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt;, defines the shearing stresses in a gas or liquid and is sometimes called the resistance to continuous deformation. In aerodynamics, the coefficient of viscosity is combined with the mass density to form the kinematic viscosity, &amp;lt;math&amp;gt;\nu&amp;lt;/math&amp;gt;, where&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\nu = \frac{coefficient\ of\ viscosity,\ \mu}{mass\ density,\ \rho} = 0.0001576\ ft^2/s\ at\ sea\ level&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The kinematic viscosity, &amp;lt;math&amp;gt;\nu&amp;lt;/math&amp;gt;, is altitude dependent and is used to calculate the Reynolds number, Re.&lt;br /&gt;
&lt;br /&gt;
=== 4.1.7 Reynolds Number ===&lt;br /&gt;
The Reynolds number, Re, defines the relationship of mass forces to viscous friction forces in liquids and gases. It is calculated as&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Re = \frac{v\cdot l}{\nu} = \frac{velocity\ (ft/s)\cdot characteristic\ length\ (ft)}{kinematic\ viscosity\ (ft^2/s)}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Reynolds number is an important criterion in subsonic, noncompressible flow, and allows comparison of model tests with full-scale flight tests. A Reynolds number effect on parachutes working in separated, turbulent flow has not yet been established, as shown in section 5.2. The following chart shows the Reynolds numbers for various air vehicles.&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
!Subject&lt;br /&gt;
!Insect&lt;br /&gt;
!Glider&lt;br /&gt;
!DC-3&lt;br /&gt;
!B-747&lt;br /&gt;
!Drogue&lt;br /&gt;
Chute&lt;br /&gt;
!Main &lt;br /&gt;
Parachute&lt;br /&gt;
!WTT&lt;br /&gt;
Model&lt;br /&gt;
|-&lt;br /&gt;
|Re&lt;br /&gt;
|6 • 10&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;&lt;br /&gt;
|2.5 • 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&lt;br /&gt;
|24 • 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&lt;br /&gt;
|100 • 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&lt;br /&gt;
|50 • 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&lt;br /&gt;
|20 • 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&lt;br /&gt;
|2 • 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
=== 4.1.8 Mach Number ===&lt;br /&gt;
Mach number is an important parameter of supersonic flight; it states how much faster than the speed of sound the air vehicle travels.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Mach\ number,\ M = \frac{flight\ velocity,\ v}{speed\ of\ sound, c_s}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The speed of sound is the velocity at which a pressure disturbance, such as the sound of the human voice, travels in any medium. The speed of sound varies considerably in different gases, liquids, and metals.&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|Speed of sound in air in MSL&lt;br /&gt;
|C&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt; = 1116.46 ft/s = 340.38 m/s&lt;br /&gt;
|-&lt;br /&gt;
|Speed of sound in water&lt;br /&gt;
|C&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt; = 4749 ft/s = 1461.21 m/s&lt;br /&gt;
|-&lt;br /&gt;
|Speed of sound in iron&lt;br /&gt;
|C&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt; = 16,410 ft/s = 5710.7 m/s&lt;br /&gt;
|}&lt;br /&gt;
The speed of sound depends on temperature and the chemical composition of the medium, A widely used equation for speed of sound in air is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;C_s = 41.4\sqrt{\gamma\cdot T}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
* &amp;lt;math&amp;gt;C_s&amp;lt;/math&amp;gt; = speed of sound in dry air, ft/s&lt;br /&gt;
* &amp;lt;math&amp;gt;\gamma&amp;lt;/math&amp;gt; = ratio of specific heat, equal to 1.4 for dry air, dimensionless&lt;br /&gt;
* &amp;lt;math&amp;gt;T&amp;lt;/math&amp;gt; = temperature in Fahrenheit absolute, equal to 459.67 + &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F&lt;br /&gt;
&lt;br /&gt;
The speed of sound changes with altitude, as temperature (see Figure 3-1). The drag of streamlined bodies such as missiles, airfoils, and airplanes increases considerably as their velocities approach Mach 1. Depending on the configuration of the body, supersonic compressibility effects may occur in the 0.75 to 0.85 Mach range, causing local supersonic flow, shock waves, flow separation, and concomitant increases in drag and changes in stability.&lt;br /&gt;
&lt;br /&gt;
Parachutes that operate in separated flow over the entire velocity range do not show the typical drag increase when operating close to or beyond Mach 1. Supersonic parachute behavior is discussed in detail in section 5.8.&lt;br /&gt;
&lt;br /&gt;
== '''4.2 CONTINUITY LAW AND BERNOULLI EQUATION''' ==&lt;br /&gt;
&lt;br /&gt;
=== 4.2.1 Continuity L.aw ===&lt;br /&gt;
Air is thought to flow in layers called streamlines. Figure 4-1 shows streamlines as layers of air without air transfer between individual layers. ne air is shown as being incompressible, a valid assumption for subsonic flow.&lt;br /&gt;
&lt;br /&gt;
[Insert Figure 4-1] 	&lt;br /&gt;
&lt;br /&gt;
If exchange of air does not occur across the streamline boundaries, the amount of air entering the streamline at point 1 must also exit at point 2, as shown in Figure 4-1. Because the cross section at point 2 is smaller than the cross section at point 1, the air must exit at a higher velocity. The following equation defines this condition:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;v_1\cdot S_1\cdot \rho_1 = v_2\cdot S_2\cdot \rho_2&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S&amp;lt;/math&amp;gt; = cross section of the streamline&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;v&amp;lt;/math&amp;gt; = velocity in the streamline&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\rho&amp;lt;/math&amp;gt; = density of the air flowing in the streamline&lt;br /&gt;
&lt;br /&gt;
This equation, which governs the flow in and around a body in gases and liquids, is important in aerodynamics and is called the Continuity Law. For incompressible subsonic flow, it can be simplified to &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;v_1\cdot S_1 = v_2\cdot S_2&amp;lt;/math&amp;gt; &lt;br /&gt;
&lt;br /&gt;
Whenever the cross section narrows, the velocity increases; when the cross section widens, the velocity decreases.&lt;br /&gt;
&lt;br /&gt;
=== 4.2.2 Bernoulli Equation ===&lt;br /&gt;
Figure 4-2 illustrates a streamline with the cross section, S, the velocity, v, and the pressure, p. If the air is incompressible, the downstream is v + Av. and the pressure is p + AP. If the air is inviscid, the inertia forces caused by the acceleration of air from v to v + Av must be balanced by differential pressure forces.&lt;br /&gt;
&lt;br /&gt;
[Insert Figure 4-2]FIGURE 4-2 Pressure and Velocity Distribution in a Streamline Element. 	&lt;br /&gt;
&lt;br /&gt;
The following equation can be written&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;p\cdot S-(p+\Delta p)S = m\cdot \frac{dv}{dt}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Simplified, the above equation yields&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;dp = - \rho vdv&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
and&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;p = - \frac{1}{2}\rho v^2 + C&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The above equation allows the following consideration: If p is pressure, then &amp;lt;math&amp;gt;1/2\ \rho v^2&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;C&amp;lt;/math&amp;gt; must also be pressure. The equation &amp;lt;math&amp;gt;1/2\ \rho v^2&amp;lt;/math&amp;gt; includes a velocity and is referred to as the dynamic pressure, or sometimes as velocity or impact pressure.&lt;br /&gt;
&lt;br /&gt;
Pressure, &amp;lt;math&amp;gt;p&amp;lt;/math&amp;gt;, is defined as static pressure; &amp;lt;math&amp;gt;1/2\ \rho v^2&amp;lt;/math&amp;gt; as dynamic pressure; and the sum of both, &amp;lt;math&amp;gt;C&amp;lt;/math&amp;gt;, as the total pressure or&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;p+\frac{1}{2} \rho v^2 = H&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
and&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;p_1 + \frac{1}{2} \rho {v_1}^2 = p_2 + \frac{1}{2} \rho {v_2}^2&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;H&amp;lt;/math&amp;gt; is the total pressure of the system, lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Dynamic pressure, &amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt;, is a frequently used quantity in aerodynamics:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;q = \frac{1}{2} \rho v^2&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
* &amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt; = dynamic pressure, lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
* &amp;lt;math&amp;gt;\rho&amp;lt;/math&amp;gt; =  air density, slugs/ft&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;&lt;br /&gt;
* &amp;lt;math&amp;gt;v&amp;lt;/math&amp;gt; =  velocity at a point of undisturbed flow, ft/s&lt;br /&gt;
&lt;br /&gt;
The following formulas are used for calculating the sea-level dynamic pressure if the velocity is given in ft/s, knots, mph, or km/h, respectively:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;q=\frac{v^2}{841.4}(ft/s), q=\frac{v^2}{295}(knots), q=\frac{v^2}{391.2}(mph), q=\frac{v^2}{1013.1}(km/h)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
                                              &lt;br /&gt;
&lt;br /&gt;
== '''4.3 NEWTON'S THREE OF MOTION''' ==&lt;br /&gt;
Engineering mechanics are governed by the following three laws of Isaac Newton:&lt;br /&gt;
&lt;br /&gt;
1.  A body remains at rest or in an unaccelerated state of motion unless acted upon.&lt;br /&gt;
&lt;br /&gt;
2.  A force acting upon a body will produce an acceleration in the direction of the force.&lt;br /&gt;
&lt;br /&gt;
3.  An action in one direction will produce an equal reaction in the opposite direction.&lt;br /&gt;
&lt;br /&gt;
The first law is self-explanatory. The second law may be expressed by the equation&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;F=m\cdot a&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;F&amp;lt;/math&amp;gt; = force in pounds acting on the mass, lb&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;m&amp;lt;/math&amp;gt; = mass of body that the force is acting upon, slugs&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; = acceleration in ft/s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; resulting from the force, F&lt;br /&gt;
&lt;br /&gt;
The mass, m, of a body is obtained by&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;m=\frac{W}{g}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;W&amp;lt;/math&amp;gt; = weight of the body, lb&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;g&amp;lt;/math&amp;gt; = acceleration of gravity, ft/s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The mass, therefore, has the dimension of&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;m = \frac{W}{g}=\frac{lb}{ft/s^2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
This unit of mass is the slug.&lt;br /&gt;
&lt;br /&gt;
The equation of Newton's second law can now be written&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;F=\frac{W}{g}\cdot a,\ or\ F=W\frac{a}{g}&amp;lt;/math&amp;gt; 	&lt;br /&gt;
&lt;br /&gt;
The factor a/g is frequently called the load factor, G, and tells how much larger a force is than a force equivalent to the weight of the body. It is customary in parachute work to state that the maximum parachute force allowed is G • W or (a/g) • W. It is appropriate to write&lt;br /&gt;
&lt;br /&gt;
Maximum allowable parachute force, &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;F=W\frac{a}{g},\ or\ W\cdot G&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Figure 4-3 illustrates Newton's third law, explaining the principle of the rocket that can produce thrust in a perfect vacuum.&lt;br /&gt;
&lt;br /&gt;
A mass, m, ejected from a rocket at the velocity, v, per unit time, t, will produce a force, F, which in turn will create a reaction force, R, of equal magnitude but acting in the opposite direction.&lt;br /&gt;
&lt;br /&gt;
== 4.4 FORCES ACTING ON A BODY MOVING THROUGH AIR ==&lt;br /&gt;
&lt;br /&gt;
=== 4.4.1 Symmetrical Body ===&lt;br /&gt;
A body moving through air experiences forces caused by air pressure acting on the body. The same forces if the body moves through air, such as a descending parachute, or if the body is fixed and the air moves against the body, such as a parachute or an airfoil in a wind tunnel (Figure 44).&lt;br /&gt;
&lt;br /&gt;
         	 &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
A stable parachute in a wind tunnel experiences only the force called &amp;quot;drag&amp;quot; in the direction of the airflow. drag force, D, is calculated to&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;D=q\cdot S\cdot C_D&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;D&amp;lt;/math&amp;gt; = drag, lb&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt; = dynamic pressure, lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S&amp;lt;/math&amp;gt; = total surface area of the parachute canopy, ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;C_D&amp;lt;/math&amp;gt; = coefficient of drag,  dimensionless&lt;br /&gt;
&lt;br /&gt;
The dynamic pressure, q, can be calculated from section 4.2.2. The surface area of the canopy, S, is selected as a reference area. The drag coefficient, C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, is a form factor that indicates the drag characteristic of a specific shape. Most aerodynamic bodies are designed for low drag or a low drag coefficient. Parachutes, generally, are designed for high drag; therefore, a high drag coefficient is desirable. this difference in drag is demonstrated by the two bodies shown in Figure 4-5.&lt;br /&gt;
&lt;br /&gt;
            	&lt;br /&gt;
&lt;br /&gt;
Both bodies have the same cross section perpendicular to the airflow. The cylindrical. streamlined body has a smooth airflow over its total body length, resulting in a drag coefficient. C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, of 0.05 to 0.1, depending on slenderness ratio, surface roughness, and shape. The drag coefficient of all streamlined bodies is much affected by Reynolds number and Mach number. The open hemisphere, which is similar to a parachute canopy, has a drag coefficient, C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, of 1.3 to 1.4 for the same body cross section. The difference in drag is explained by the smooth airflow around the streamlined body and a separated, turbulent flow around the open hemisphere. The drag of bodies with separated flow, like parachute canopies, is little affected by Reynolds number.&lt;br /&gt;
&lt;br /&gt;
=== 4.4.2 Airflow Around an Asymmetrical Body (Airfoil) ===&lt;br /&gt;
Figure 4-6 shows an airfoil fixed at an angle of attack, a. against the airflow in a wind tunnel. This airfoil creates a drag force, D, in the direction of the flow; a lift force L perpendicular to the direction of the flow; and a moment, M. around the attachment point of the airfoil. fie sign convention of moments and forces shown are positive. Lift and drag can be combined for the resultant force, R.&lt;br /&gt;
&lt;br /&gt;
FIGURE. 4-6, Wind-Tunnel Forces Acting on an Airfoil.&lt;br /&gt;
&lt;br /&gt;
The lift, L is calculated&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;L = q\cdot S\cdot C_L&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; = measured lift, lb&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt; = dynamic pressure, lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S&amp;lt;/math&amp;gt; = reference area, ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;C_L&amp;lt;/math&amp;gt; = lift coefficient, dimensionless&lt;br /&gt;
&lt;br /&gt;
The moment is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;M=q\cdot S\cdot c_m\cdot c&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Where&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;M&amp;lt;/math&amp;gt; = measured lift, lb&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt; = dynamic pressure, lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S&amp;lt;/math&amp;gt; = reference area, ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;c_m&amp;lt;/math&amp;gt; = moment coefficient, dimensionless&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;c&amp;lt;/math&amp;gt; = average chord width of the wing, ft&lt;br /&gt;
&lt;br /&gt;
The reference area, S, is defined by agreement. For streamlined bodies, the maximum body cross section is used. Airfoils use the planform of the wing, and parachutes use the canopy surface area. The selection of the wing planform and the parachute surface area as references was made for practical reasons. The wing planform for a specific wing is fixed, whereas the cross section of the wing in the direction of the flow changes with the angle of attack. Similarly, the surface area of the parachute canopy is fixed; however, the frontal projected area of the inflated parachute canopy changes with airspeed, porosity, line length, and type of parachute.&lt;br /&gt;
&lt;br /&gt;
Forces and moments acting on an airfoil or a parachute canopy may be presented in several ways. The two most frequently used methods, as shown in Figure 4-7, are with forces oriented to the axis of flight and with forces oriented to the axis of the airfoil.&lt;br /&gt;
&lt;br /&gt;
The tangential force, and the normal force, N, are calculated&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;T = C_T\cdot S\cdot q&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
and 	&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;N = C_N\cdot S\cdot q&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
C&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; = tangential force coefficient, dimensionless&lt;br /&gt;
&lt;br /&gt;
C&amp;lt;sub&amp;gt;N&amp;lt;/sub&amp;gt; = normal force coefficient, dimensionless&lt;br /&gt;
&lt;br /&gt;
The resultant force, R, and the moment, M, in both presentations have the same direction and the same magnitude. The airflow fixed system is preferred for aerodynamic performance calculations, and the airfoil fixed system for wing stress calculations. me aerodynamic coefficients C&amp;lt;sub&amp;gt;L&amp;lt;/sub&amp;gt;, C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, C&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, C&amp;lt;sub&amp;gt;N&amp;lt;/sub&amp;gt;, and C&amp;lt;sub&amp;gt;m&amp;lt;/sub&amp;gt; can easily be determined in wind•tunnel measurements.&lt;br /&gt;
&lt;br /&gt;
Figure 4-8 shows the relationship of both force systems on a parachute. By definition, a negative moment is stabilizing, as illustrated in Figure 4-8. It is interesting to note that in Europe the stabilizing moment is defined as positive. Wind-tunnel installations frequently measure normal and tangential force instead of lift and drag. If α, T, and N are known, the drag D, can be calculated&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;D=T\cdot cos(\alpha)+N\cdot sin(\alpha)&amp;lt;/math&amp;gt;For a parachute with an angle of attack, &amp;lt;math&amp;gt;\alpha&amp;lt;/math&amp;gt;, equal to zero, the drag force and the tangential force are synonymous.&lt;br /&gt;
&lt;br /&gt;
Figure 4-9 shows the coefficients C&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, and C&amp;lt;sub&amp;gt;m&amp;lt;/sub&amp;gt; versus angle of attack for stable and unstable parachutes.&lt;br /&gt;
&lt;br /&gt;
The coefficient presentation shows two interesting facts. The slope of the moment coefficient curve, dC&amp;lt;sub&amp;gt;m&amp;lt;/sub&amp;gt;/dα, for the unstable parachute is positive between -25 degrees and + 25 degrees; this is, by definition, destabilizing. This parachute will oscillate approximately ± 25&lt;br /&gt;
&lt;br /&gt;
FIGURE 4-9. Coefficients C&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, and C&amp;lt;sub&amp;gt;M&amp;lt;/sub&amp;gt; Versus Angle of Attack, α, for a Stable and Unstable Parachute.&lt;br /&gt;
&lt;br /&gt;
degrees. The slope of the moment, dC&amp;lt;sub&amp;gt;m&amp;lt;/sub&amp;gt;/dα, for the stable parachute is negative over the total angle of attack; this is, by definition, stabilizing. The steeper the negative dC&amp;lt;sub&amp;gt;m&amp;lt;/sub&amp;gt;/dα slope, the greater is the stabilizing tendency of the parachute, and the better is its damping capability against unstabilizing forces such as sudden gusts of wind.&lt;br /&gt;
&lt;br /&gt;
Figure 4-10, from Reference 4.1, demonstrates the effect of airflow around a cylinder and an airfoil. The circulation around a rotating cylinder creates lift caused by the increase in velocity on one side of the cylinder and a decrease on the opposite side. This is called the Magnus effect.&lt;br /&gt;
&lt;br /&gt;
= 4.5 EQUILIBRIUM OF FORCES IN STUDY DESCENT OR FLIGHT =&lt;br /&gt;
&lt;br /&gt;
=== 4.5.1 Parachute in Steady Descent ===&lt;br /&gt;
A stable parachute in unaccelerated descent has an equilibrium between the total drag of the parachute and the load, Dr, and the weight of the load and the parachute assembly, WT (Figure 4-11). For steady descent&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
D&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; = total drag, 1b&lt;br /&gt;
&lt;br /&gt;
D&amp;lt;sub&amp;gt;P&amp;lt;/sub&amp;gt; = drag of parachute, 1b&lt;br /&gt;
&lt;br /&gt;
W&amp;lt;sub&amp;gt;C&amp;lt;/sub&amp;gt; = weight of load. 1b&lt;br /&gt;
&lt;br /&gt;
In most cases, the drag of the load can be neglected in relation to the large drag of the parachute, With drag, D — (C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;S)&amp;lt;sub&amp;gt;p&amp;lt;/sub&amp;gt; • p/2• v&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; and D&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; = W&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;. and solving for v, the important equation for rate of descent, v&amp;lt;sub&amp;gt;e&amp;lt;/sub&amp;gt;, is obtained,&lt;br /&gt;
&lt;br /&gt;
Rate of descent,&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
FIGURE 4-11. Forces Acting on a Parachute in Steady Descent.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
or in parachute terminology for rate of descent at sea level&lt;br /&gt;
&lt;br /&gt;
and rate of descent at any altitude&lt;br /&gt;
&lt;br /&gt;
For 1/, see column 4 in Table 3-3,&lt;br /&gt;
&lt;br /&gt;
In the equation for rate of descent. V&amp;lt;sub&amp;gt;e&amp;lt;/sub&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
W&amp;lt;sub&amp;gt;T =&amp;lt;/sub&amp;gt; weight of load and parachute assembly, 1b&lt;br /&gt;
&lt;br /&gt;
S&amp;lt;sub&amp;gt;o&amp;lt;/sub&amp;gt; = canopy surface area, ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
C&amp;lt;sub&amp;gt;Do&amp;lt;/sub&amp;gt; = parachute drag coefficient related to S&amp;lt;sub&amp;gt;o&amp;lt;/sub&amp;gt;&lt;br /&gt;
&lt;br /&gt;
p = air density at a specific altitude in slugs/ft&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;, as shown in Table 3-3&lt;br /&gt;
&lt;br /&gt;
During descent from altitude, the parachute system is constantly decelerated because of the increasing air density. This can be ignored for slowly descending main parachutes. However, for drogue chute systems that descend at 200 ft/s or faster, the constant deceleration may result in velocities 3 to 5% higher than the steady rate of descent.&lt;br /&gt;
&lt;br /&gt;
=== 4.5.2 Gliding Parachutes ===&lt;br /&gt;
Figure 4-12 shows the balance of forces on a gliding parachute. The total weight of the system, W&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; . must be balanced by the resultant force. R. However, a lifting force is required for glide. To satisfy the force balance&lt;br /&gt;
&lt;br /&gt;
R = C&amp;lt;sub&amp;gt;R&amp;lt;/sub&amp;gt; * S * p/2 * v&lt;br /&gt;
&lt;br /&gt;
Trajectory velocity, V&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, is calculated&lt;br /&gt;
&lt;br /&gt;
Horizontal velocity is calculated&lt;br /&gt;
&lt;br /&gt;
V&amp;lt;sub&amp;gt;H&amp;lt;/sub&amp;gt; = V&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; • cosø, and vertical velocity, v&amp;lt;sub&amp;gt;v&amp;lt;/sub&amp;gt; = V&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; • sinø&lt;br /&gt;
&lt;br /&gt;
The glide ratio is obtained from&lt;br /&gt;
&lt;br /&gt;
Analysis of Figure 4-12 indicates that the larger the ratio of lift to drag, the better the glide ratio, I./D A high resultant coefficient, C&amp;lt;sub&amp;gt;R&amp;lt;/sub&amp;gt;, results in a low glide or trajectory V&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, desirable for landing. A small C&amp;lt;sub&amp;gt;R&amp;lt;/sub&amp;gt; results in a high glide velocity, V&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, which is desirable for flying toward a target, compensating for head winds, or covering a distance quickly. Generally, gliding parachutes follow the same aerodynamic rules as low-aspect-ratio wings.&lt;br /&gt;
&lt;br /&gt;
           	   	&lt;br /&gt;
&lt;br /&gt;
FIGUR E 4-12, Forces Acting on a Gliding Parachute&lt;br /&gt;
&lt;br /&gt;
=== 4.5.3 Parasite Drag and Induced Drag ===&lt;br /&gt;
The drag acting on a lift-producing air vehicle, such as a gliding parachute or an aircraft, has two primary components: the parasite drag, D&amp;lt;sub&amp;gt;P&amp;lt;/sub&amp;gt; , and the induced drag. D&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Parasite drag is produced by the form drag from individual components such as the suspension lines, canopy, and the jumper of a gliding parachute, and the fuselage, tail sectiora, and control surfaces of an airplane. Large surfaces produce surface friction drag as part of the parasite drag.&lt;br /&gt;
&lt;br /&gt;
Induced drag is caused by the lifting action of the parachute canopy or the aircraft wing. Section 4.7 includes books with detailed discussions of induced drag.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Total drag, D&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, can be defined as&lt;br /&gt;
&lt;br /&gt;
or, in the coefficient form&lt;br /&gt;
&lt;br /&gt;
The parasite drag, D&amp;lt;sub&amp;gt;p&amp;lt;/sub&amp;gt;, and the coefficient, C&amp;lt;sub&amp;gt;DP&amp;lt;/sub&amp;gt;, can be determined in wind-tunnel tests or calculated as the sum of the individual component drags.&lt;br /&gt;
&lt;br /&gt;
The induced drag coefficient, C&amp;lt;sub&amp;gt;Di&amp;lt;/sub&amp;gt; , of a gliding parachute canopy or a wing profile can be calculated&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
C = coefficient of induced drag, dimensionless&lt;br /&gt;
&lt;br /&gt;
The expression b&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;/S is defined as the aspect ratio of a wing or parachute with the notation AR b&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;/S. Therefore&lt;br /&gt;
&lt;br /&gt;
The equation for induced drag indicates that increasing the aspect ratio, AR, reduces the induced drag coefficient,  , and therefore reduces the drag, D. ms, in turn, increases the glide ratio, L/D. Increasing the glide ratio by increasing the aspect ratio is optimized on high-performance sailplanes with aspect ratios higher than 20. Increasing the glide ratio of gliding parachutes by increasing the aspect ratio has limitations, which are discussed in section 5.9.&lt;br /&gt;
&lt;br /&gt;
=== 4.5.4 Aircraft in Horizontal Flight ===&lt;br /&gt;
Figure 4-13 shows forces and moments on an aircraft in steady, horizontal flight. In steady, horizontal flight, an equilibrium exists between all forces and moments acting on the aircraft. Lift on the wing and tail, L&amp;lt;sub&amp;gt;W&amp;lt;/sub&amp;gt; and L&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;. and the weight of the aircraft, W&amp;lt;sub&amp;gt;A&amp;lt;/sub&amp;gt;, balance in the vertical plane. Thrust, T and drag. D, balance each other in the horizontal plane, and the positive or negative moment, M, is balanced by the positive or negative lift of the tail multiplied by the moment arm, L&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
FIGURE 4-13. Forces and Moments Acting on an Aircraft in Steady night,&lt;br /&gt;
&lt;br /&gt;
Any imbalance in these forces results in descent or climb in the vertical plane or faster or slower speed in the horizontal plane. A change in the lift of the elevator initiates climb or descent. Thrust, T, is the prime contributor for climb or descent and faster or slower speed, However, a balance of forces must always be maintained for horizontal flight or steady rate oi climb or descent.&lt;br /&gt;
&lt;br /&gt;
== 4.6 WIND-TUNNEL TESTING OF PARACHUTES ==&lt;br /&gt;
Wind tunnels are an effective tool for testing air vehicles and air-vehicle components and have been used successfully for testing parachutes and parachute systems. Experience has shown that certain rules apply for the wind-tunnel testing of parachutes. Small parachutes manufactured from textiles cannot be made sufficiently similar to large parachutes in geometric design and flexibility, Lightweight material. required to obtain design similarity, is difficult to manufacture or is unobtainable.&lt;br /&gt;
&lt;br /&gt;
One cardinal rule has been established through many years of parachute wind-tunnel testing: A modification that changes the performance of a model parachute in wind-tunnel testing produces the same type and percentage of performance change in a large parachute. This rule is true for drag. stability, and opening-force characteristics.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
=== 4.6.1 Blowers ===&lt;br /&gt;
The simple air blower (Figure 4-14) is a proven tool for preliminary parachute testing of a chiefly qualitative nature. Unless special test conditions prevail, parachutes tested should be a minimum of 1.5 to 2 feet in diameter to obtain meaningful results.&lt;br /&gt;
&lt;br /&gt;
                                                                    &lt;br /&gt;
&lt;br /&gt;
 FIGURE 4-14. Typical Air Blower.&lt;br /&gt;
&lt;br /&gt;
An air blower is a preliminary test too! because it permits quick parachute• configuration changes and excellent visual observation.&lt;br /&gt;
&lt;br /&gt;
=== 4.6.2 Open-Throat, No-Return Wind Tunnels ===&lt;br /&gt;
The open-throat, no-return wind tunnel shown in Figure 4-15 permits exact measurements if parachutes of sufficient size are used. Parachutes 3 feet or more in diameter are well suited for obtaining good, quantitative test results.&lt;br /&gt;
&lt;br /&gt;
              FIGURE 4-15. Open-Throat, No-Return Wind Tunnel&lt;br /&gt;
&lt;br /&gt;
In air blowers and open-throat wind tunnels, the velocity at the skirt of the parachute (Section a-a of Figures 4-14 and 4-15) is lower than the velocity at the nozzle exit of the wind tunnel (Section b&amp;lt;sup&amp;gt;-&amp;lt;/sup&amp;gt;b of Figures 4-14 and 4-15), Care must be taken to measure the parachute test&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
velocity at Section a-a and not at Section b-b, the customary attachment point for airfoils and models.&lt;br /&gt;
&lt;br /&gt;
Wind tunnels frequently cannot test at the descent velocity of most main parachutes of 20 to 30 feet per second. Obtaining proper test results at this low is hampered by a poor velocity distribution in the wind-tunnel-test section, and by the weight of the test parachute. The latter has a tendency to pull the parachute downward, thereby providing a negative angle of attack, lusting unstable parachutes at higher presents the problem that the drag coefficient C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, of unstable parachutes is sensitive. The drag coefficient of unstable parachutes is described in section 5.2.&lt;br /&gt;
&lt;br /&gt;
An open-throat wind tunnel permits quick changes in parachute configuration, such as changing the suspension and reefing line lengths. Large open-throat wind tunnels that are not sealed against outside elements suffer atmospheric problems such as fog formation in the test section.&lt;br /&gt;
&lt;br /&gt;
=== 4.6.3 Closed-Throat, Full-Return Wind Tunnel ===&lt;br /&gt;
Figure 4-16 is a drawing of a full-return, closed-throat wind tunnel. fic full-return, closed-throat wind tunnel is generally considered best suited for obtaining good. qualitative, aerodynamic data, since it has a uniform distribution in the test section. A disadvantage is the difficulty in gaining access to the test section for changing the parachute configuration.&lt;br /&gt;
&lt;br /&gt;
FIGURE 4-16. Closed-Throat, Full-Reuurn Wind Tunnel.&lt;br /&gt;
&lt;br /&gt;
=== 4.6.4 General Comments for Wind-Tunnel Testing of Parachutes ===&lt;br /&gt;
1. Parachute models for wind-tunnel testing should be as large and as similar as possible in geometry and flexibility to full-scale parachutes. Parachutes of less than 1.5 feet in diameter usually lack geometric similarity and material flexibility, which results in inflation characteristics and dissimilar inflated shapes.&lt;br /&gt;
&lt;br /&gt;
2.  The finished dimensions of model parachutes must be measured as accurately as possible to determine the nominal diameter, Do, and the surface area, So. Model parachutes will shrink from 5 to 10% during manufacture because of sewing take-up, which results in a notable difference in the dimensions between the drawing and the completed parachute.&lt;br /&gt;
&lt;br /&gt;
3.  Wind&amp;lt;sup&amp;gt;-&amp;lt;/sup&amp;gt;tunnel tests of parachutes are excellent for comparing different models and modifications: also, they are the most effective means for measuring coefficients of lift, drag. and normal and tangential forces, as well as for determining the load coefficient, for infinite load.&lt;br /&gt;
&lt;br /&gt;
4.  In wind-tunnel tests, velocity decay does not occur during parachute inflation and operation; this is defined as testing under &amp;quot;infinite mass condition. &amp;quot; First-stage drogue chutes and parachutes with a canopy loading, W/C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;S. in excess of 100 lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; approach this condition. Low-canopy-loading main parachutes with rates of descent of 20 to 30 ft/s have a large velocity decay during opening, which requires careful interpretation of the opening-force data obtained in wind-tunnel tests.&lt;br /&gt;
&lt;br /&gt;
5.  In the past, to avoid wind-tunnel blockage and questionable test data. the diameter of a test parachute could not exceed about 5 to 6% of the wind-tunnel test section area. Recent Sandia investigations of single and clustered ribbon parachutes with wind-tunnel blockage ratios of up to 30% have resulted in correction methods that make it possible to test much larger parachutes (Reference 4.2).&lt;br /&gt;
&lt;br /&gt;
= 4.7 REFERENCE MATERIAL =&lt;br /&gt;
4.1 H. H. Hurt. Aerodynamics for Naval Aviators Navy Manual NAVWEPS 00 80T 80. Chief of Naval Operations, Aviation Training Division.&lt;br /&gt;
&lt;br /&gt;
4.2 J, M. Macha and R J. Buffington. &amp;quot;Wall-Interference Corrections for Parachutes in a Closed Wind Tunnel.&amp;quot; AIM Paper, April 1989. (AIM 89-0900-cp.)&lt;br /&gt;
&lt;br /&gt;
For readers interested in a more detailed study of aerodynamics, the following books are recommended.&lt;br /&gt;
&lt;br /&gt;
4.3 J, H, Dwinnel, Principle of Aerodynamics. McGraw-Hill     	Co., New York, 1949.&lt;br /&gt;
&lt;br /&gt;
4.4 J. Morane. Introduction to Theoretical and Computational Aerodynamics. John Wiley &amp;amp; Sons.&lt;br /&gt;
&lt;br /&gt;
4.5 R.S. Shevell. Fundamentals of Flight. Prentice-Hall. 1983.&lt;br /&gt;
&lt;br /&gt;
4.6 J. D. Anderson, Jr. Introduction to Flights, ILS Engineering and History. McGraw-Hill Book co., New York 1978.&lt;br /&gt;
&lt;br /&gt;
4.7 D. J. Cockrell. The Aerodynamics of Parachutes.&amp;quot; AGARDograph No. 6295, available from NASA Langley Research Center, M/S 1M), Hampton, Va., 236.&lt;/div&gt;</summary>
		<author><name>TuanHTruong</name></author>
	</entry>
	<entry>
		<id>https://mediawiki.aerodecelerator.org/index.php?title=Parachute_Aerodynamics&amp;diff=31</id>
		<title>Parachute Aerodynamics</title>
		<link rel="alternate" type="text/html" href="https://mediawiki.aerodecelerator.org/index.php?title=Parachute_Aerodynamics&amp;diff=31"/>
		<updated>2024-05-07T02:35:57Z</updated>

		<summary type="html">&lt;p&gt;TuanHTruong: Added equations to section 4.3 and 4.4.&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&lt;br /&gt;
= CHAPTER 4: AERODYNAMICS AS RELATED TO PARACHUTES =&lt;br /&gt;
== 4.1 PROPERTIES OF THE ATMOSPHERE ==&lt;br /&gt;
All forces acting on parachutes and all movements of parachutes are affected by the atmosphere, or air, surrounding the Earth. The air at the Earth's surface is approximately 78% nitrogen; 21% oxygen; and 1% a mixture of gases such as argon, neon, helium, water vapor, and carbon dioxide. This chemical composition remains relatively constant to an altitude of about 160,000 feet (50 kilometers). The following air qualities are of major significance in the dynamics of bodies moving in the atmosphere:&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
!Air quality&lt;br /&gt;
!Symbol&lt;br /&gt;
!Dimension&lt;br /&gt;
|-&lt;br /&gt;
|Specific weight of air&lt;br /&gt;
|w&lt;br /&gt;
|lb/ft&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;, kg/m&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;&lt;br /&gt;
|-&lt;br /&gt;
|Static pressure&lt;br /&gt;
|p&lt;br /&gt;
|atm, lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;, Pa, bar, torr&lt;br /&gt;
|-&lt;br /&gt;
|Temperature&lt;br /&gt;
|T&lt;br /&gt;
|&amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F, &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;C&lt;br /&gt;
|-&lt;br /&gt;
|Mass density&lt;br /&gt;
|&amp;lt;math&amp;gt;\rho&amp;lt;/math&amp;gt;&lt;br /&gt;
|slugs/ft&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;, kg s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;/m&amp;lt;sup&amp;gt;4&amp;lt;/sup&amp;gt;&lt;br /&gt;
|-&lt;br /&gt;
|Gravity&lt;br /&gt;
|''g''&lt;br /&gt;
|ft/s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;, m/s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
|-&lt;br /&gt;
|Speed of sound&lt;br /&gt;
|C&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt;&lt;br /&gt;
|ft/s, m/s&lt;br /&gt;
|}&lt;br /&gt;
All of these qualities are altitude-dependent and may vary slightly on the Earth's surface with geographic latitude because of variations of the Earth's radius caused by the centrifugal forces of the rotation of the Earth. All standard data used herein refer to a latitude of 45 degrees. Sea level is defined as mean sea level (MSL). To compare performance data on an equal basis, the United States Bureau of Standards has defined standard day conditions as follows:&lt;br /&gt;
&lt;br /&gt;
* Temperature = 15 degrees Celsius (&amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;C) or 59 degrees Fahrenheit (&amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F)&lt;br /&gt;
* Pressure = 760 millimeters (mm) of mercury (Hg) or 29.9213 inches (in.) Hg&lt;br /&gt;
&lt;br /&gt;
=== 4.1.1 Specific Weight of Air ===&lt;br /&gt;
For standard day conditions of 59 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F temperature and a pressure of 29.9213 in. Hg, the specific weight of air, w, is 0.07648 lb/ft&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt; or 1.2250 kg/m&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;. The specific weight of air changes with pressure, temperature, and humidity. Further data can be found in References 3.4 and 4.1, and in technical handbooks.&lt;br /&gt;
&lt;br /&gt;
=== 4.1.2 Static Pressure ===&lt;br /&gt;
Static pressure depends on geographic latitude, weather conditions, and altitude. The static pressure at any altitude results from the weight of the air above that altitude. For MSL and standard day conditions, the pressure, p&amp;lt;sub&amp;gt;o&amp;lt;/sub&amp;gt;, is 29.9213 in. Hg = 760 mm Hg = 1.0 atmosphere (atm). For conversion to Pascal, torr, or bar, see the conversion tables in section 3.2.&lt;br /&gt;
&lt;br /&gt;
=== 4.1.3 Temperature ===&lt;br /&gt;
Temperatures are defined in the English and metric systems in the so-called absolute and engineering scales. The absolute temperature minimum at 0 degrees, pressure is 0 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;K = -273.16 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;C, and 0 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;R = -459.69 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F. This is also written&lt;br /&gt;
&lt;br /&gt;
* Degrees Kelvin = degrees Celsius + 273.16&lt;br /&gt;
* Degrees Rankine = degrees Fahrenheit + 459.69&lt;br /&gt;
&lt;br /&gt;
The freezing point of water is 32 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F or 0 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;C. The boiling point of water is 212 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F or 100 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;C.&lt;br /&gt;
&lt;br /&gt;
=== 4.1.4 Mass Density of Air ===&lt;br /&gt;
Mass density defines the amount of mass contained in a unit volume of air. The mass density, &amp;lt;math&amp;gt;\rho&amp;lt;/math&amp;gt;, of air is of special importance in aerodynamic calculations.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\rho = \frac{specific\ weight\ of\ air,\ w}{acceleration\ of\ gravity,\ g} = \frac{lb/ft^3}{ft/s^2} = \frac{kg\ s^2}{m^4}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;slug = \frac{weight}{acceleration\ of\ gravity} = \frac{lb}{ft/s^2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Frequently the density ratio, &amp;lt;math&amp;gt;\sigma&amp;lt;/math&amp;gt;, is used&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\sigma = \frac{ambient\ air\ density,\ \rho}{standard\ sea-level\ density, \rho_o}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The factor, &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;1/\sqrt{\rho/\rho_o}&amp;lt;/math&amp;gt;, determines the increase in parachute rate of descent with altitude. The density at 40,000 feet is ¼ of the MSL density, and the density at 100,000 feet is 1/75 of the MSL density. Therefore, the parachute rate of descent is about twice as high at 40,000 feet and about nine times as high at 100,000 feet. MSL density is 0.00237689 slugs/ft&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;, or 0.1249 kg s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;/m&amp;lt;sup&amp;gt;4&amp;lt;/sup&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
=== 4.1.5 Gravity ===&lt;br /&gt;
Any mass attracts another mass with a force called gravity. If the Earth were surrounded by a vacuum, a body suspended above the Earth and released would fall toward the center of the Earth with increasing velocity caused by the acceleration of gravity, ''g''. In reality, the falling body is decelerated by its air drag until the air drag, D, equals the weight of the body, W, and an equilibrium velocity is reached; for parachutes, this is called the steady-state rate of descent.&lt;br /&gt;
&lt;br /&gt;
The acceleration of gravity, ''g'', at sea lavel is&lt;br /&gt;
&lt;br /&gt;
* ''g'' = 32.174 ft/s2 or 9.80665 m/s2.&lt;br /&gt;
&lt;br /&gt;
The value g = 9.08665 m/s is standardized internationally but is accurate only for a latitude of 45 degrees.&lt;br /&gt;
&lt;br /&gt;
With increasing altitude above the Earth's surface, the acceleration of gravity decreases in accordance with the equation&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;g = g_o(\frac{r}{r+h})^2&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
* ''g'' = acceleration of gravity at any altitude, ft/s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
* g&amp;lt;sub&amp;gt;o&amp;lt;/sub&amp;gt; = acceleration of gravity at sea level, ft/s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
* r = average Earth radius = 2.08556 x 10&amp;lt;sup&amp;gt;7&amp;lt;/sup&amp;gt; ft&lt;br /&gt;
* h = altitude above sea level, ft&lt;br /&gt;
&lt;br /&gt;
For other planets and heavenly bodies, the acceleration of gravity varies with the mass of the body. For example, the acceleration of gravity on Mars is about 1/3 of the acceleration of gravity on Earth. For more details on planets and heavenly bodies, see page XII of Reference 2.1.&lt;br /&gt;
&lt;br /&gt;
=== 4.1.6 Kinematic Viscosity ===&lt;br /&gt;
The coefficient of viscosity, &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt;, defines the shearing stresses in a gas or liquid and is sometimes called the resistance to continuous deformation. In aerodynamics, the coefficient of viscosity is combined with the mass density to form the kinematic viscosity, &amp;lt;math&amp;gt;\nu&amp;lt;/math&amp;gt;, where&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\nu = \frac{coefficient\ of\ viscosity,\ \mu}{mass\ density,\ \rho} = 0.0001576\ ft^2/s\ at\ sea\ level&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The kinematic viscosity, &amp;lt;math&amp;gt;\nu&amp;lt;/math&amp;gt;, is altitude dependent and is used to calculate the Reynolds number, Re.&lt;br /&gt;
&lt;br /&gt;
=== 4.1.7 Reynolds Number ===&lt;br /&gt;
The Reynolds number, Re, defines the relationship of mass forces to viscous friction forces in liquids and gases. It is calculated as&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Re = \frac{v\cdot l}{\nu} = \frac{velocity\ (ft/s)\cdot characteristic\ length\ (ft)}{kinematic\ viscosity\ (ft^2/s)}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Reynolds number is an important criterion in subsonic, noncompressible flow, and allows comparison of model tests with full-scale flight tests. A Reynolds number effect on parachutes working in separated, turbulent flow has not yet been established, as shown in section 5.2. The following chart shows the Reynolds numbers for various air vehicles.&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
!Subject&lt;br /&gt;
!Insect&lt;br /&gt;
!Glider&lt;br /&gt;
!DC-3&lt;br /&gt;
!B-747&lt;br /&gt;
!Drogue&lt;br /&gt;
Chute&lt;br /&gt;
!Main &lt;br /&gt;
Parachute&lt;br /&gt;
!WTT&lt;br /&gt;
Model&lt;br /&gt;
|-&lt;br /&gt;
|Re&lt;br /&gt;
|6 • 10&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;&lt;br /&gt;
|2.5 • 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&lt;br /&gt;
|24 • 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&lt;br /&gt;
|100 • 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&lt;br /&gt;
|50 • 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&lt;br /&gt;
|20 • 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&lt;br /&gt;
|2 • 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
=== 4.1.8 Mach Number ===&lt;br /&gt;
Mach number is an important parameter of supersonic flight; it states how much faster than the speed of sound the air vehicle travels.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Mach\ number,\ M = \frac{flight\ velocity,\ v}{speed\ of\ sound, c_s}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The speed of sound is the velocity at which a pressure disturbance, such as the sound of the human voice, travels in any medium. The speed of sound varies considerably in different gases, liquids, and metals.&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|Speed of sound in air in MSL&lt;br /&gt;
|C&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt; = 1116.46 ft/s = 340.38 m/s&lt;br /&gt;
|-&lt;br /&gt;
|Speed of sound in water&lt;br /&gt;
|C&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt; = 4749 ft/s = 1461.21 m/s&lt;br /&gt;
|-&lt;br /&gt;
|Speed of sound in iron&lt;br /&gt;
|C&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt; = 16,410 ft/s = 5710.7 m/s&lt;br /&gt;
|}&lt;br /&gt;
The speed of sound depends on temperature and the chemical composition of the medium, A widely used equation for speed of sound in air is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;C_s = 41.4\sqrt{\gamma\cdot T}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
* &amp;lt;math&amp;gt;C_s&amp;lt;/math&amp;gt; = speed of sound in dry air, ft/s&lt;br /&gt;
* &amp;lt;math&amp;gt;\gamma&amp;lt;/math&amp;gt; = ratio of specific heat, equal to 1.4 for dry air, dimensionless&lt;br /&gt;
* &amp;lt;math&amp;gt;T&amp;lt;/math&amp;gt; = temperature in Fahrenheit absolute, equal to 459.67 + &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F&lt;br /&gt;
&lt;br /&gt;
The speed of sound changes with altitude, as temperature (see Figure 3-1). The drag of streamlined bodies such as missiles, airfoils, and airplanes increases considerably as their velocities approach Mach 1. Depending on the configuration of the body, supersonic compressibility effects may occur in the 0.75 to 0.85 Mach range, causing local supersonic flow, shock waves, flow separation, and concomitant increases in drag and changes in stability.&lt;br /&gt;
&lt;br /&gt;
Parachutes that operate in separated flow over the entire velocity range do not show the typical drag increase when operating close to or beyond Mach 1. Supersonic parachute behavior is discussed in detail in section 5.8.&lt;br /&gt;
&lt;br /&gt;
== '''4.2 CONTINUITY LAW AND BERNOULLI EQUATION''' ==&lt;br /&gt;
&lt;br /&gt;
=== 4.2.1 Continuity L.aw ===&lt;br /&gt;
Air is thought to flow in layers called streamlines. Figure 4-1 shows streamlines as layers of air without air transfer between individual layers. ne air is shown as being incompressible, a valid assumption for subsonic flow.&lt;br /&gt;
&lt;br /&gt;
[Insert Figure 4-1] 	&lt;br /&gt;
&lt;br /&gt;
If exchange of air does not occur across the streamline boundaries, the amount of air entering the streamline at point 1 must also exit at point 2, as shown in Figure 4-1. Because the cross section at point 2 is smaller than the cross section at point 1, the air must exit at a higher velocity. The following equation defines this condition:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;v_1\cdot S_1\cdot \rho_1 = v_2\cdot S_2\cdot \rho_2&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S&amp;lt;/math&amp;gt; = cross section of the streamline&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;v&amp;lt;/math&amp;gt; = velocity in the streamline&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\rho&amp;lt;/math&amp;gt; = density of the air flowing in the streamline&lt;br /&gt;
&lt;br /&gt;
This equation, which governs the flow in and around a body in gases and liquids, is important in aerodynamics and is called the Continuity Law. For incompressible subsonic flow, it can be simplified to &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;v_1\cdot S_1 = v_2\cdot S_2&amp;lt;/math&amp;gt; &lt;br /&gt;
&lt;br /&gt;
Whenever the cross section narrows, the velocity increases; when the cross section widens, the velocity decreases.&lt;br /&gt;
&lt;br /&gt;
=== 4.2.2 Bernoulli Equation ===&lt;br /&gt;
Figure 4-2 illustrates a streamline with the cross section, S, the velocity, v, and the pressure, p. If the air is incompressible, the downstream is v + Av. and the pressure is p + AP. If the air is inviscid, the inertia forces caused by the acceleration of air from v to v + Av must be balanced by differential pressure forces.&lt;br /&gt;
&lt;br /&gt;
[Insert Figure 4-2]FIGURE 4-2 Pressure and Velocity Distribution in a Streamline Element. 	&lt;br /&gt;
&lt;br /&gt;
The following equation can be written&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;p\cdot S-(p+\Delta p)S = m\cdot \frac{dv}{dt}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Simplified, the above equation yields&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;dp = - \rho vdv&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
and&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;p = - \frac{1}{2}\rho v^2 + C&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The above equation allows the following consideration: If p is pressure, then &amp;lt;math&amp;gt;1/2\ \rho v^2&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;C&amp;lt;/math&amp;gt; must also be pressure. The equation &amp;lt;math&amp;gt;1/2\ \rho v^2&amp;lt;/math&amp;gt; includes a velocity and is referred to as the dynamic pressure, or sometimes as velocity or impact pressure.&lt;br /&gt;
&lt;br /&gt;
Pressure, &amp;lt;math&amp;gt;p&amp;lt;/math&amp;gt;, is defined as static pressure; &amp;lt;math&amp;gt;1/2\ \rho v^2&amp;lt;/math&amp;gt; as dynamic pressure; and the sum of both, &amp;lt;math&amp;gt;C&amp;lt;/math&amp;gt;, as the total pressure or&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;p+\frac{1}{2} \rho v^2 = H&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
and&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;p_1 + \frac{1}{2} \rho {v_1}^2 = p_2 + \frac{1}{2} \rho {v_2}^2&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;H&amp;lt;/math&amp;gt; is the total pressure of the system, lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Dynamic pressure, &amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt;, is a frequently used quantity in aerodynamics:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;q = \frac{1}{2} \rho v^2&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
* &amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt; = dynamic pressure, lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
* &amp;lt;math&amp;gt;\rho&amp;lt;/math&amp;gt; =  air density, slugs/ft&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;&lt;br /&gt;
* &amp;lt;math&amp;gt;v&amp;lt;/math&amp;gt; =  velocity at a point of undisturbed flow, ft/s&lt;br /&gt;
&lt;br /&gt;
The following formulas are used for calculating the sea-level dynamic pressure if the velocity is given in ft/s, knots, mph, or km/h, respectively:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;q=\frac{v^2}{841.4}(ft/s), q=\frac{v^2}{295}(knots), q=\frac{v^2}{391.2}(mph), q=\frac{v^2}{1013.1}(km/h)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
                                              &lt;br /&gt;
&lt;br /&gt;
== '''4.3 NEWTON'S THREE OF MOTION''' ==&lt;br /&gt;
Engineering mechanics are governed by the following three laws of Isaac Newton:&lt;br /&gt;
&lt;br /&gt;
1.  A body remains at rest or in an unaccelerated state of motion unless acted upon.&lt;br /&gt;
&lt;br /&gt;
2.  A force acting upon a body will produce an acceleration in the direction of the force.&lt;br /&gt;
&lt;br /&gt;
3.  An action in one direction will produce an equal reaction in the opposite direction.&lt;br /&gt;
&lt;br /&gt;
The first law is self-explanatory. The second law may be expressed by the equation&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;F=m\cdot a&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;F&amp;lt;/math&amp;gt; = force in pounds acting on the mass, lb&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;m&amp;lt;/math&amp;gt; = mass of body that the force is acting upon, slugs&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;a&amp;lt;/math&amp;gt; = acceleration in ft/s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; resulting from the force, F&lt;br /&gt;
&lt;br /&gt;
The mass, m, of a body is obtained by&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;m=\frac{W}{g}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;W&amp;lt;/math&amp;gt; = weight of the body, lb&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;g&amp;lt;/math&amp;gt; = acceleration of gravity, ft/s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The mass, therefore, has the dimension of&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;m = \frac{W}{g}=\frac{lb}{ft/s^2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
This unit of mass is the slug.&lt;br /&gt;
&lt;br /&gt;
The equation of Newton's second law can now be written&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;F=\frac{W}{g}\cdot a,\ or\ F=W\frac{a}{g}&amp;lt;/math&amp;gt; 	&lt;br /&gt;
&lt;br /&gt;
The factor a/g is frequently called the load factor, G, and tells how much larger a force is than a force equivalent to the weight of the body. It is customary in parachute work to state that the maximum parachute force allowed is G • W or (a/g) • W. It is appropriate to write&lt;br /&gt;
&lt;br /&gt;
Maximum allowable parachute force, &amp;lt;math display=&amp;quot;inline&amp;quot;&amp;gt;F=W\frac{a}{g},\ or\ W\cdot G&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Figure 4-3 illustrates Newton's third law, explaining the principle of the rocket that can produce thrust in a perfect vacuum.&lt;br /&gt;
&lt;br /&gt;
A mass, m, ejected from a rocket at the velocity, v, per unit time, t, will produce a force, F, which in turn will create a reaction force, R, of equal magnitude but acting in the opposite direction.&lt;br /&gt;
&lt;br /&gt;
== 4.4 FORCES ACTING ON A BODY MOVING THROUGH AIR ==&lt;br /&gt;
&lt;br /&gt;
=== 4.4.1 Symmetrical Body ===&lt;br /&gt;
A body moving through air experiences forces caused by air pressure acting on the body. The same forces if the body moves through air, such as a descending parachute, or if the body is fixed and the air moves against the body, such as a parachute or an airfoil in a wind tunnel (Figure 44).&lt;br /&gt;
&lt;br /&gt;
         	 &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
A stable parachute in a wind tunnel experiences only the force called &amp;quot;drag&amp;quot; in the direction of the airflow. drag force, D, is calculated to&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;D=q\cdot S\cdot C_D&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;D&amp;lt;/math&amp;gt; = drag, lb&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt; = dynamic pressure, lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S&amp;lt;/math&amp;gt; = total surface area of the parachute canopy, ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;C_D&amp;lt;/math&amp;gt; = coefficient of drag,  dimensionless&lt;br /&gt;
&lt;br /&gt;
The dynamic pressure, q, can be calculated from section 4.2.2. The surface area of the canopy, S, is selected as a reference area. The drag coefficient, C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, is a form factor that indicates the drag characteristic of a specific shape. Most aerodynamic bodies are designed for low drag or a low drag coefficient. Parachutes, generally, are designed for high drag; therefore, a high drag coefficient is desirable. this difference in drag is demonstrated by the two bodies shown in Figure 4-5.&lt;br /&gt;
&lt;br /&gt;
            	&lt;br /&gt;
&lt;br /&gt;
Both bodies have the same cross section perpendicular to the airflow. The cylindrical. streamlined body has a smooth airflow over its total body length, resulting in a drag coefficient. C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, of 0.05 to 0.1, depending on slenderness ratio, surface roughness, and shape. The drag coefficient of all streamlined bodies is much affected by Reynolds number and Mach number. The open hemisphere, which is similar to a parachute canopy, has a drag coefficient, C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, of 1.3 to 1.4 for the same body cross section. The difference in drag is explained by the smooth airflow around the streamlined body and a separated, turbulent flow around the open hemisphere. The drag of bodies with separated flow, like parachute canopies, is little affected by Reynolds number.&lt;br /&gt;
&lt;br /&gt;
=== 4.4.2 Airflow Around an Asymmetrical Body (Airfoil) ===&lt;br /&gt;
Figure 4-6 shows an airfoil fixed at an angle of attack, a. against the airflow in a wind tunnel. This airfoil creates a drag force, D, in the direction of the flow; a lift force L perpendicular to the direction of the flow; and a moment, M. around the attachment point of the airfoil. fie sign convention of moments and forces shown are positive. Lift and drag can be combined for the resultant force, R.&lt;br /&gt;
&lt;br /&gt;
FIGURE. 4-6, Wind-Tunnel Forces Acting on an Airfoil.&lt;br /&gt;
&lt;br /&gt;
The lift, L is calculated&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;L = q\cdot S\cdot C_L&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;L&amp;lt;/math&amp;gt; = measured lift, lb&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt; = dynamic pressure, lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S&amp;lt;/math&amp;gt; = reference area, ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;C_L&amp;lt;/math&amp;gt; = lift coefficient, dimensionless&lt;br /&gt;
&lt;br /&gt;
The moment is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;M=q\cdot S\cdot c_m\cdot c&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Where&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;M&amp;lt;/math&amp;gt; = measured lift, lb&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt; = dynamic pressure, lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S&amp;lt;/math&amp;gt; = reference area, ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;c_m&amp;lt;/math&amp;gt; = moment coefficient, dimensionless&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;c&amp;lt;/math&amp;gt; = average chord width of the wing, ft&lt;br /&gt;
&lt;br /&gt;
The reference area, S, is defined by agreement. For streamlined bodies, the maximum body cross section is used. Airfoils use the planform of the wing, and parachutes use the canopy surface area. The selection of the wing planform and the parachute surface area as references was made for practical reasons. The wing planform for a specific wing is fixed, whereas the cross section of the wing in the direction of the flow changes with the angle of attack. Similarly, the surface area of the parachute canopy is fixed; however, the frontal projected area of the inflated parachute canopy changes with airspeed, porosity, line length, and type of parachute.&lt;br /&gt;
&lt;br /&gt;
Forces and moments acting on an airfoil or a parachute canopy may be presented in several ways. The two most frequently used methods, as shown in Figure 4-7, are with forces oriented to the axis of flight and with forces oriented to the axis of the airfoil.&lt;br /&gt;
&lt;br /&gt;
The tangential force, and the normal force, N, are calculated&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;T = C_T\cdot S\cdot q&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
and 	&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;N = C_N\cdot S\cdot q&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
C&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; = tangential force coefficient, dimensionless&lt;br /&gt;
&lt;br /&gt;
C&amp;lt;sub&amp;gt;N&amp;lt;/sub&amp;gt; = normal force coefficient, dimensionless&lt;br /&gt;
&lt;br /&gt;
The resultant force, R, and the moment, M, in both presentations have the same direction and the same magnitude. The airflow fixed system is preferred for aerodynamic performance calculations, and the airfoil fixed system for wing stress calculations. me aerodynamic coefficients C&amp;lt;sub&amp;gt;L&amp;lt;/sub&amp;gt;, C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, C&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, C&amp;lt;sub&amp;gt;N&amp;lt;/sub&amp;gt;, and C&amp;lt;sub&amp;gt;m&amp;lt;/sub&amp;gt; can easily be determined in wind•tunnel measurements.&lt;br /&gt;
&lt;br /&gt;
Figure 4-8 shows the relationship of both force systems on a parachute. By definition, a negative moment is stabilizing, as illustrated in Figure 4-8. It is interesting to note that in Europe the stabilizing moment is defined as positive. Wind-tunnel installations frequently measure normal and tangential force instead of lift and drag. If α, T, and N are known, the drag D, can be calculated&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;D=T\cdot cos(\alpha)+N\cdot sin(\alpha)&amp;lt;/math&amp;gt;For a parachute with an angle of attack, &amp;lt;math&amp;gt;\alpha&amp;lt;/math&amp;gt;, equal to zero, the drag force and the tangential force are synonymous.&lt;br /&gt;
&lt;br /&gt;
Figure 4-9 shows the coefficients C&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, and C&amp;lt;sub&amp;gt;m&amp;lt;/sub&amp;gt; versus angle of attack for stable and unstable parachutes.&lt;br /&gt;
&lt;br /&gt;
The coefficient presentation shows two interesting facts. The slope of the moment coefficient curve, dC&amp;lt;sub&amp;gt;m&amp;lt;/sub&amp;gt;/dα, for the unstable parachute is positive between -25 degrees and + 25 degrees; this is, by definition, destabilizing. This parachute will oscillate approximately ± 25&lt;br /&gt;
&lt;br /&gt;
FIGURE 4-9. Coefficients C&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, and C&amp;lt;sub&amp;gt;M&amp;lt;/sub&amp;gt; Versus Angle of Attack, α, for a Stable and Unstable Parachute.&lt;br /&gt;
&lt;br /&gt;
degrees. The slope of the moment, dC&amp;lt;sub&amp;gt;m&amp;lt;/sub&amp;gt;/dα, for the stable parachute is negative over the total angle of attack; this is, by definition, stabilizing. The steeper the negative dC&amp;lt;sub&amp;gt;m&amp;lt;/sub&amp;gt;/dα slope, the greater is the stabilizing tendency of the parachute, and the better is its damping capability against unstabilizing forces such as sudden gusts of wind.&lt;br /&gt;
&lt;br /&gt;
Figure 4-10, from Reference 4.1, demonstrates the effect of airflow around a cylinder and an airfoil. The circulation around a rotating cylinder creates lift caused by the increase in velocity on one side of the cylinder and a decrease on the opposite side. This is called the Magnus effect.&lt;br /&gt;
&lt;br /&gt;
= 4.5 EQUILIBRIUM OF FORCES IN STUDY DESCENT OR FLIGHT =&lt;br /&gt;
&lt;br /&gt;
=== 4.5.1 Parachute in Steady Descent ===&lt;br /&gt;
A stable parachute in unaccelerated descent has an equilibrium between the total drag of the parachute and the load, Dr, and the weight of the load and the parachute assembly, WT (Figure 4-11). For steady descent&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
D&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; = total drag, 1b&lt;br /&gt;
&lt;br /&gt;
D&amp;lt;sub&amp;gt;P&amp;lt;/sub&amp;gt; = drag of parachute, 1b&lt;br /&gt;
&lt;br /&gt;
W&amp;lt;sub&amp;gt;C&amp;lt;/sub&amp;gt; = weight of load. 1b&lt;br /&gt;
&lt;br /&gt;
In most cases, the drag of the load can be neglected in relation to the large drag of the parachute, With drag, D — (C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;S)&amp;lt;sub&amp;gt;p&amp;lt;/sub&amp;gt; • p/2• v&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; and D&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; = W&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;. and solving for v, the important equation for rate of descent, v&amp;lt;sub&amp;gt;e&amp;lt;/sub&amp;gt;, is obtained,&lt;br /&gt;
&lt;br /&gt;
Rate of descent,&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
FIGURE 4-11. Forces Acting on a Parachute in Steady Descent.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
or in parachute terminology for rate of descent at sea level&lt;br /&gt;
&lt;br /&gt;
and rate of descent at any altitude&lt;br /&gt;
&lt;br /&gt;
== For 1/, see column 4 in Table 3-3, ==&lt;br /&gt;
In the equation for rate of descent. V&amp;lt;sub&amp;gt;e&amp;lt;/sub&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
W&amp;lt;sub&amp;gt;T =&amp;lt;/sub&amp;gt; weight of load and parachute assembly, 1b&lt;br /&gt;
&lt;br /&gt;
S&amp;lt;sub&amp;gt;o&amp;lt;/sub&amp;gt; = canopy surface area, ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
C&amp;lt;sub&amp;gt;Do&amp;lt;/sub&amp;gt; = parachute drag coefficient related to S&amp;lt;sub&amp;gt;o&amp;lt;/sub&amp;gt;&lt;br /&gt;
&lt;br /&gt;
p = air density at a specific altitude in slugs/ft&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;, as shown in Table 3-3&lt;br /&gt;
&lt;br /&gt;
During descent from altitude, the parachute system is constantly decelerated because of the increasing air density. This can be ignored for slowly descending main parachutes. However, for drogue chute systems that descend at 200 ft/s or faster, the constant deceleration may result in velocities 3 to 5% higher than the steady rate of descent.&lt;br /&gt;
&lt;br /&gt;
4.5.2 Gliding Parachutes&lt;br /&gt;
&lt;br /&gt;
Figure 4-12 shows the balance of forces on a gliding parachute. The total weight of the system, W&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; . must be balanced by the resultant force. R. However, a lifting force is required for glide. To satisfy the force balance&lt;br /&gt;
&lt;br /&gt;
R = C&amp;lt;sub&amp;gt;R&amp;lt;/sub&amp;gt; * S * p/2 * v&lt;br /&gt;
&lt;br /&gt;
Trajectory velocity, V&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, is calculated&lt;br /&gt;
&lt;br /&gt;
Horizontal velocity is calculated&lt;br /&gt;
&lt;br /&gt;
V&amp;lt;sub&amp;gt;H&amp;lt;/sub&amp;gt; = V&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; • cosø, and vertical velocity, v&amp;lt;sub&amp;gt;v&amp;lt;/sub&amp;gt; = V&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; • sinø&lt;br /&gt;
&lt;br /&gt;
The glide ratio is obtained from&lt;br /&gt;
&lt;br /&gt;
Analysis of Figure 4-12 indicates that the larger the ratio of lift to drag, the better the glide ratio, I./D A high resultant coefficient, C&amp;lt;sub&amp;gt;R&amp;lt;/sub&amp;gt;, results in a low glide or trajectory V&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, desirable for landing. A small C&amp;lt;sub&amp;gt;R&amp;lt;/sub&amp;gt; results in a high glide velocity, V&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, which is desirable for flying toward a target, compensating for head winds, or covering a distance quickly. Generally, gliding parachutes follow the same aerodynamic rules as low-aspect-ratio wings.&lt;br /&gt;
&lt;br /&gt;
           	   	&lt;br /&gt;
&lt;br /&gt;
FIGUR E 4-12, Forces Acting on a Gliding Parachute&lt;br /&gt;
&lt;br /&gt;
4.5-3 Parasite Drag and Induced Drag&lt;br /&gt;
&lt;br /&gt;
The drag acting on a lift-producing air vehicle, such as a gliding parachute or an aircraft, has two primary components: the parasite drag, D&amp;lt;sub&amp;gt;P&amp;lt;/sub&amp;gt; , and the induced drag. D&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Parasite drag is produced by the form drag from individual components such as the suspension lines, canopy, and the jumper of a gliding parachute, and the fuselage, tail sectiora, and control surfaces of an airplane. Large surfaces produce surface friction drag as part of the parasite drag.&lt;br /&gt;
&lt;br /&gt;
Induced drag is caused by the lifting action of the parachute canopy or the aircraft wing. Section 4.7 includes books with detailed discussions of induced drag.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Total drag, D&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, can be defined as&lt;br /&gt;
&lt;br /&gt;
or, in the coefficient form&lt;br /&gt;
&lt;br /&gt;
The parasite drag, D&amp;lt;sub&amp;gt;p&amp;lt;/sub&amp;gt;, and the coefficient, C&amp;lt;sub&amp;gt;DP&amp;lt;/sub&amp;gt;, can be determined in wind-tunnel tests or calculated as the sum of the individual component drags.&lt;br /&gt;
&lt;br /&gt;
The induced drag coefficient, C&amp;lt;sub&amp;gt;Di&amp;lt;/sub&amp;gt; , of a gliding parachute canopy or a wing profile can be calculated&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
C = coefficient of induced drag, dimensionless&lt;br /&gt;
&lt;br /&gt;
The expression b&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;/S is defined as the aspect ratio of a wing or parachute with the notation AR b&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;/S. Therefore&lt;br /&gt;
&lt;br /&gt;
== '''                       ''' 	 ==&lt;br /&gt;
The equation for induced drag indicates that increasing the aspect ratio, AR, reduces the induced drag coefficient,  , and therefore reduces the drag, D. ms, in turn, increases the glide ratio, L/D. Increasing the glide ratio by increasing the aspect ratio is optimized on high-performance sailplanes with aspect ratios higher than 20. Increasing the glide ratio of gliding parachutes by increasing the aspect ratio has limitations, which are discussed in section 5.9.&lt;br /&gt;
&lt;br /&gt;
4.5.4 Aircraft in Horizontal Flight&lt;br /&gt;
&lt;br /&gt;
Figure 4-13 shows forces and moments on an aircraft in steady, horizontal flight. In steady, horizontal flight, an equilibrium exists between all forces and moments acting on the aircraft. Lift on the wing and tail, L&amp;lt;sub&amp;gt;W&amp;lt;/sub&amp;gt; and L&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;. and the weight of the aircraft, W&amp;lt;sub&amp;gt;A&amp;lt;/sub&amp;gt;, balance in the vertical plane. Thrust, T and drag. D, balance each other in the horizontal plane, and the positive or negative moment, M, is balanced by the positive or negative lift of the tail multiplied by the moment arm, L&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
FIGURE 4-13. Forces and Moments Acting on an Aircraft in Steady night,&lt;br /&gt;
&lt;br /&gt;
Any imbalance in these forces results in descent or climb in the vertical plane or faster or slower speed in the horizontal plane. A change in the lift of the elevator initiates climb or descent. Thrust, T, is the prime contributor for climb or descent and faster or slower speed, However, a balance of forces must always be maintained for horizontal flight or steady rate oi climb or descent.&lt;br /&gt;
&lt;br /&gt;
== 4.6 WIND-TUNNEL TESTING OF PARACHUTES ==&lt;br /&gt;
Wind tunnels are an effective tool for testing air vehicles and air-vehicle components and have been used successfully for testing parachutes and parachute systems. Experience has shown that certain rules apply for the wind-tunnel testing of parachutes. Small parachutes manufactured from textiles cannot be made sufficiently similar to large parachutes in geometric design and flexibility, Lightweight material. required to obtain design similarity, is difficult to manufacture or is unobtainable.&lt;br /&gt;
&lt;br /&gt;
One cardinal rule has been established through many years of parachute wind-tunnel testing: A modification that changes the performance of a model parachute in wind-tunnel testing produces the same type and percentage of performance change in a large parachute. This rule is true for drag. stability, and opening-force characteristics.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
4.6.1 Blowers&lt;br /&gt;
&lt;br /&gt;
The simple air blower (Figure 4-14) is a proven tool for preliminary parachute testing of a chiefly qualitative nature. Unless special test conditions prevail, parachutes tested should be a minimum of 1.5 to 2 feet in diameter to obtain meaningful results.&lt;br /&gt;
&lt;br /&gt;
                                                                    &lt;br /&gt;
&lt;br /&gt;
 FIGURE 4-14. Typical Air Blower.&lt;br /&gt;
&lt;br /&gt;
An air blower is a preliminary test too! because it permits quick parachute• configuration changes and excellent visual observation.&lt;br /&gt;
&lt;br /&gt;
4.6.2 Open-Throat, No-Return Wind Tunnels&lt;br /&gt;
&lt;br /&gt;
The open-throat, no-return wind tunnel shown in Figure 4-15 permits exact measurements if parachutes of sufficient size are used. Parachutes 3 feet or more in diameter are well suited for obtaining good, quantitative test results.&lt;br /&gt;
&lt;br /&gt;
              FIGURE 4-15. Open-Throat, No-Return Wind Tunnel&lt;br /&gt;
&lt;br /&gt;
In air blowers and open-throat wind tunnels, the velocity at the skirt of the parachute (Section a-a of Figures 4-14 and 4-15) is lower than the velocity at the nozzle exit of the wind tunnel (Section b&amp;lt;sup&amp;gt;-&amp;lt;/sup&amp;gt;b of Figures 4-14 and 4-15), Care must be taken to measure the parachute test&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
velocity at Section a-a and not at Section b-b, the customary attachment point for airfoils and models.&lt;br /&gt;
&lt;br /&gt;
Wind tunnels frequently cannot test at the descent velocity of most main parachutes of 20 to 30 feet per second. Obtaining proper test results at this low is hampered by a poor velocity distribution in the wind-tunnel-test section, and by the weight of the test parachute. The latter has a tendency to pull the parachute downward, thereby providing a negative angle of attack, lusting unstable parachutes at higher presents the problem that the drag coefficient C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, of unstable parachutes is sensitive. The drag coefficient of unstable parachutes is described in section 5.2.&lt;br /&gt;
&lt;br /&gt;
An open-throat wind tunnel permits quick changes in parachute configuration, such as changing the suspension and reefing line lengths. Large open-throat wind tunnels that are not sealed against outside elements suffer atmospheric problems such as fog formation in the test section.&lt;br /&gt;
&lt;br /&gt;
4.6.3 Closed-Throat, Full-Return Wind Tunnel&lt;br /&gt;
&lt;br /&gt;
Figure 4-16 is a drawing of a full-return, closed-throat wind tunnel. fic full-return, closed-throat wind tunnel is generally considered best suited for obtaining good. qualitative, aerodynamic data, since it has a uniform distribution in the test section. A disadvantage is the difficulty in gaining access to the test section for changing the parachute configuration.&lt;br /&gt;
&lt;br /&gt;
FIGURE 4-16. Closed-Throat, Full-Reuurn Wind Tunnel.&lt;br /&gt;
&lt;br /&gt;
4.6.4 General Comments for Wind-Tunnel Testing of Parachutes&lt;br /&gt;
&lt;br /&gt;
1. Parachute models for wind-tunnel testing should be as large and as similar as possible in geometry and flexibility to full-scale parachutes. Parachutes of less than 1.5 feet in diameter usually lack geometric similarity and material flexibility, which results in inflation characteristics and dissimilar inflated shapes.&lt;br /&gt;
&lt;br /&gt;
2.  The finished dimensions of model parachutes must be measured as accurately as possible to determine the nominal diameter, Do, and the surface area, So. Model parachutes will shrink from 5 to 10% during manufacture because of sewing take-up, which results in a notable difference in the dimensions between the drawing and the completed parachute.&lt;br /&gt;
&lt;br /&gt;
3.  Wind&amp;lt;sup&amp;gt;-&amp;lt;/sup&amp;gt;tunnel tests of parachutes are excellent for comparing different models and modifications: also, they are the most effective means for measuring coefficients of lift, drag. and normal and tangential forces, as well as for determining the load coefficient, for infinite load.&lt;br /&gt;
&lt;br /&gt;
4.  In wind-tunnel tests, velocity decay does not occur during parachute inflation and operation; this is defined as testing under &amp;quot;infinite mass condition. &amp;quot; First-stage drogue chutes and parachutes with a canopy loading, W/C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;S. in excess of 100 lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; approach this condition. Low-canopy-loading main parachutes with rates of descent of 20 to 30 ft/s have a large velocity decay during opening, which requires careful interpretation of the opening-force data obtained in wind-tunnel tests.&lt;br /&gt;
&lt;br /&gt;
5.  In the past, to avoid wind-tunnel blockage and questionable test data. the diameter of a test parachute could not exceed about 5 to 6% of the wind-tunnel test section area. Recent Sandia investigations of single and clustered ribbon parachutes with wind-tunnel blockage ratios of up to 30% have resulted in correction methods that make it possible to test much larger parachutes (Reference 4.2).&lt;br /&gt;
&lt;br /&gt;
= 4.7 REFERENCE MATERIAL =&lt;br /&gt;
4.1 H. H. Hurt. Aerodynamics for Naval Aviators Navy Manual NAVWEPS 00 80T 80. Chief of Naval Operations, Aviation Training Division.&lt;br /&gt;
&lt;br /&gt;
4.2 J, M. Macha and R J. Buffington. &amp;quot;Wall-Interference Corrections for Parachutes in a Closed Wind Tunnel.&amp;quot; AIM Paper, April 1989. (AIM 89-0900-cp.)&lt;br /&gt;
&lt;br /&gt;
For readers interested in a more detailed study of aerodynamics, the following books are recommended.&lt;br /&gt;
&lt;br /&gt;
4.3 J, H, Dwinnel, Principle of Aerodynamics. McGraw-Hill     	Co., New York, 1949.&lt;br /&gt;
&lt;br /&gt;
4.4 J. Morane. Introduction to Theoretical and Computational Aerodynamics. John Wiley &amp;amp; Sons.&lt;br /&gt;
&lt;br /&gt;
4.5 R.S. Shevell. Fundamentals of Flight. Prentice-Hall. 1983.&lt;br /&gt;
&lt;br /&gt;
4.6 J. D. Anderson, Jr. Introduction to Flights, ILS Engineering and History. McGraw-Hill Book co., New York 1978.&lt;br /&gt;
&lt;br /&gt;
4.7 D. J. Cockrell. The Aerodynamics of Parachutes.&amp;quot; AGARDograph No. 6295, available from NASA Langley Research Center, M/S 1M), Hampton, Va., 236.&lt;/div&gt;</summary>
		<author><name>TuanHTruong</name></author>
	</entry>
	<entry>
		<id>https://mediawiki.aerodecelerator.org/index.php?title=Parachute_Aerodynamics&amp;diff=30</id>
		<title>Parachute Aerodynamics</title>
		<link rel="alternate" type="text/html" href="https://mediawiki.aerodecelerator.org/index.php?title=Parachute_Aerodynamics&amp;diff=30"/>
		<updated>2024-05-04T00:39:25Z</updated>

		<summary type="html">&lt;p&gt;TuanHTruong: Finished section 4.2 except for graphics and images.&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&lt;br /&gt;
= CHAPTER 4: AERODYNAMICS AS RELATED TO PARACHUTES =&lt;br /&gt;
== 4.1 PROPERTIES OF THE ATMOSPHERE ==&lt;br /&gt;
All forces acting on parachutes and all movements of parachutes are affected by the atmosphere, or air, surrounding the Earth. The air at the Earth's surface is approximately 78% nitrogen; 21% oxygen; and 1% a mixture of gases such as argon, neon, helium, water vapor, and carbon dioxide. This chemical composition remains relatively constant to an altitude of about 160,000 feet (50 kilometers). The following air qualities are of major significance in the dynamics of bodies moving in the atmosphere:&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
!Air quality&lt;br /&gt;
!Symbol&lt;br /&gt;
!Dimension&lt;br /&gt;
|-&lt;br /&gt;
|Specific weight of air&lt;br /&gt;
|w&lt;br /&gt;
|lb/ft&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;, kg/m&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;&lt;br /&gt;
|-&lt;br /&gt;
|Static pressure&lt;br /&gt;
|p&lt;br /&gt;
|atm, lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;, Pa, bar, torr&lt;br /&gt;
|-&lt;br /&gt;
|Temperature&lt;br /&gt;
|T&lt;br /&gt;
|&amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F, &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;C&lt;br /&gt;
|-&lt;br /&gt;
|Mass density&lt;br /&gt;
|&amp;lt;math&amp;gt;\rho&amp;lt;/math&amp;gt;&lt;br /&gt;
|slugs/ft&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;, kg s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;/m&amp;lt;sup&amp;gt;4&amp;lt;/sup&amp;gt;&lt;br /&gt;
|-&lt;br /&gt;
|Gravity&lt;br /&gt;
|''g''&lt;br /&gt;
|ft/s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;, m/s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
|-&lt;br /&gt;
|Speed of sound&lt;br /&gt;
|C&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt;&lt;br /&gt;
|ft/s, m/s&lt;br /&gt;
|}&lt;br /&gt;
All of these qualities are altitude-dependent and may vary slightly on the Earth's surface with geographic latitude because of variations of the Earth's radius caused by the centrifugal forces of the rotation of the Earth. All standard data used herein refer to a latitude of 45 degrees. Sea level is defined as mean sea level (MSL). To compare performance data on an equal basis, the United States Bureau of Standards has defined standard day conditions as follows:&lt;br /&gt;
&lt;br /&gt;
* Temperature = 15 degrees Celsius (&amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;C) or 59 degrees Fahrenheit (&amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F)&lt;br /&gt;
* Pressure = 760 millimeters (mm) of mercury (Hg) or 29.9213 inches (in.) Hg&lt;br /&gt;
&lt;br /&gt;
=== 4.1.1 Specific Weight of Air ===&lt;br /&gt;
For standard day conditions of 59 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F temperature and a pressure of 29.9213 in. Hg, the specific weight of air, w, is 0.07648 lb/ft&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt; or 1.2250 kg/m&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;. The specific weight of air changes with pressure, temperature, and humidity. Further data can be found in References 3.4 and 4.1, and in technical handbooks.&lt;br /&gt;
&lt;br /&gt;
=== 4.1.2 Static Pressure ===&lt;br /&gt;
Static pressure depends on geographic latitude, weather conditions, and altitude. The static pressure at any altitude results from the weight of the air above that altitude. For MSL and standard day conditions, the pressure, p&amp;lt;sub&amp;gt;o&amp;lt;/sub&amp;gt;, is 29.9213 in. Hg = 760 mm Hg = 1.0 atmosphere (atm). For conversion to Pascal, torr, or bar, see the conversion tables in section 3.2.&lt;br /&gt;
&lt;br /&gt;
=== 4.1.3 Temperature ===&lt;br /&gt;
Temperatures are defined in the English and metric systems in the so-called absolute and engineering scales. The absolute temperature minimum at 0 degrees, pressure is 0 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;K = -273.16 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;C, and 0 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;R = -459.69 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F. This is also written&lt;br /&gt;
&lt;br /&gt;
* Degrees Kelvin = degrees Celsius + 273.16&lt;br /&gt;
* Degrees Rankine = degrees Fahrenheit + 459.69&lt;br /&gt;
&lt;br /&gt;
The freezing point of water is 32 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F or 0 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;C. The boiling point of water is 212 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F or 100 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;C.&lt;br /&gt;
&lt;br /&gt;
=== 4.1.4 Mass Density of Air ===&lt;br /&gt;
Mass density defines the amount of mass contained in a unit volume of air. The mass density, &amp;lt;math&amp;gt;\rho&amp;lt;/math&amp;gt;, of air is of special importance in aerodynamic calculations.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\rho = \frac{specific\ weight\ of\ air,\ w}{acceleration\ of\ gravity,\ g} = \frac{lb/ft^3}{ft/s^2} = \frac{kg\ s^2}{m^4}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;slug = \frac{weight}{acceleration\ of\ gravity} = \frac{lb}{ft/s^2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Frequently the density ratio, &amp;lt;math&amp;gt;\sigma&amp;lt;/math&amp;gt;, is used&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\sigma = \frac{ambient\ air\ density,\ \rho}{standard\ sea-level\ density, \rho_o}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The factor, &amp;lt;math&amp;gt;1/\sqrt{\rho/\rho_o}&amp;lt;/math&amp;gt;, determines the increase in parachute rate of descent with altitude. The density at 40,000 feet is ¼ of the MSL density, and the density at 100,000 feet is 1/75 of the MSL density. Therefore, the parachute rate of descent is about twice as high at 40,000 feet and about nine times as high at 100,000 feet. MSL density is 0.00237689 slugs/ft&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;, or 0.1249 kg s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;/m&amp;lt;sup&amp;gt;4&amp;lt;/sup&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
=== 4.1.5 Gravity ===&lt;br /&gt;
Any mass attracts another mass with a force called gravity. If the Earth were surrounded by a vacuum, a body suspended above the Earth and released would fall toward the center of the Earth with increasing velocity caused by the acceleration of gravity, ''g''. In reality, the falling body is decelerated by its air drag until the air drag, D, equals the weight of the body, W, and an equilibrium velocity is reached; for parachutes, this is called the steady-state rate of descent.&lt;br /&gt;
&lt;br /&gt;
The acceleration of gravity, ''g'', at sea lavel is&lt;br /&gt;
&lt;br /&gt;
* ''g'' = 32.174 ft/s2 or 9.80665 m/s2.&lt;br /&gt;
&lt;br /&gt;
The value g = 9.08665 m/s is standardized internationally but is accurate only for a latitude of 45 degrees.&lt;br /&gt;
&lt;br /&gt;
With increasing altitude above the Earth's surface, the acceleration of gravity decreases in accordance with the equation&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;g = g_o(\frac{r}{r+h})^2&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
* ''g'' = acceleration of gravity at any altitude, ft/s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
* g&amp;lt;sub&amp;gt;o&amp;lt;/sub&amp;gt; = acceleration of gravity at sea level, ft/s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
* r = average Earth radius = 2.08556 x 10&amp;lt;sup&amp;gt;7&amp;lt;/sup&amp;gt; ft&lt;br /&gt;
* h = altitude above sea level, ft&lt;br /&gt;
&lt;br /&gt;
For other planets and heavenly bodies, the acceleration of gravity varies with the mass of the body. For example, the acceleration of gravity on Mars is about 1/3 of the acceleration of gravity on Earth. For more details on planets and heavenly bodies, see page XII of Reference 2.1.&lt;br /&gt;
&lt;br /&gt;
=== 4.1.6 Kinematic Viscosity ===&lt;br /&gt;
The coefficient of viscosity, &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt;, defines the shearing stresses in a gas or liquid and is sometimes called the resistance to continuous deformation. In aerodynamics, the coefficient of viscosity is combined with the mass density to form the kinematic viscosity, &amp;lt;math&amp;gt;\nu&amp;lt;/math&amp;gt;, where&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\nu = \frac{coefficient\ of\ viscosity,\ \mu}{mass\ density,\ \rho} = 0.0001576\ ft^2/s\ at\ sea\ level&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The kinematic viscosity, &amp;lt;math&amp;gt;\nu&amp;lt;/math&amp;gt;, is altitude dependent and is used to calculate the Reynolds number, Re.&lt;br /&gt;
&lt;br /&gt;
=== 4.1.7 Reynolds Number ===&lt;br /&gt;
The Reynolds number, Re, defines the relationship of mass forces to viscous friction forces in liquids and gases. It is calculated as&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Re = \frac{v\cdot l}{\nu} = \frac{velocity\ (ft/s)\cdot characteristic\ length\ (ft)}{kinematic\ viscosity\ (ft^2/s)}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Reynolds number is an important criterion in subsonic, noncompressible flow, and allows comparison of model tests with full-scale flight tests. A Reynolds number effect on parachutes working in separated, turbulent flow has not yet been established, as shown in section 5.2. The following chart shows the Reynolds numbers for various air vehicles.&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
!Subject&lt;br /&gt;
!Insect&lt;br /&gt;
!Glider&lt;br /&gt;
!DC-3&lt;br /&gt;
!B-747&lt;br /&gt;
!Drogue&lt;br /&gt;
Chute&lt;br /&gt;
!Main &lt;br /&gt;
Parachute&lt;br /&gt;
!WTT&lt;br /&gt;
Model&lt;br /&gt;
|-&lt;br /&gt;
|Re&lt;br /&gt;
|6 • 10&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;&lt;br /&gt;
|2.5 • 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&lt;br /&gt;
|24 • 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&lt;br /&gt;
|100 • 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&lt;br /&gt;
|50 • 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&lt;br /&gt;
|20 • 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&lt;br /&gt;
|2 • 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
=== 4.1.8 Mach Number ===&lt;br /&gt;
Mach number is an important parameter of supersonic flight; it states how much faster than the speed of sound the air vehicle travels.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Mach\ number,\ M = \frac{flight\ velocity,\ v}{speed\ of\ sound, c_s}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The speed of sound is the velocity at which a pressure disturbance, such as the sound of the human voice, travels in any medium. The speed of sound varies considerably in different gases, liquids, and metals.&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|Speed of sound in air in MSL&lt;br /&gt;
|C&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt; = 1116.46 ft/s = 340.38 m/s&lt;br /&gt;
|-&lt;br /&gt;
|Speed of sound in water&lt;br /&gt;
|C&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt; = 4749 ft/s = 1461.21 m/s&lt;br /&gt;
|-&lt;br /&gt;
|Speed of sound in iron&lt;br /&gt;
|C&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt; = 16,410 ft/s = 5710.7 m/s&lt;br /&gt;
|}&lt;br /&gt;
The speed of sound depends on temperature and the chemical composition of the medium, A widely used equation for speed of sound in air is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;C_s = 41.4\sqrt{\gamma\cdot T}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
* &amp;lt;math&amp;gt;C_s&amp;lt;/math&amp;gt; = speed of sound in dry air, ft/s&lt;br /&gt;
* &amp;lt;math&amp;gt;\gamma&amp;lt;/math&amp;gt; = ratio of specific heat, equal to 1.4 for dry air, dimensionless&lt;br /&gt;
* &amp;lt;math&amp;gt;T&amp;lt;/math&amp;gt; = temperature in Fahrenheit absolute, equal to 459.67 + &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F&lt;br /&gt;
&lt;br /&gt;
The speed of sound changes with altitude, as temperature (see Figure 3-1). The drag of streamlined bodies such as missiles, airfoils, and airplanes increases considerably as their velocities approach Mach 1. Depending on the configuration of the body, supersonic compressibility effects may occur in the 0.75 to 0.85 Mach range, causing local supersonic flow, shock waves, flow separation, and concomitant increases in drag and changes in stability.&lt;br /&gt;
&lt;br /&gt;
Parachutes that operate in separated flow over the entire velocity range do not show the typical drag increase when operating close to or beyond Mach 1. Supersonic parachute behavior is discussed in detail in section 5.8.&lt;br /&gt;
&lt;br /&gt;
== '''4.2 CONTINUITY LAW AND BERNOULLI EQUATION''' ==&lt;br /&gt;
&lt;br /&gt;
=== 4.2.1 Continuity L.aw ===&lt;br /&gt;
Air is thought to flow in layers called streamlines. Figure 4-1 shows streamlines as layers of air without air transfer between individual layers. ne air is shown as being incompressible, a valid assumption for subsonic flow.&lt;br /&gt;
&lt;br /&gt;
[Insert Figure 4-1] 	&lt;br /&gt;
&lt;br /&gt;
If exchange of air does not occur across the streamline boundaries, the amount of air entering the streamline at point 1 must also exit at point 2, as shown in Figure 4-1. Because the cross section at point 2 is smaller than the cross section at point 1, the air must exit at a higher velocity. The following equation defines this condition:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;v_1\cdot S_1\cdot \rho_1 = v_2\cdot S_2\cdot \rho_2&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;S&amp;lt;/math&amp;gt; = cross section of the streamline&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;v&amp;lt;/math&amp;gt; = velocity in the streamline&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\rho&amp;lt;/math&amp;gt; = density of the air flowing in the streamline&lt;br /&gt;
&lt;br /&gt;
This equation, which governs the flow in and around a body in gases and liquids, is important in aerodynamics and is called the Continuity Law. For incompressible subsonic flow, it can be simplified to &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;v_1\cdot S_1 = v_2\cdot S_2&amp;lt;/math&amp;gt; &lt;br /&gt;
&lt;br /&gt;
Whenever the cross section narrows, the velocity increases; when the cross section widens, the velocity decreases.&lt;br /&gt;
&lt;br /&gt;
=== 4.2.2 Bernoulli Equation ===&lt;br /&gt;
Figure 4-2 illustrates a streamline with the cross section, S, the velocity, v, and the pressure, p. If the air is incompressible, the downstream is v + Av. and the pressure is p + AP. If the air is inviscid, the inertia forces caused by the acceleration of air from v to v + Av must be balanced by differential pressure forces.&lt;br /&gt;
&lt;br /&gt;
[Insert Figure 4-2]FIGURE 4-2 Pressure and Velocity Distribution in a Streamline Element. 	&lt;br /&gt;
&lt;br /&gt;
The following equation can be written&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;p\cdot S-(p+\Delta p)S = m\cdot \frac{dv}{dt}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Simplified, the above equation yields&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;dp = - \rho vdv&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
and&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;p = - \frac{1}{2}\rho v^2 + C&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The above equation allows the following consideration: If p is pressure, then &amp;lt;math&amp;gt;1/2\ \rho v^2&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;C&amp;lt;/math&amp;gt; must also be pressure. The equation &amp;lt;math&amp;gt;1/2\ \rho v^2&amp;lt;/math&amp;gt; includes a velocity and is referred to as the dynamic pressure, or sometimes as velocity or impact pressure.&lt;br /&gt;
&lt;br /&gt;
Pressure, &amp;lt;math&amp;gt;p&amp;lt;/math&amp;gt;, is defined as static pressure; &amp;lt;math&amp;gt;1/2\ \rho v^2&amp;lt;/math&amp;gt; as dynamic pressure; and the sum of both, &amp;lt;math&amp;gt;C&amp;lt;/math&amp;gt;, as the total pressure or&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;p+\frac{1}{2} \rho v^2 = H&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
and&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;p_1 + \frac{1}{2} \rho {v_1}^2 = p_2 + \frac{1}{2} \rho {v_2}^2&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;H&amp;lt;/math&amp;gt; is the total pressure of the system, lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Dynamic pressure, &amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt;, is a frequently used quantity in aerodynamics:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;q = \frac{1}{2} \rho v^2&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
* &amp;lt;math&amp;gt;q&amp;lt;/math&amp;gt; = dynamic pressure, lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
* &amp;lt;math&amp;gt;\rho&amp;lt;/math&amp;gt; =  air density, slugs/ft&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;&lt;br /&gt;
* &amp;lt;math&amp;gt;v&amp;lt;/math&amp;gt; =  velocity at a point of undisturbed flow, ft/s&lt;br /&gt;
&lt;br /&gt;
The following formulas are used for calculating the sea-level dynamic pressure if the velocity is given in ft/s, knots, mph, or km/h, respectively:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;q=\frac{v^2}{841.4}(ft/s), q=\frac{v^2}{295}(knots), q=\frac{v^2}{391.2}(mph), q=\frac{v^2}{1013.1}(km/h)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
                                              &lt;br /&gt;
&lt;br /&gt;
== '''4.3 NEWTON'S THREE OF MOTION''' ==&lt;br /&gt;
Engineering mechanics are governed by the following three laws of Isaac Newton:&lt;br /&gt;
&lt;br /&gt;
1.  A body remains at rest or in an unaccelerated state of motion unless acted upon.&lt;br /&gt;
&lt;br /&gt;
2.  A force acting upon a body will produce an acceleration in the direction of the force.&lt;br /&gt;
&lt;br /&gt;
3.  An action in one direction will produce an equal reaction in the opposite direction.&lt;br /&gt;
&lt;br /&gt;
The first law is self-explanatory. The second law may be expressed by the equation&lt;br /&gt;
&lt;br /&gt;
F = m * a&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
F = force in pounds acting on the mass, 1b&lt;br /&gt;
&lt;br /&gt;
m = mass of body that the force is acting upon, slugs&lt;br /&gt;
&lt;br /&gt;
a = acceleration in ft/s2 resulting from the force, F&lt;br /&gt;
&lt;br /&gt;
The mass, m, of a body is obtained by&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
W = weight of the body, lb&lt;br /&gt;
&lt;br /&gt;
g = acceleration of gravity, ft/s2&lt;br /&gt;
&lt;br /&gt;
The mass, therefore, has the dimension of&lt;br /&gt;
&lt;br /&gt;
This unit of mass is the slug.&lt;br /&gt;
&lt;br /&gt;
the equation of Newton's second law can now be written&lt;br /&gt;
&lt;br /&gt;
                                        	&lt;br /&gt;
&lt;br /&gt;
The factor a/g is frequently called the load factor, G, and tells how much larger a force is than a force equivalent to the weight of the body. It is customary in parachute work to state that the maximum parachute force allowed is G • W or (a]g) • W. It is appropriate to write&lt;br /&gt;
&lt;br /&gt;
Maximum allowable parachute force,&lt;br /&gt;
&lt;br /&gt;
Figure 4-3 illustrates Newton's third law, explaining the principle of the rocket that can produce thrust in a perfect vacuum.&lt;br /&gt;
&lt;br /&gt;
A mass, m. ejected from a rocket at the velocity, v, per unit time, t, will produce a force, F, which in turn will create a reaction force, R. of equal magnitude but acting in the opposite direction.&lt;br /&gt;
&lt;br /&gt;
=== 4.4 FORCES ACTING ON A BODY MOVING THROUGH AIR ===&lt;br /&gt;
4.4.1 Symmetrical Body&lt;br /&gt;
&lt;br /&gt;
A body moving through air experiences forces caused by air pressure acting on the body. fie same forces if the body moves through air, such as a descending parachute, or if the body is fixed and the air moves against the body, such as a parachute or an airfoil in a wind tunnel (Figure 44).&lt;br /&gt;
&lt;br /&gt;
         	 &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
A stable parachute in a wind tunnel experiences only the force called &amp;quot;drag&amp;quot; in the direction of the airflow. drag force, D, is calculated to&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
D = drag, 1b&lt;br /&gt;
&lt;br /&gt;
Q = dynamic pressure, lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
S = total surface area of the parachute canopy, ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt; = coefficient of drag.  dimensionless&lt;br /&gt;
&lt;br /&gt;
the dynamic pressure, q, can be calculated from section 4.2.2. The surface area of the canopy, S, is selected as a reference area. The drag coefficient  C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, is a form factor that indicates the drag characteristic of a specific shape. Most aerodynamic bodies are designed for low drag or a low drag coefficient. Parachutes, generally, are designed for high drag; therefore, a high drag coefficient is desirable. this difference in drag is demonstrated by the two bodies shown in Figure 4-5.&lt;br /&gt;
&lt;br /&gt;
            	&lt;br /&gt;
&lt;br /&gt;
Both bodies have the same cross section perpendicular to the airflow. The cylindrical. streamlined body has a smooth airflow over its total body length, resulting in a drag coefficient. C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, of 0.05 to 0.1, depending on slenderness ratio, surface roughness, and shape. The drag coefficient of all streamlined bodies is much affected by Reynolds number and Mach number. fie open hemisphere, which is similar to a parachute canopy, has a drag coefficient, C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, of 1.3 to 1.4 for the same body cross section. The difference in drag is explained by the smooth airflow around the streamlined body and a separated. turbulent flow around the open hemisphere. The drag of bodies with separated flow, like parachute canopies, is little affected by Reynolds number.&lt;br /&gt;
&lt;br /&gt;
4.4.2 Airflow Around an Asymmetrical Body (Airfoil)&lt;br /&gt;
&lt;br /&gt;
Figure 4-6 shows an airfoil fixed at an angle of attack, a. against the airflow in a wind tunnel. This airfoil creates a drag force, D, in the direction of the flow; a lift force L perpendicular to the direction of the flow; and a moment, M. around the attachment point of the airfoil. fie sign convention of moments and forces shown are positive. Lift and drag can be combined for the resultant force, R.&lt;br /&gt;
&lt;br /&gt;
FIGURE. 44, Wind-Tunnel Forces Acting on an Airfoil.&lt;br /&gt;
&lt;br /&gt;
The lift, L is calculated&lt;br /&gt;
&lt;br /&gt;
L = q * S * C&amp;lt;sub&amp;gt;L&amp;lt;/sub&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
L = measured lift, 1b&lt;br /&gt;
&lt;br /&gt;
q = dynamic pressure, lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
s = reference area, ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
CL = lift coefficient, dimensionless&lt;br /&gt;
&lt;br /&gt;
The moment is&lt;br /&gt;
&lt;br /&gt;
       M = q * S * c&amp;lt;sub&amp;gt;m&amp;lt;/sub&amp;gt; * c&lt;br /&gt;
&lt;br /&gt;
Where&lt;br /&gt;
&lt;br /&gt;
The reference area, S is defined by agreement, For streamlined bodies, the maximum body cross section is used. Airfoils use the planform of the wing, and parachutes use the canopy surface area. The selection of the wing planform and the parachute surface area as references was made for practical reasons. &amp;lt;sup&amp;gt;e&amp;lt;/sup&amp;gt;me wing planform for a specific wing is fixedt whereas the cross section of the wing in the direction of the flow changes with the angle of attack. Similarly, the surface area of the parachute canopy is fixed; however, the frontal projected area of the inflated parachute canopy changes with airspeed, porosity, line length, and tm of parachute.&lt;br /&gt;
&lt;br /&gt;
Forces and moments acting on an airfoil or a parachute canopy may be presented in several ways. The two most frequently used methods, as shown in Figure 4-7, are with forces oriented to the of flight and with forces oriented to the axis of the airfoil.&lt;br /&gt;
&lt;br /&gt;
me tangential force, and the normal force, N, are calculated&lt;br /&gt;
&lt;br /&gt;
T = C&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; * S * q&lt;br /&gt;
&lt;br /&gt;
        	&lt;br /&gt;
&lt;br /&gt;
and&lt;br /&gt;
&lt;br /&gt;
      	N = C&amp;lt;sub&amp;gt;N&amp;lt;/sub&amp;gt; * S * q&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
C&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; = tangential force coefficient, dimensionless&lt;br /&gt;
&lt;br /&gt;
C&amp;lt;sub&amp;gt;N&amp;lt;/sub&amp;gt; = normal force coefficient, dimensionless&lt;br /&gt;
&lt;br /&gt;
The resultant force, R, and the moment, M, in both presentations have the same direction and the same magnitude. The airflow fixed system is preferred for aerodynamic performance calculations, and the airfoil fixed system for wing stress calculations. me aerodynamic coefficients C&amp;lt;sub&amp;gt;L&amp;lt;/sub&amp;gt;, C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, C&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, C&amp;lt;sub&amp;gt;N&amp;lt;/sub&amp;gt;, and C&amp;lt;sub&amp;gt;m&amp;lt;/sub&amp;gt; can easily be determined in wind•tunnel measurements.&lt;br /&gt;
&lt;br /&gt;
Figure 4-8 shows the relationship of both force systems on a parachute. By definition, a negative moment is stabilizing, as illustrated in Figure 4-8. It is interesting to note that in Europe the stabilizing moment is defined as positive. Wind-tunnel installations frequently measure normal and tangential force instead of lift and drag. If α, T, and N are known, the drag D, can be calculated&lt;br /&gt;
&lt;br /&gt;
D = T*cosα + N * sinα&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
For a parachute with an angle of attack, a, equal to zero, the drag force and the tangential force are synonymous.&lt;br /&gt;
&lt;br /&gt;
Figure 4-9 shows the coefficients C&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, and C&amp;lt;sub&amp;gt;m&amp;lt;/sub&amp;gt; versus angle of attack for stable and unstable parachutes.&lt;br /&gt;
&lt;br /&gt;
The coefficient presentation shows two interesting facts. ne slope of the moment coefficient curve, dC&amp;lt;sub&amp;gt;m&amp;lt;/sub&amp;gt;/dα, for the unstable parachute is positive between -25 degrees and + 25 degrees; this is, by definition, destabilizing. This parachute will oscillate approximately ± 25&lt;br /&gt;
&lt;br /&gt;
FIGURE 4-9. Coefficients C&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, and C&amp;lt;sub&amp;gt;M&amp;lt;/sub&amp;gt; Versus Angle of Attack, α, for a Stable and Unstable Parachute.&lt;br /&gt;
&lt;br /&gt;
degrees. The slope of the moment, dC&amp;lt;sub&amp;gt;m&amp;lt;/sub&amp;gt;/dα, for the stable parachute is negative over the total angle of attack; this is, by definition, stabilizing. The steeper the negative dC&amp;lt;sub&amp;gt;m&amp;lt;/sub&amp;gt;/dα slope, the greater is the stabilizing tendency of the parachute, and the better is its damping capability against unstabilizing forces such as sudden gusts of wind.&lt;br /&gt;
&lt;br /&gt;
Figure 4-10, from Reference 4.1, demonstrates the effect of airflow around a cylinder and an airfoil. The circulation around a rotating cylinder creates lift caused by the increase in velocity on one side of the cylinder and a decrease on the opposite side. This is called the Magnus effect.&lt;br /&gt;
&lt;br /&gt;
= 4.5 EQUILIBRIUM OF FORCES IN STUDY DESCENT OR FLIGHT =&lt;br /&gt;
4.5.1 Parachute in Steady Descent&lt;br /&gt;
&lt;br /&gt;
A stable parachute in unaccelerated descent has an equilibrium between the total drag of the parachute and the load, Dr, and the weight of the load and the parachute assembly, WT (Figure 4-11). For steady descent&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
D&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; = total drag, 1b&lt;br /&gt;
&lt;br /&gt;
D&amp;lt;sub&amp;gt;P&amp;lt;/sub&amp;gt; = drag of parachute, 1b&lt;br /&gt;
&lt;br /&gt;
W&amp;lt;sub&amp;gt;C&amp;lt;/sub&amp;gt; = weight of load. 1b&lt;br /&gt;
&lt;br /&gt;
In most cases, the drag of the load can be neglected in relation to the large drag of the parachute, With drag, D — (C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;S)&amp;lt;sub&amp;gt;p&amp;lt;/sub&amp;gt; • p/2• v&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; and D&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; = W&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;. and solving for v, the important equation for rate of descent, v&amp;lt;sub&amp;gt;e&amp;lt;/sub&amp;gt;, is obtained,&lt;br /&gt;
&lt;br /&gt;
Rate of descent,&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
FIGURE 4-11. Forces Acting on a Parachute in Steady Descent.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
or in parachute terminology for rate of descent at sea level&lt;br /&gt;
&lt;br /&gt;
and rate of descent at any altitude&lt;br /&gt;
&lt;br /&gt;
== For 1/, see column 4 in Table 3-3, ==&lt;br /&gt;
In the equation for rate of descent. V&amp;lt;sub&amp;gt;e&amp;lt;/sub&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
W&amp;lt;sub&amp;gt;T =&amp;lt;/sub&amp;gt; weight of load and parachute assembly, 1b&lt;br /&gt;
&lt;br /&gt;
S&amp;lt;sub&amp;gt;o&amp;lt;/sub&amp;gt; = canopy surface area, ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
C&amp;lt;sub&amp;gt;Do&amp;lt;/sub&amp;gt; = parachute drag coefficient related to S&amp;lt;sub&amp;gt;o&amp;lt;/sub&amp;gt;&lt;br /&gt;
&lt;br /&gt;
p = air density at a specific altitude in slugs/ft&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;, as shown in Table 3-3&lt;br /&gt;
&lt;br /&gt;
During descent from altitude, the parachute system is constantly decelerated because of the increasing air density. This can be ignored for slowly descending main parachutes. However, for drogue chute systems that descend at 200 ft/s or faster, the constant deceleration may result in velocities 3 to 5% higher than the steady rate of descent.&lt;br /&gt;
&lt;br /&gt;
4.5.2 Gliding Parachutes&lt;br /&gt;
&lt;br /&gt;
Figure 4-12 shows the balance of forces on a gliding parachute. The total weight of the system, W&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; . must be balanced by the resultant force. R. However, a lifting force is required for glide. To satisfy the force balance&lt;br /&gt;
&lt;br /&gt;
R = C&amp;lt;sub&amp;gt;R&amp;lt;/sub&amp;gt; * S * p/2 * v&lt;br /&gt;
&lt;br /&gt;
Trajectory velocity, V&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, is calculated&lt;br /&gt;
&lt;br /&gt;
Horizontal velocity is calculated&lt;br /&gt;
&lt;br /&gt;
V&amp;lt;sub&amp;gt;H&amp;lt;/sub&amp;gt; = V&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; • cosø, and vertical velocity, v&amp;lt;sub&amp;gt;v&amp;lt;/sub&amp;gt; = V&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; • sinø&lt;br /&gt;
&lt;br /&gt;
The glide ratio is obtained from&lt;br /&gt;
&lt;br /&gt;
Analysis of Figure 4-12 indicates that the larger the ratio of lift to drag, the better the glide ratio, I./D A high resultant coefficient, C&amp;lt;sub&amp;gt;R&amp;lt;/sub&amp;gt;, results in a low glide or trajectory V&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, desirable for landing. A small C&amp;lt;sub&amp;gt;R&amp;lt;/sub&amp;gt; results in a high glide velocity, V&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, which is desirable for flying toward a target, compensating for head winds, or covering a distance quickly. Generally, gliding parachutes follow the same aerodynamic rules as low-aspect-ratio wings.&lt;br /&gt;
&lt;br /&gt;
           	   	&lt;br /&gt;
&lt;br /&gt;
FIGUR E 4-12, Forces Acting on a Gliding Parachute&lt;br /&gt;
&lt;br /&gt;
4.5-3 Parasite Drag and Induced Drag&lt;br /&gt;
&lt;br /&gt;
The drag acting on a lift-producing air vehicle, such as a gliding parachute or an aircraft, has two primary components: the parasite drag, D&amp;lt;sub&amp;gt;P&amp;lt;/sub&amp;gt; , and the induced drag. D&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Parasite drag is produced by the form drag from individual components such as the suspension lines, canopy, and the jumper of a gliding parachute, and the fuselage, tail sectiora, and control surfaces of an airplane. Large surfaces produce surface friction drag as part of the parasite drag.&lt;br /&gt;
&lt;br /&gt;
Induced drag is caused by the lifting action of the parachute canopy or the aircraft wing. Section 4.7 includes books with detailed discussions of induced drag.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Total drag, D&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, can be defined as&lt;br /&gt;
&lt;br /&gt;
or, in the coefficient form&lt;br /&gt;
&lt;br /&gt;
The parasite drag, D&amp;lt;sub&amp;gt;p&amp;lt;/sub&amp;gt;, and the coefficient, C&amp;lt;sub&amp;gt;DP&amp;lt;/sub&amp;gt;, can be determined in wind-tunnel tests or calculated as the sum of the individual component drags.&lt;br /&gt;
&lt;br /&gt;
The induced drag coefficient, C&amp;lt;sub&amp;gt;Di&amp;lt;/sub&amp;gt; , of a gliding parachute canopy or a wing profile can be calculated&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
C = coefficient of induced drag, dimensionless&lt;br /&gt;
&lt;br /&gt;
The expression b&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;/S is defined as the aspect ratio of a wing or parachute with the notation AR b&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;/S. Therefore&lt;br /&gt;
&lt;br /&gt;
== '''                       ''' 	 ==&lt;br /&gt;
The equation for induced drag indicates that increasing the aspect ratio, AR, reduces the induced drag coefficient,  , and therefore reduces the drag, D. ms, in turn, increases the glide ratio, L/D. Increasing the glide ratio by increasing the aspect ratio is optimized on high-performance sailplanes with aspect ratios higher than 20. Increasing the glide ratio of gliding parachutes by increasing the aspect ratio has limitations, which are discussed in section 5.9.&lt;br /&gt;
&lt;br /&gt;
4.5.4 Aircraft in Horizontal Flight&lt;br /&gt;
&lt;br /&gt;
Figure 4-13 shows forces and moments on an aircraft in steady, horizontal flight. In steady, horizontal flight, an equilibrium exists between all forces and moments acting on the aircraft. Lift on the wing and tail, L&amp;lt;sub&amp;gt;W&amp;lt;/sub&amp;gt; and L&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;. and the weight of the aircraft, W&amp;lt;sub&amp;gt;A&amp;lt;/sub&amp;gt;, balance in the vertical plane. Thrust, T and drag. D, balance each other in the horizontal plane, and the positive or negative moment, M, is balanced by the positive or negative lift of the tail multiplied by the moment arm, L&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
FIGURE 4-13. Forces and Moments Acting on an Aircraft in Steady night,&lt;br /&gt;
&lt;br /&gt;
Any imbalance in these forces results in descent or climb in the vertical plane or faster or slower speed in the horizontal plane. A change in the lift of the elevator initiates climb or descent. Thrust, T, is the prime contributor for climb or descent and faster or slower speed, However, a balance of forces must always be maintained for horizontal flight or steady rate oi climb or descent.&lt;br /&gt;
&lt;br /&gt;
== 4.6 WIND-TUNNEL TESTING OF PARACHUTES ==&lt;br /&gt;
Wind tunnels are an effective tool for testing air vehicles and air-vehicle components and have been used successfully for testing parachutes and parachute systems. Experience has shown that certain rules apply for the wind-tunnel testing of parachutes. Small parachutes manufactured from textiles cannot be made sufficiently similar to large parachutes in geometric design and flexibility, Lightweight material. required to obtain design similarity, is difficult to manufacture or is unobtainable.&lt;br /&gt;
&lt;br /&gt;
One cardinal rule has been established through many years of parachute wind-tunnel testing: A modification that changes the performance of a model parachute in wind-tunnel testing produces the same type and percentage of performance change in a large parachute. This rule is true for drag. stability, and opening-force characteristics.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
4.6.1 Blowers&lt;br /&gt;
&lt;br /&gt;
The simple air blower (Figure 4-14) is a proven tool for preliminary parachute testing of a chiefly qualitative nature. Unless special test conditions prevail, parachutes tested should be a minimum of 1.5 to 2 feet in diameter to obtain meaningful results.&lt;br /&gt;
&lt;br /&gt;
                                                                    &lt;br /&gt;
&lt;br /&gt;
 FIGURE 4-14. Typical Air Blower.&lt;br /&gt;
&lt;br /&gt;
An air blower is a preliminary test too! because it permits quick parachute• configuration changes and excellent visual observation.&lt;br /&gt;
&lt;br /&gt;
4.6.2 Open-Throat, No-Return Wind Tunnels&lt;br /&gt;
&lt;br /&gt;
The open-throat, no-return wind tunnel shown in Figure 4-15 permits exact measurements if parachutes of sufficient size are used. Parachutes 3 feet or more in diameter are well suited for obtaining good, quantitative test results.&lt;br /&gt;
&lt;br /&gt;
              FIGURE 4-15. Open-Throat, No-Return Wind Tunnel&lt;br /&gt;
&lt;br /&gt;
In air blowers and open-throat wind tunnels, the velocity at the skirt of the parachute (Section a-a of Figures 4-14 and 4-15) is lower than the velocity at the nozzle exit of the wind tunnel (Section b&amp;lt;sup&amp;gt;-&amp;lt;/sup&amp;gt;b of Figures 4-14 and 4-15), Care must be taken to measure the parachute test&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
velocity at Section a-a and not at Section b-b, the customary attachment point for airfoils and models.&lt;br /&gt;
&lt;br /&gt;
Wind tunnels frequently cannot test at the descent velocity of most main parachutes of 20 to 30 feet per second. Obtaining proper test results at this low is hampered by a poor velocity distribution in the wind-tunnel-test section, and by the weight of the test parachute. The latter has a tendency to pull the parachute downward, thereby providing a negative angle of attack, lusting unstable parachutes at higher presents the problem that the drag coefficient C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, of unstable parachutes is sensitive. The drag coefficient of unstable parachutes is described in section 5.2.&lt;br /&gt;
&lt;br /&gt;
An open-throat wind tunnel permits quick changes in parachute configuration, such as changing the suspension and reefing line lengths. Large open-throat wind tunnels that are not sealed against outside elements suffer atmospheric problems such as fog formation in the test section.&lt;br /&gt;
&lt;br /&gt;
4.6.3 Closed-Throat, Full-Return Wind Tunnel&lt;br /&gt;
&lt;br /&gt;
Figure 4-16 is a drawing of a full-return, closed-throat wind tunnel. fic full-return, closed-throat wind tunnel is generally considered best suited for obtaining good. qualitative, aerodynamic data, since it has a uniform distribution in the test section. A disadvantage is the difficulty in gaining access to the test section for changing the parachute configuration.&lt;br /&gt;
&lt;br /&gt;
FIGURE 4-16. Closed-Throat, Full-Reuurn Wind Tunnel.&lt;br /&gt;
&lt;br /&gt;
4.6.4 General Comments for Wind-Tunnel Testing of Parachutes&lt;br /&gt;
&lt;br /&gt;
1. Parachute models for wind-tunnel testing should be as large and as similar as possible in geometry and flexibility to full-scale parachutes. Parachutes of less than 1.5 feet in diameter usually lack geometric similarity and material flexibility, which results in inflation characteristics and dissimilar inflated shapes.&lt;br /&gt;
&lt;br /&gt;
2.  The finished dimensions of model parachutes must be measured as accurately as possible to determine the nominal diameter, Do, and the surface area, So. Model parachutes will shrink from 5 to 10% during manufacture because of sewing take-up, which results in a notable difference in the dimensions between the drawing and the completed parachute.&lt;br /&gt;
&lt;br /&gt;
3.  Wind&amp;lt;sup&amp;gt;-&amp;lt;/sup&amp;gt;tunnel tests of parachutes are excellent for comparing different models and modifications: also, they are the most effective means for measuring coefficients of lift, drag. and normal and tangential forces, as well as for determining the load coefficient, for infinite load.&lt;br /&gt;
&lt;br /&gt;
4.  In wind-tunnel tests, velocity decay does not occur during parachute inflation and operation; this is defined as testing under &amp;quot;infinite mass condition. &amp;quot; First-stage drogue chutes and parachutes with a canopy loading, W/C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;S. in excess of 100 lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; approach this condition. Low-canopy-loading main parachutes with rates of descent of 20 to 30 ft/s have a large velocity decay during opening, which requires careful interpretation of the opening-force data obtained in wind-tunnel tests.&lt;br /&gt;
&lt;br /&gt;
5.  In the past, to avoid wind-tunnel blockage and questionable test data. the diameter of a test parachute could not exceed about 5 to 6% of the wind-tunnel test section area. Recent Sandia investigations of single and clustered ribbon parachutes with wind-tunnel blockage ratios of up to 30% have resulted in correction methods that make it possible to test much larger parachutes (Reference 4.2).&lt;br /&gt;
&lt;br /&gt;
= 4.7 REFERENCE MATERIAL =&lt;br /&gt;
4.1 H. H. Hurt. Aerodynamics for Naval Aviators Navy Manual NAVWEPS 00 80T 80. Chief of Naval Operations, Aviation Training Division.&lt;br /&gt;
&lt;br /&gt;
4.2 J, M. Macha and R J. Buffington. &amp;quot;Wall-Interference Corrections for Parachutes in a Closed Wind Tunnel.&amp;quot; AIM Paper, April 1989. (AIM 89-0900-cp.)&lt;br /&gt;
&lt;br /&gt;
For readers interested in a more detailed study of aerodynamics, the following books are recommended.&lt;br /&gt;
&lt;br /&gt;
4.3 J, H, Dwinnel, Principle of Aerodynamics. McGraw-Hill     	Co., New York, 1949.&lt;br /&gt;
&lt;br /&gt;
4.4 J. Morane. Introduction to Theoretical and Computational Aerodynamics. John Wiley &amp;amp; Sons.&lt;br /&gt;
&lt;br /&gt;
4.5 R.S. Shevell. Fundamentals of Flight. Prentice-Hall. 1983.&lt;br /&gt;
&lt;br /&gt;
4.6 J. D. Anderson, Jr. Introduction to Flights, ILS Engineering and History. McGraw-Hill Book co., New York 1978.&lt;br /&gt;
&lt;br /&gt;
4.7 D. J. Cockrell. The Aerodynamics of Parachutes.&amp;quot; AGARDograph No. 6295, available from NASA Langley Research Center, M/S 1M), Hampton, Va., 236.&lt;/div&gt;</summary>
		<author><name>TuanHTruong</name></author>
	</entry>
	<entry>
		<id>https://mediawiki.aerodecelerator.org/index.php?title=Parachute_Aerodynamics&amp;diff=29</id>
		<title>Parachute Aerodynamics</title>
		<link rel="alternate" type="text/html" href="https://mediawiki.aerodecelerator.org/index.php?title=Parachute_Aerodynamics&amp;diff=29"/>
		<updated>2024-05-03T22:34:52Z</updated>

		<summary type="html">&lt;p&gt;TuanHTruong: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&lt;br /&gt;
= CHAPTER 4: AERODYNAMICS AS RELATED TO PARACHUTES =&lt;br /&gt;
== 4.1 PROPERTIES OF THE ATMOSPHERE ==&lt;br /&gt;
All forces acting on parachutes and all movements of parachutes are affected by the atmosphere, or air, surrounding the Earth. The air at the Earth's surface is approximately 78% nitrogen; 21% oxygen; and 1% a mixture of gases such as argon, neon, helium, water vapor, and carbon dioxide. This chemical composition remains relatively constant to an altitude of about 160,000 feet (50 kilometers). The following air qualities are of major significance in the dynamics of bodies moving in the atmosphere:&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
!Air quality&lt;br /&gt;
!Symbol&lt;br /&gt;
!Dimension&lt;br /&gt;
|-&lt;br /&gt;
|Specific weight of air&lt;br /&gt;
|w&lt;br /&gt;
|lb/ft&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;, kg/m&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;&lt;br /&gt;
|-&lt;br /&gt;
|Static pressure&lt;br /&gt;
|p&lt;br /&gt;
|atm, lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;, Pa, bar, torr&lt;br /&gt;
|-&lt;br /&gt;
|Temperature&lt;br /&gt;
|T&lt;br /&gt;
|&amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F, &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;C&lt;br /&gt;
|-&lt;br /&gt;
|Mass density&lt;br /&gt;
|&amp;lt;math&amp;gt;\rho&amp;lt;/math&amp;gt;&lt;br /&gt;
|slugs/ft&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;, kg s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;/m&amp;lt;sup&amp;gt;4&amp;lt;/sup&amp;gt;&lt;br /&gt;
|-&lt;br /&gt;
|Gravity&lt;br /&gt;
|''g''&lt;br /&gt;
|ft/s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;, m/s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
|-&lt;br /&gt;
|Speed of sound&lt;br /&gt;
|C&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt;&lt;br /&gt;
|ft/s, m/s&lt;br /&gt;
|}&lt;br /&gt;
All of these qualities are altitude-dependent and may vary slightly on the Earth's surface with geographic latitude because of variations of the Earth's radius caused by the centrifugal forces of the rotation of the Earth. All standard data used herein refer to a latitude of 45 degrees. Sea level is defined as mean sea level (MSL). To compare performance data on an equal basis, the United States Bureau of Standards has defined standard day conditions as follows:&lt;br /&gt;
&lt;br /&gt;
* Temperature = 15 degrees Celsius (&amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;C) or 59 degrees Fahrenheit (&amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F)&lt;br /&gt;
* Pressure = 760 millimeters (mm) of mercury (Hg) or 29.9213 inches (in.) Hg&lt;br /&gt;
&lt;br /&gt;
=== 4.1.1 Specific Weight of Air ===&lt;br /&gt;
For standard day conditions of 59 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F temperature and a pressure of 29.9213 in. Hg, the specific weight of air, w, is 0.07648 lb/ft&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt; or 1.2250 kg/m&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;. The specific weight of air changes with pressure, temperature, and humidity. Further data can be found in References 3.4 and 4.1, and in technical handbooks.&lt;br /&gt;
&lt;br /&gt;
=== 4.1.2 Static Pressure ===&lt;br /&gt;
Static pressure depends on geographic latitude, weather conditions, and altitude. The static pressure at any altitude results from the weight of the air above that altitude. For MSL and standard day conditions, the pressure, p&amp;lt;sub&amp;gt;o&amp;lt;/sub&amp;gt;, is 29.9213 in. Hg = 760 mm Hg = 1.0 atmosphere (atm). For conversion to Pascal, torr, or bar, see the conversion tables in section 3.2.&lt;br /&gt;
&lt;br /&gt;
=== 4.1.3 Temperature ===&lt;br /&gt;
Temperatures are defined in the English and metric systems in the so-called absolute and engineering scales. The absolute temperature minimum at 0 degrees, pressure is 0 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;K = -273.16 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;C, and 0 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;R = -459.69 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F. This is also written&lt;br /&gt;
&lt;br /&gt;
* Degrees Kelvin = degrees Celsius + 273.16&lt;br /&gt;
* Degrees Rankine = degrees Fahrenheit + 459.69&lt;br /&gt;
&lt;br /&gt;
The freezing point of water is 32 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F or 0 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;C. The boiling point of water is 212 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F or 100 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;C.&lt;br /&gt;
&lt;br /&gt;
=== 4.1.4 Mass Density of Air ===&lt;br /&gt;
Mass density defines the amount of mass contained in a unit volume of air. The mass density, &amp;lt;math&amp;gt;\rho&amp;lt;/math&amp;gt;, of air is of special importance in aerodynamic calculations.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\rho = \frac{specific\ weight\ of\ air,\ w}{acceleration\ of\ gravity,\ g} = \frac{lb/ft^3}{ft/s^2} = \frac{kg\ s^2}{m^4}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;slug = \frac{weight}{acceleration\ of\ gravity} = \frac{lb}{ft/s^2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Frequently the density ratio, &amp;lt;math&amp;gt;\sigma&amp;lt;/math&amp;gt;, is used&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\sigma = \frac{ambient\ air\ density,\ \rho}{standard\ sea-level\ density, \rho_o}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The factor, &amp;lt;math&amp;gt;1/\sqrt{\rho/\rho_o}&amp;lt;/math&amp;gt;, determines the increase in parachute rate of descent with altitude. The density at 40,000 feet is ¼ of the MSL density, and the density at 100,000 feet is 1/75 of the MSL density. Therefore, the parachute rate of descent is about twice as high at 40,000 feet and about nine times as high at 100,000 feet. MSL density is 0.00237689 slugs/ft&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;, or 0.1249 kg s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;/m&amp;lt;sup&amp;gt;4&amp;lt;/sup&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
=== 4.1.5 Gravity ===&lt;br /&gt;
Any mass attracts another mass with a force called gravity. If the Earth were surrounded by a vacuum, a body suspended above the Earth and released would fall toward the center of the Earth with increasing velocity caused by the acceleration of gravity, ''g''. In reality, the falling body is decelerated by its air drag until the air drag, D, equals the weight of the body, W, and an equilibrium velocity is reached; for parachutes, this is called the steady-state rate of descent.&lt;br /&gt;
&lt;br /&gt;
The acceleration of gravity, ''g'', at sea lavel is&lt;br /&gt;
&lt;br /&gt;
* ''g'' = 32.174 ft/s2 or 9.80665 m/s2.&lt;br /&gt;
&lt;br /&gt;
The value g = 9.08665 m/s is standardized internationally but is accurate only for a latitude of 45 degrees.&lt;br /&gt;
&lt;br /&gt;
With increasing altitude above the Earth's surface, the acceleration of gravity decreases in accordance with the equation&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;g = g_o(\frac{r}{r+h})^2&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
* ''g'' = acceleration of gravity at any altitude, ft/s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
* g&amp;lt;sub&amp;gt;o&amp;lt;/sub&amp;gt; = acceleration of gravity at sea level, ft/s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
* r = average Earth radius = 2.08556 x 10&amp;lt;sup&amp;gt;7&amp;lt;/sup&amp;gt; ft&lt;br /&gt;
* h = altitude above sea level, ft&lt;br /&gt;
&lt;br /&gt;
For other planets and heavenly bodies, the acceleration of gravity varies with the mass of the body. For example, the acceleration of gravity on Mars is about 1/3 of the acceleration of gravity on Earth. For more details on planets and heavenly bodies, see page XII of Reference 2.1.&lt;br /&gt;
&lt;br /&gt;
=== 4.1.6 Kinematic Viscosity ===&lt;br /&gt;
The coefficient of viscosity, &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt;, defines the shearing stresses in a gas or liquid and is sometimes called the resistance to continuous deformation. In aerodynamics, the coefficient of viscosity is combined with the mass density to form the kinematic viscosity, &amp;lt;math&amp;gt;\nu&amp;lt;/math&amp;gt;, where&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\nu = \frac{coefficient\ of\ viscosity,\ \mu}{mass\ density,\ \rho} = 0.0001576\ ft^2/s\ at\ sea\ level&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The kinematic viscosity, &amp;lt;math&amp;gt;\nu&amp;lt;/math&amp;gt;, is altitude dependent and is used to calculate the Reynolds number, Re.&lt;br /&gt;
&lt;br /&gt;
=== 4.1.7 Reynolds Number ===&lt;br /&gt;
The Reynolds number, Re, defines the relationship of mass forces to viscous friction forces in liquids and gases. It is calculated as&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Re = \frac{v\cdot l}{\nu} = \frac{velocity\ (ft/s)\cdot characteristic\ length\ (ft)}{kinematic\ viscosity\ (ft^2/s)}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Reynolds number is an important criterion in subsonic, noncompressible flow, and allows comparison of model tests with full-scale flight tests. A Reynolds number effect on parachutes working in separated, turbulent flow has not yet been established, as shown in section 5.2. The following chart shows the Reynolds numbers for various air vehicles.&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
!Subject&lt;br /&gt;
!Insect&lt;br /&gt;
!Glider&lt;br /&gt;
!DC-3&lt;br /&gt;
!B-747&lt;br /&gt;
!Drogue&lt;br /&gt;
Chute&lt;br /&gt;
!Main &lt;br /&gt;
Parachute&lt;br /&gt;
!WTT&lt;br /&gt;
Model&lt;br /&gt;
|-&lt;br /&gt;
|Re&lt;br /&gt;
|6 • 10&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;&lt;br /&gt;
|2.5 • 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&lt;br /&gt;
|24 • 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&lt;br /&gt;
|100 • 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&lt;br /&gt;
|50 • 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&lt;br /&gt;
|20 • 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&lt;br /&gt;
|2 • 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
=== 4.1.8 Mach Number ===&lt;br /&gt;
Mach number is an important parameter of supersonic flight; it states how much faster than the speed of sound the air vehicle travels.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Mach\ number,\ M = \frac{flight\ velocity,\ v}{speed\ of\ sound, c_s}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The speed of sound is the velocity at which a pressure disturbance, such as the sound of the human voice, travels in any medium. The speed of sound varies considerably in different gases, liquids, and metals.&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|Speed of sound in air in MSL&lt;br /&gt;
|C&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt; = 1116.46 ft/s = 340.38 m/s&lt;br /&gt;
|-&lt;br /&gt;
|Speed of sound in water&lt;br /&gt;
|C&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt; = 4749 ft/s = 1461.21 m/s&lt;br /&gt;
|-&lt;br /&gt;
|Speed of sound in iron&lt;br /&gt;
|C&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt; = 16,410 ft/s = 5710.7 m/s&lt;br /&gt;
|}&lt;br /&gt;
The speed of sound depends on temperature and the chemical composition of the medium, A widely used equation for speed of sound in air is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;C_s = 41.4\sqrt{\gamma\cdot T}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
* &amp;lt;math&amp;gt;C_s&amp;lt;/math&amp;gt; = speed of sound in dry air, ft/s&lt;br /&gt;
* &amp;lt;math&amp;gt;\gamma&amp;lt;/math&amp;gt; = ratio of specific heat, equal to 1.4 for dry air, dimensionless&lt;br /&gt;
* &amp;lt;math&amp;gt;T&amp;lt;/math&amp;gt; = temperature in Fahrenheit absolute, equal to 459.67 + &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F&lt;br /&gt;
&lt;br /&gt;
The speed of sound changes with altitude, as temperature (see Figure 3-1). The drag of streamlined bodies such as missiles, airfoils, and airplanes increases considerably as their velocities approach Mach 1. Depending on the configuration of the body, supersonic compressibility effects may occur in the 0.75 to 0.85 Mach range, causing local supersonic flow, shock waves, flow separation, and concomitant increases in drag and changes in stability.&lt;br /&gt;
&lt;br /&gt;
Parachutes that operate in separated flow over the entire velocity range do not show the typical drag increase when operating close to or beyond Mach 1. Supersonic parachute behavior is discussed in detail in section 5.8.&lt;br /&gt;
&lt;br /&gt;
== '''4.2 CONTINUITY LAW AND BERNOULLI EQUATION''' ==&lt;br /&gt;
4.2.1 Continuity L.aw&lt;br /&gt;
&lt;br /&gt;
Air is thought to flow in layers called streamlines. Figure 4-1 shows streamlines as layers of air without air transfer between individual layers. ne air is shown as being incompressible, a valid assumption for subsonic flow.&lt;br /&gt;
&lt;br /&gt;
  	&lt;br /&gt;
&lt;br /&gt;
If exchange of air does not occur across the streamline boundaries, the amount of air entering the streamline at point 1 must also exit at point 2. as shown in Figure 4*1. Because the cross section at point 2 is smaller than the cross section at point 1, the air must exit at a higher velocity. The following equation defines this condition:&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
this equation which governs the now in and around a body in gases and liquids, is important in aerodynamics and is called the continuity law. For imcompressilble subsonic now, it can be simplified to &lt;br /&gt;
&lt;br /&gt;
Whenever the cross section narrows. the velocity increases; when the cross section widens, the velocity decreases.&lt;br /&gt;
&lt;br /&gt;
4.2.2 Bernoulli Equation&lt;br /&gt;
&lt;br /&gt;
Figure 4-2 illustrates a streamline with the cross section, S, the velocity, v, and the pressure, p. If the air is incompressible, the downstream is v + Av. and the pressure is p + AP. If the air is inviscid, the inertia forces caused by the acceleration of air from v to v + Av must be balanced by differential pressure forces.&lt;br /&gt;
&lt;br /&gt;
    	                                       	&lt;br /&gt;
&lt;br /&gt;
FIGURE 4-2 Pressure and Velocity Distribution in a Streamline Element.&lt;br /&gt;
&lt;br /&gt;
The following equation can be written&lt;br /&gt;
&lt;br /&gt;
Simplified, the above equation yields&lt;br /&gt;
&lt;br /&gt;
'''dp = -pvdv'''&lt;br /&gt;
&lt;br /&gt;
the above equation allows the following consideration: If p is pressure, then 1/2 pv&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; and C must also be pressure. The equation 1/2 pv&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; includes a and is referred to as the dynamic pressure. or sometimes velocity as or impact pressure.&lt;br /&gt;
&lt;br /&gt;
Pressure, p, is defined as static pressure; 1/2 pv&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; as dynamic pressure; and the sum of both, C, as the total pressure or&lt;br /&gt;
&lt;br /&gt;
p + 1/2pv&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; = H&lt;br /&gt;
&lt;br /&gt;
and&lt;br /&gt;
&lt;br /&gt;
where H is the total pressure of the system, lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Dynamic pressure, q, is a frequently used quantity in aerodynamics:&lt;br /&gt;
&lt;br /&gt;
q = 1/2 pv&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
q = dynamic pressure, lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
p =  air density, slugs/ft&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
v =  velocity at a point of undisturbed flow, ft/s&lt;br /&gt;
&lt;br /&gt;
The following formulas are used for calculating the sea-level dynamic pressure if the velocity is given in ft/s, knots, mph, or km/h, respectively:&lt;br /&gt;
&lt;br /&gt;
                                              &lt;br /&gt;
&lt;br /&gt;
'''4.3 NEWTON'S THREE OF MOTION'''&lt;br /&gt;
&lt;br /&gt;
Engineering mechanics are governed by the following three laws of Isaac Newton:&lt;br /&gt;
&lt;br /&gt;
1.  A body remains at rest or in an unaccelerated state of motion unless acted upon.&lt;br /&gt;
&lt;br /&gt;
2.  A force acting upon a body will produce an acceleration in the direction of the force.&lt;br /&gt;
&lt;br /&gt;
3.  An action in one direction will produce an equal reaction in the opposite direction.&lt;br /&gt;
&lt;br /&gt;
The first law is self-explanatory. The second law may be expressed by the equation&lt;br /&gt;
&lt;br /&gt;
F = m * a&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
F = force in pounds acting on the mass, 1b&lt;br /&gt;
&lt;br /&gt;
m = mass of body that the force is acting upon, slugs&lt;br /&gt;
&lt;br /&gt;
a = acceleration in ft/s2 resulting from the force, F&lt;br /&gt;
&lt;br /&gt;
The mass, m, of a body is obtained by&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
W = weight of the body, lb&lt;br /&gt;
&lt;br /&gt;
g = acceleration of gravity, ft/s2&lt;br /&gt;
&lt;br /&gt;
The mass, therefore, has the dimension of&lt;br /&gt;
&lt;br /&gt;
This unit of mass is the slug.&lt;br /&gt;
&lt;br /&gt;
the equation of Newton's second law can now be written&lt;br /&gt;
&lt;br /&gt;
                                        	&lt;br /&gt;
&lt;br /&gt;
The factor a/g is frequently called the load factor, G, and tells how much larger a force is than a force equivalent to the weight of the body. It is customary in parachute work to state that the maximum parachute force allowed is G • W or (a]g) • W. It is appropriate to write&lt;br /&gt;
&lt;br /&gt;
Maximum allowable parachute force,&lt;br /&gt;
&lt;br /&gt;
Figure 4-3 illustrates Newton's third law, explaining the principle of the rocket that can produce thrust in a perfect vacuum.&lt;br /&gt;
&lt;br /&gt;
A mass, m. ejected from a rocket at the velocity, v, per unit time, t, will produce a force, F, which in turn will create a reaction force, R. of equal magnitude but acting in the opposite direction.&lt;br /&gt;
&lt;br /&gt;
=== 4.4 FORCES ACTING ON A BODY MOVING THROUGH AIR ===&lt;br /&gt;
4.4.1 Symmetrical Body&lt;br /&gt;
&lt;br /&gt;
A body moving through air experiences forces caused by air pressure acting on the body. fie same forces if the body moves through air, such as a descending parachute, or if the body is fixed and the air moves against the body, such as a parachute or an airfoil in a wind tunnel (Figure 44).&lt;br /&gt;
&lt;br /&gt;
         	 &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
A stable parachute in a wind tunnel experiences only the force called &amp;quot;drag&amp;quot; in the direction of the airflow. drag force, D, is calculated to&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
D = drag, 1b&lt;br /&gt;
&lt;br /&gt;
Q = dynamic pressure, lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
S = total surface area of the parachute canopy, ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt; = coefficient of drag.  dimensionless&lt;br /&gt;
&lt;br /&gt;
the dynamic pressure, q, can be calculated from section 4.2.2. The surface area of the canopy, S, is selected as a reference area. The drag coefficient  C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, is a form factor that indicates the drag characteristic of a specific shape. Most aerodynamic bodies are designed for low drag or a low drag coefficient. Parachutes, generally, are designed for high drag; therefore, a high drag coefficient is desirable. this difference in drag is demonstrated by the two bodies shown in Figure 4-5.&lt;br /&gt;
&lt;br /&gt;
            	&lt;br /&gt;
&lt;br /&gt;
Both bodies have the same cross section perpendicular to the airflow. The cylindrical. streamlined body has a smooth airflow over its total body length, resulting in a drag coefficient. C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, of 0.05 to 0.1, depending on slenderness ratio, surface roughness, and shape. The drag coefficient of all streamlined bodies is much affected by Reynolds number and Mach number. fie open hemisphere, which is similar to a parachute canopy, has a drag coefficient, C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, of 1.3 to 1.4 for the same body cross section. The difference in drag is explained by the smooth airflow around the streamlined body and a separated. turbulent flow around the open hemisphere. The drag of bodies with separated flow, like parachute canopies, is little affected by Reynolds number.&lt;br /&gt;
&lt;br /&gt;
4.4.2 Airflow Around an Asymmetrical Body (Airfoil)&lt;br /&gt;
&lt;br /&gt;
Figure 4-6 shows an airfoil fixed at an angle of attack, a. against the airflow in a wind tunnel. This airfoil creates a drag force, D, in the direction of the flow; a lift force L perpendicular to the direction of the flow; and a moment, M. around the attachment point of the airfoil. fie sign convention of moments and forces shown are positive. Lift and drag can be combined for the resultant force, R.&lt;br /&gt;
&lt;br /&gt;
FIGURE. 44, Wind-Tunnel Forces Acting on an Airfoil.&lt;br /&gt;
&lt;br /&gt;
The lift, L is calculated&lt;br /&gt;
&lt;br /&gt;
L = q * S * C&amp;lt;sub&amp;gt;L&amp;lt;/sub&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
L = measured lift, 1b&lt;br /&gt;
&lt;br /&gt;
q = dynamic pressure, lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
s = reference area, ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
CL = lift coefficient, dimensionless&lt;br /&gt;
&lt;br /&gt;
The moment is&lt;br /&gt;
&lt;br /&gt;
       M = q * S * c&amp;lt;sub&amp;gt;m&amp;lt;/sub&amp;gt; * c&lt;br /&gt;
&lt;br /&gt;
Where&lt;br /&gt;
&lt;br /&gt;
The reference area, S is defined by agreement, For streamlined bodies, the maximum body cross section is used. Airfoils use the planform of the wing, and parachutes use the canopy surface area. The selection of the wing planform and the parachute surface area as references was made for practical reasons. &amp;lt;sup&amp;gt;e&amp;lt;/sup&amp;gt;me wing planform for a specific wing is fixedt whereas the cross section of the wing in the direction of the flow changes with the angle of attack. Similarly, the surface area of the parachute canopy is fixed; however, the frontal projected area of the inflated parachute canopy changes with airspeed, porosity, line length, and tm of parachute.&lt;br /&gt;
&lt;br /&gt;
Forces and moments acting on an airfoil or a parachute canopy may be presented in several ways. The two most frequently used methods, as shown in Figure 4-7, are with forces oriented to the of flight and with forces oriented to the axis of the airfoil.&lt;br /&gt;
&lt;br /&gt;
me tangential force, and the normal force, N, are calculated&lt;br /&gt;
&lt;br /&gt;
T = C&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; * S * q&lt;br /&gt;
&lt;br /&gt;
        	&lt;br /&gt;
&lt;br /&gt;
and&lt;br /&gt;
&lt;br /&gt;
      	N = C&amp;lt;sub&amp;gt;N&amp;lt;/sub&amp;gt; * S * q&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
C&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; = tangential force coefficient, dimensionless&lt;br /&gt;
&lt;br /&gt;
C&amp;lt;sub&amp;gt;N&amp;lt;/sub&amp;gt; = normal force coefficient, dimensionless&lt;br /&gt;
&lt;br /&gt;
The resultant force, R, and the moment, M, in both presentations have the same direction and the same magnitude. The airflow fixed system is preferred for aerodynamic performance calculations, and the airfoil fixed system for wing stress calculations. me aerodynamic coefficients C&amp;lt;sub&amp;gt;L&amp;lt;/sub&amp;gt;, C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, C&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, C&amp;lt;sub&amp;gt;N&amp;lt;/sub&amp;gt;, and C&amp;lt;sub&amp;gt;m&amp;lt;/sub&amp;gt; can easily be determined in wind•tunnel measurements.&lt;br /&gt;
&lt;br /&gt;
Figure 4-8 shows the relationship of both force systems on a parachute. By definition, a negative moment is stabilizing, as illustrated in Figure 4-8. It is interesting to note that in Europe the stabilizing moment is defined as positive. Wind-tunnel installations frequently measure normal and tangential force instead of lift and drag. If α, T, and N are known, the drag D, can be calculated&lt;br /&gt;
&lt;br /&gt;
D = T*cosα + N * sinα&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
For a parachute with an angle of attack, a, equal to zero, the drag force and the tangential force are synonymous.&lt;br /&gt;
&lt;br /&gt;
Figure 4-9 shows the coefficients C&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, and C&amp;lt;sub&amp;gt;m&amp;lt;/sub&amp;gt; versus angle of attack for stable and unstable parachutes.&lt;br /&gt;
&lt;br /&gt;
The coefficient presentation shows two interesting facts. ne slope of the moment coefficient curve, dC&amp;lt;sub&amp;gt;m&amp;lt;/sub&amp;gt;/dα, for the unstable parachute is positive between -25 degrees and + 25 degrees; this is, by definition, destabilizing. This parachute will oscillate approximately ± 25&lt;br /&gt;
&lt;br /&gt;
FIGURE 4-9. Coefficients C&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, and C&amp;lt;sub&amp;gt;M&amp;lt;/sub&amp;gt; Versus Angle of Attack, α, for a Stable and Unstable Parachute.&lt;br /&gt;
&lt;br /&gt;
degrees. The slope of the moment, dC&amp;lt;sub&amp;gt;m&amp;lt;/sub&amp;gt;/dα, for the stable parachute is negative over the total angle of attack; this is, by definition, stabilizing. The steeper the negative dC&amp;lt;sub&amp;gt;m&amp;lt;/sub&amp;gt;/dα slope, the greater is the stabilizing tendency of the parachute, and the better is its damping capability against unstabilizing forces such as sudden gusts of wind.&lt;br /&gt;
&lt;br /&gt;
Figure 4-10, from Reference 4.1, demonstrates the effect of airflow around a cylinder and an airfoil. The circulation around a rotating cylinder creates lift caused by the increase in velocity on one side of the cylinder and a decrease on the opposite side. This is called the Magnus effect.&lt;br /&gt;
&lt;br /&gt;
= 4.5 EQUILIBRIUM OF FORCES IN STUDY DESCENT OR FLIGHT =&lt;br /&gt;
4.5.1 Parachute in Steady Descent&lt;br /&gt;
&lt;br /&gt;
A stable parachute in unaccelerated descent has an equilibrium between the total drag of the parachute and the load, Dr, and the weight of the load and the parachute assembly, WT (Figure 4-11). For steady descent&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
D&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; = total drag, 1b&lt;br /&gt;
&lt;br /&gt;
D&amp;lt;sub&amp;gt;P&amp;lt;/sub&amp;gt; = drag of parachute, 1b&lt;br /&gt;
&lt;br /&gt;
W&amp;lt;sub&amp;gt;C&amp;lt;/sub&amp;gt; = weight of load. 1b&lt;br /&gt;
&lt;br /&gt;
In most cases, the drag of the load can be neglected in relation to the large drag of the parachute, With drag, D — (C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;S)&amp;lt;sub&amp;gt;p&amp;lt;/sub&amp;gt; • p/2• v&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; and D&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; = W&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;. and solving for v, the important equation for rate of descent, v&amp;lt;sub&amp;gt;e&amp;lt;/sub&amp;gt;, is obtained,&lt;br /&gt;
&lt;br /&gt;
Rate of descent,&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
FIGURE 4-11. Forces Acting on a Parachute in Steady Descent.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
or in parachute terminology for rate of descent at sea level&lt;br /&gt;
&lt;br /&gt;
and rate of descent at any altitude&lt;br /&gt;
&lt;br /&gt;
== For 1/, see column 4 in Table 3-3, ==&lt;br /&gt;
In the equation for rate of descent. V&amp;lt;sub&amp;gt;e&amp;lt;/sub&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
W&amp;lt;sub&amp;gt;T =&amp;lt;/sub&amp;gt; weight of load and parachute assembly, 1b&lt;br /&gt;
&lt;br /&gt;
S&amp;lt;sub&amp;gt;o&amp;lt;/sub&amp;gt; = canopy surface area, ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
C&amp;lt;sub&amp;gt;Do&amp;lt;/sub&amp;gt; = parachute drag coefficient related to S&amp;lt;sub&amp;gt;o&amp;lt;/sub&amp;gt;&lt;br /&gt;
&lt;br /&gt;
p = air density at a specific altitude in slugs/ft&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;, as shown in Table 3-3&lt;br /&gt;
&lt;br /&gt;
During descent from altitude, the parachute system is constantly decelerated because of the increasing air density. This can be ignored for slowly descending main parachutes. However, for drogue chute systems that descend at 200 ft/s or faster, the constant deceleration may result in velocities 3 to 5% higher than the steady rate of descent.&lt;br /&gt;
&lt;br /&gt;
4.5.2 Gliding Parachutes&lt;br /&gt;
&lt;br /&gt;
Figure 4-12 shows the balance of forces on a gliding parachute. The total weight of the system, W&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; . must be balanced by the resultant force. R. However, a lifting force is required for glide. To satisfy the force balance&lt;br /&gt;
&lt;br /&gt;
R = C&amp;lt;sub&amp;gt;R&amp;lt;/sub&amp;gt; * S * p/2 * v&lt;br /&gt;
&lt;br /&gt;
Trajectory velocity, V&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, is calculated&lt;br /&gt;
&lt;br /&gt;
Horizontal velocity is calculated&lt;br /&gt;
&lt;br /&gt;
V&amp;lt;sub&amp;gt;H&amp;lt;/sub&amp;gt; = V&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; • cosø, and vertical velocity, v&amp;lt;sub&amp;gt;v&amp;lt;/sub&amp;gt; = V&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; • sinø&lt;br /&gt;
&lt;br /&gt;
The glide ratio is obtained from&lt;br /&gt;
&lt;br /&gt;
Analysis of Figure 4-12 indicates that the larger the ratio of lift to drag, the better the glide ratio, I./D A high resultant coefficient, C&amp;lt;sub&amp;gt;R&amp;lt;/sub&amp;gt;, results in a low glide or trajectory V&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, desirable for landing. A small C&amp;lt;sub&amp;gt;R&amp;lt;/sub&amp;gt; results in a high glide velocity, V&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, which is desirable for flying toward a target, compensating for head winds, or covering a distance quickly. Generally, gliding parachutes follow the same aerodynamic rules as low-aspect-ratio wings.&lt;br /&gt;
&lt;br /&gt;
           	   	&lt;br /&gt;
&lt;br /&gt;
FIGUR E 4-12, Forces Acting on a Gliding Parachute&lt;br /&gt;
&lt;br /&gt;
4.5-3 Parasite Drag and Induced Drag&lt;br /&gt;
&lt;br /&gt;
The drag acting on a lift-producing air vehicle, such as a gliding parachute or an aircraft, has two primary components: the parasite drag, D&amp;lt;sub&amp;gt;P&amp;lt;/sub&amp;gt; , and the induced drag. D&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Parasite drag is produced by the form drag from individual components such as the suspension lines, canopy, and the jumper of a gliding parachute, and the fuselage, tail sectiora, and control surfaces of an airplane. Large surfaces produce surface friction drag as part of the parasite drag.&lt;br /&gt;
&lt;br /&gt;
Induced drag is caused by the lifting action of the parachute canopy or the aircraft wing. Section 4.7 includes books with detailed discussions of induced drag.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Total drag, D&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, can be defined as&lt;br /&gt;
&lt;br /&gt;
or, in the coefficient form&lt;br /&gt;
&lt;br /&gt;
The parasite drag, D&amp;lt;sub&amp;gt;p&amp;lt;/sub&amp;gt;, and the coefficient, C&amp;lt;sub&amp;gt;DP&amp;lt;/sub&amp;gt;, can be determined in wind-tunnel tests or calculated as the sum of the individual component drags.&lt;br /&gt;
&lt;br /&gt;
The induced drag coefficient, C&amp;lt;sub&amp;gt;Di&amp;lt;/sub&amp;gt; , of a gliding parachute canopy or a wing profile can be calculated&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
C = coefficient of induced drag, dimensionless&lt;br /&gt;
&lt;br /&gt;
The expression b&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;/S is defined as the aspect ratio of a wing or parachute with the notation AR b&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;/S. Therefore&lt;br /&gt;
&lt;br /&gt;
== '''                       ''' 	 ==&lt;br /&gt;
The equation for induced drag indicates that increasing the aspect ratio, AR, reduces the induced drag coefficient,  , and therefore reduces the drag, D. ms, in turn, increases the glide ratio, L/D. Increasing the glide ratio by increasing the aspect ratio is optimized on high-performance sailplanes with aspect ratios higher than 20. Increasing the glide ratio of gliding parachutes by increasing the aspect ratio has limitations, which are discussed in section 5.9.&lt;br /&gt;
&lt;br /&gt;
4.5.4 Aircraft in Horizontal Flight&lt;br /&gt;
&lt;br /&gt;
Figure 4-13 shows forces and moments on an aircraft in steady, horizontal flight. In steady, horizontal flight, an equilibrium exists between all forces and moments acting on the aircraft. Lift on the wing and tail, L&amp;lt;sub&amp;gt;W&amp;lt;/sub&amp;gt; and L&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;. and the weight of the aircraft, W&amp;lt;sub&amp;gt;A&amp;lt;/sub&amp;gt;, balance in the vertical plane. Thrust, T and drag. D, balance each other in the horizontal plane, and the positive or negative moment, M, is balanced by the positive or negative lift of the tail multiplied by the moment arm, L&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
FIGURE 4-13. Forces and Moments Acting on an Aircraft in Steady night,&lt;br /&gt;
&lt;br /&gt;
Any imbalance in these forces results in descent or climb in the vertical plane or faster or slower speed in the horizontal plane. A change in the lift of the elevator initiates climb or descent. Thrust, T, is the prime contributor for climb or descent and faster or slower speed, However, a balance of forces must always be maintained for horizontal flight or steady rate oi climb or descent.&lt;br /&gt;
&lt;br /&gt;
== 4.6 WIND-TUNNEL TESTING OF PARACHUTES ==&lt;br /&gt;
Wind tunnels are an effective tool for testing air vehicles and air-vehicle components and have been used successfully for testing parachutes and parachute systems. Experience has shown that certain rules apply for the wind-tunnel testing of parachutes. Small parachutes manufactured from textiles cannot be made sufficiently similar to large parachutes in geometric design and flexibility, Lightweight material. required to obtain design similarity, is difficult to manufacture or is unobtainable.&lt;br /&gt;
&lt;br /&gt;
One cardinal rule has been established through many years of parachute wind-tunnel testing: A modification that changes the performance of a model parachute in wind-tunnel testing produces the same type and percentage of performance change in a large parachute. This rule is true for drag. stability, and opening-force characteristics.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
4.6.1 Blowers&lt;br /&gt;
&lt;br /&gt;
The simple air blower (Figure 4-14) is a proven tool for preliminary parachute testing of a chiefly qualitative nature. Unless special test conditions prevail, parachutes tested should be a minimum of 1.5 to 2 feet in diameter to obtain meaningful results.&lt;br /&gt;
&lt;br /&gt;
                                                                    &lt;br /&gt;
&lt;br /&gt;
 FIGURE 4-14. Typical Air Blower.&lt;br /&gt;
&lt;br /&gt;
An air blower is a preliminary test too! because it permits quick parachute• configuration changes and excellent visual observation.&lt;br /&gt;
&lt;br /&gt;
4.6.2 Open-Throat, No-Return Wind Tunnels&lt;br /&gt;
&lt;br /&gt;
The open-throat, no-return wind tunnel shown in Figure 4-15 permits exact measurements if parachutes of sufficient size are used. Parachutes 3 feet or more in diameter are well suited for obtaining good, quantitative test results.&lt;br /&gt;
&lt;br /&gt;
              FIGURE 4-15. Open-Throat, No-Return Wind Tunnel&lt;br /&gt;
&lt;br /&gt;
In air blowers and open-throat wind tunnels, the velocity at the skirt of the parachute (Section a-a of Figures 4-14 and 4-15) is lower than the velocity at the nozzle exit of the wind tunnel (Section b&amp;lt;sup&amp;gt;-&amp;lt;/sup&amp;gt;b of Figures 4-14 and 4-15), Care must be taken to measure the parachute test&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
velocity at Section a-a and not at Section b-b, the customary attachment point for airfoils and models.&lt;br /&gt;
&lt;br /&gt;
Wind tunnels frequently cannot test at the descent velocity of most main parachutes of 20 to 30 feet per second. Obtaining proper test results at this low is hampered by a poor velocity distribution in the wind-tunnel-test section, and by the weight of the test parachute. The latter has a tendency to pull the parachute downward, thereby providing a negative angle of attack, lusting unstable parachutes at higher presents the problem that the drag coefficient C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, of unstable parachutes is sensitive. The drag coefficient of unstable parachutes is described in section 5.2.&lt;br /&gt;
&lt;br /&gt;
An open-throat wind tunnel permits quick changes in parachute configuration, such as changing the suspension and reefing line lengths. Large open-throat wind tunnels that are not sealed against outside elements suffer atmospheric problems such as fog formation in the test section.&lt;br /&gt;
&lt;br /&gt;
4.6.3 Closed-Throat, Full-Return Wind Tunnel&lt;br /&gt;
&lt;br /&gt;
Figure 4-16 is a drawing of a full-return, closed-throat wind tunnel. fic full-return, closed-throat wind tunnel is generally considered best suited for obtaining good. qualitative, aerodynamic data, since it has a uniform distribution in the test section. A disadvantage is the difficulty in gaining access to the test section for changing the parachute configuration.&lt;br /&gt;
&lt;br /&gt;
FIGURE 4-16. Closed-Throat, Full-Reuurn Wind Tunnel.&lt;br /&gt;
&lt;br /&gt;
4.6.4 General Comments for Wind-Tunnel Testing of Parachutes&lt;br /&gt;
&lt;br /&gt;
1. Parachute models for wind-tunnel testing should be as large and as similar as possible in geometry and flexibility to full-scale parachutes. Parachutes of less than 1.5 feet in diameter usually lack geometric similarity and material flexibility, which results in inflation characteristics and dissimilar inflated shapes.&lt;br /&gt;
&lt;br /&gt;
2.  The finished dimensions of model parachutes must be measured as accurately as possible to determine the nominal diameter, Do, and the surface area, So. Model parachutes will shrink from 5 to 10% during manufacture because of sewing take-up, which results in a notable difference in the dimensions between the drawing and the completed parachute.&lt;br /&gt;
&lt;br /&gt;
3.  Wind&amp;lt;sup&amp;gt;-&amp;lt;/sup&amp;gt;tunnel tests of parachutes are excellent for comparing different models and modifications: also, they are the most effective means for measuring coefficients of lift, drag. and normal and tangential forces, as well as for determining the load coefficient, for infinite load.&lt;br /&gt;
&lt;br /&gt;
4.  In wind-tunnel tests, velocity decay does not occur during parachute inflation and operation; this is defined as testing under &amp;quot;infinite mass condition. &amp;quot; First-stage drogue chutes and parachutes with a canopy loading, W/C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;S. in excess of 100 lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; approach this condition. Low-canopy-loading main parachutes with rates of descent of 20 to 30 ft/s have a large velocity decay during opening, which requires careful interpretation of the opening-force data obtained in wind-tunnel tests.&lt;br /&gt;
&lt;br /&gt;
5.  In the past, to avoid wind-tunnel blockage and questionable test data. the diameter of a test parachute could not exceed about 5 to 6% of the wind-tunnel test section area. Recent Sandia investigations of single and clustered ribbon parachutes with wind-tunnel blockage ratios of up to 30% have resulted in correction methods that make it possible to test much larger parachutes (Reference 4.2).&lt;br /&gt;
&lt;br /&gt;
= 4.7 REFERENCE MATERIAL =&lt;br /&gt;
4.1 H. H. Hurt. Aerodynamics for Naval Aviators Navy Manual NAVWEPS 00 80T 80. Chief of Naval Operations, Aviation Training Division.&lt;br /&gt;
&lt;br /&gt;
4.2 J, M. Macha and R J. Buffington. &amp;quot;Wall-Interference Corrections for Parachutes in a Closed Wind Tunnel.&amp;quot; AIM Paper, April 1989. (AIM 89-0900-cp.)&lt;br /&gt;
&lt;br /&gt;
For readers interested in a more detailed study of aerodynamics, the following books are recommended.&lt;br /&gt;
&lt;br /&gt;
4.3 J, H, Dwinnel, Principle of Aerodynamics. McGraw-Hill     	Co., New York, 1949.&lt;br /&gt;
&lt;br /&gt;
4.4 J. Morane. Introduction to Theoretical and Computational Aerodynamics. John Wiley &amp;amp; Sons.&lt;br /&gt;
&lt;br /&gt;
4.5 R.S. Shevell. Fundamentals of Flight. Prentice-Hall. 1983.&lt;br /&gt;
&lt;br /&gt;
4.6 J. D. Anderson, Jr. Introduction to Flights, ILS Engineering and History. McGraw-Hill Book co., New York 1978.&lt;br /&gt;
&lt;br /&gt;
4.7 D. J. Cockrell. The Aerodynamics of Parachutes.&amp;quot; AGARDograph No. 6295, available from NASA Langley Research Center, M/S 1M), Hampton, Va., 236.&lt;/div&gt;</summary>
		<author><name>TuanHTruong</name></author>
	</entry>
	<entry>
		<id>https://mediawiki.aerodecelerator.org/index.php?title=Parachute_Aerodynamics&amp;diff=28</id>
		<title>Parachute Aerodynamics</title>
		<link rel="alternate" type="text/html" href="https://mediawiki.aerodecelerator.org/index.php?title=Parachute_Aerodynamics&amp;diff=28"/>
		<updated>2024-05-03T22:25:44Z</updated>

		<summary type="html">&lt;p&gt;TuanHTruong: Tables, equations and corrections for section Knacke section 4.1&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&lt;br /&gt;
= CHAPTER 4: AERODYNAMICS AS RELATED TO PARACHUTES =&lt;br /&gt;
== 4.1 PROPERTIES OF THE ATMOSPHERE ==&lt;br /&gt;
All forces acting on parachutes and all movements of parachutes are affected by the atmosphere, or air, surrounding the Earth. The air at the Earth's surface is approximately 78% nitrogen; 21% oxygen; and 1% a mixture of gases such as argon, neon, helium, water vapor, and carbon dioxide. This chemical composition remains relatively constant to an altitude of about 160,000 feet (50 kilometers). The following air qualities are of major significance in the dynamics of bodies moving in the atmosphere:&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
!Air quality&lt;br /&gt;
!Symbol&lt;br /&gt;
!Dimension&lt;br /&gt;
|-&lt;br /&gt;
|Specific weight of air&lt;br /&gt;
|w&lt;br /&gt;
|lb/ft&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;, kg/m&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;&lt;br /&gt;
|-&lt;br /&gt;
|Static pressure&lt;br /&gt;
|p&lt;br /&gt;
|atm, lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;, Pa, bar, torr&lt;br /&gt;
|-&lt;br /&gt;
|Temperature&lt;br /&gt;
|T&lt;br /&gt;
|&amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F, &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;C&lt;br /&gt;
|-&lt;br /&gt;
|Mass density&lt;br /&gt;
|&amp;lt;math&amp;gt;\rho&amp;lt;/math&amp;gt;&lt;br /&gt;
|slugs/ft3, kg s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;/m&amp;lt;sup&amp;gt;4&amp;lt;/sup&amp;gt;&lt;br /&gt;
|-&lt;br /&gt;
|Gravity&lt;br /&gt;
|''g''&lt;br /&gt;
|ft/s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;, m/s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
|-&lt;br /&gt;
|Speed of sound&lt;br /&gt;
|C&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt;&lt;br /&gt;
|ft/s, m/s&lt;br /&gt;
|}&lt;br /&gt;
All of these qualities are altitude-dependent and may vary slightly on the Earth's surface with geographic latitude because of variations of the Earth's radius caused by the centrifugal forces of the rotation of the Earth. All standard data used herein refer to a latitude of 45 degrees. Sea level is defined as mean sea level (MSL). To compare performance data on an equal basis, the United States Bureau of Standards has defined standard day conditions as follows:&lt;br /&gt;
&lt;br /&gt;
* Temperature = 15 degrees Celsius (&amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;C) or 59 degrees Fahrenheit (&amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F)&lt;br /&gt;
* Pressure = 760 millimeters (mm) of mercury (Hg) or 29.9213 inches (in.) Hg&lt;br /&gt;
&lt;br /&gt;
=== 4.1.1 Specific Weight of Air ===&lt;br /&gt;
For standard day conditions of 59 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F temperature and a pressure of 29.9213 in. Hg, the specific weight of air, w, is 0.07648 lb/ft&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt; or 1.2250 kg/m&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;. The specific weight of air changes with pressure, temperature, and humidity. Further data can be found in References 3.4 and 4.1, and in technical handbooks.&lt;br /&gt;
&lt;br /&gt;
=== 4.1.2 Static Pressure ===&lt;br /&gt;
Static pressure depends on geographic latitude, weather conditions, and altitude. The static pressure at any altitude results from the weight of the air above that altitude. For MSL and standard day conditions, the pressure, p&amp;lt;sub&amp;gt;o&amp;lt;/sub&amp;gt;, is 29.9213 in. Hg = 760 mm Hg = 1.0 atmosphere (atm). For conversion to Pascal, torr, or bar, see the conversion tables in section 3.2.&lt;br /&gt;
&lt;br /&gt;
=== 4.1.3 Temperature ===&lt;br /&gt;
Temperatures are defined in the English and metric systems in the so-called absolute and engineering scales. The absolute temperature minimum at 0 degrees, pressure is 0 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;K = -273.16 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;C, and 0 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;R = -459.69 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F. This is also written&lt;br /&gt;
&lt;br /&gt;
* Degrees Kelvin = degrees Celsius + 273.16&lt;br /&gt;
* Degrees Rankine = degrees Fahrenheit + 459.69&lt;br /&gt;
&lt;br /&gt;
The freezing point of water is 32 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F or 0 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;C. The boiling point of water is 212 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F or 100 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;C.&lt;br /&gt;
&lt;br /&gt;
=== 4.1.4 Mass Density of Air ===&lt;br /&gt;
Mass density defines the amount of mass contained in a unit volume of air. The mass density, &amp;lt;math&amp;gt;\rho&amp;lt;/math&amp;gt;, of air is of special importance in aerodynamic calculations.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\rho = \frac{specific\ weight\ of\ air,\ w}{acceleration\ of\ gravity,\ g} = \frac{lb/ft^3}{ft/s^2} = \frac{kg\ s^2}{m^4}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;slug = \frac{weight}{acceleration\ of\ gravity} = \frac{lb}{ft/s^2}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Frequently the density ratio, &amp;lt;math&amp;gt;\sigma&amp;lt;/math&amp;gt;, is used&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\sigma = \frac{ambient\ air\ density,\ \rho}{standard\ sea-level\ density, \rho_o}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The factor, &amp;lt;math&amp;gt;1/\sqrt{\rho/\rho_o}&amp;lt;/math&amp;gt;, determines the increase in parachute rate of descent with altitude. The density at 40,000 feet is ¼ of the MSL density, and the density at 100,000 feet is 1/75 of the MSL density. Therefore, the parachute rate of descent is about twice as high at 40,000 feet and about nine times as high at 100,000 feet. MSL density is 0.00237689 slugs/ft&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;, or 0.1249 kg s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;/m&amp;lt;sup&amp;gt;4&amp;lt;/sup&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
=== 4.1.5 Gravity ===&lt;br /&gt;
Any mass attracts another mass with a force called gravity. If the Earth were surrounded by a vacuum, a body suspended above the Earth and released would fall toward the center of the Earth with increasing velocity caused by the acceleration of gravity, ''g''. In reality, the falling body is decelerated by its air drag until the air drag, D, equals the weight of the body, W, and an equilibrium velocity is reached; for parachutes, this is called the steady-state rate of descent.&lt;br /&gt;
&lt;br /&gt;
The acceleration of gravity, ''g'', at sea lavel is&lt;br /&gt;
&lt;br /&gt;
* ''g'' = 32.174 ft/s2 or 9.80665 m/s2.&lt;br /&gt;
&lt;br /&gt;
The value g = 9.08665 m/s is standardized internationally but is accurate only for a latitude of 45 degrees.&lt;br /&gt;
&lt;br /&gt;
With increasing altitude above the Earth's surface, the acceleration of gravity decreases in accordance with the equation&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;g = g_o(\frac{r}{r+h})^2&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
* ''g'' = acceleration of gravity at any altitude, ft/s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
* g&amp;lt;sub&amp;gt;o&amp;lt;/sub&amp;gt; = acceleration of gravity at sea level, ft/s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
* r = average Earth radius = 2.08556 x 10&amp;lt;sup&amp;gt;7&amp;lt;/sup&amp;gt; ft&lt;br /&gt;
* h = altitude above sea level, ft&lt;br /&gt;
&lt;br /&gt;
For other planets and heavenly bodies, the acceleration of gravity varies with the mass of the body. For example, the acceleration of gravity on Mars is about 1/3 of the acceleration of gravity on Earth. For more details on planets and heavenly bodies, see page XII of Reference 2.1.&lt;br /&gt;
&lt;br /&gt;
=== 4.1.6 Kinematic Viscosity ===&lt;br /&gt;
The coefficient of viscosity, &amp;lt;math&amp;gt;\mu&amp;lt;/math&amp;gt;, defines the shearing stresses in a gas or liquid and is sometimes called the resistance to continuous deformation. In aerodynamics, the coefficient of viscosity is combined with the mass density to form the kinematic viscosity, &amp;lt;math&amp;gt;\nu&amp;lt;/math&amp;gt;, where&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\nu = \frac{coefficient\ of\ viscosity,\ \mu}{mass\ density,\ \rho} = 0.0001576\ ft^2/s\ at\ sea\ level&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The kinematic viscosity, &amp;lt;math&amp;gt;\nu&amp;lt;/math&amp;gt;, is altitude dependent and is used to calculate the Reynolds number, Re.&lt;br /&gt;
&lt;br /&gt;
=== 4.1.7 Reynolds Number ===&lt;br /&gt;
The Reynolds number, Re, defines the relationship of mass forces to viscous friction forces in liquids and gases. It is calculated as&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Re = \frac{v\cdot l}{\nu} = \frac{velocity\ (ft/s)\cdot characteristic\ length\ (ft)}{kinematic\ viscosity\ (ft^2/s)}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Reynolds number is an important criterion in subsonic, noncompressible flow, and allows comparison of model tests with full-scale flight tests. A Reynolds number effect on parachutes working in separated, turbulent flow has not yet been established, as shown in section 5.2. The following chart shows the Reynolds numbers for various air vehicles.&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
!Subject&lt;br /&gt;
!Insect&lt;br /&gt;
!Glider&lt;br /&gt;
!DC-3&lt;br /&gt;
!B-747&lt;br /&gt;
!Drogue&lt;br /&gt;
Chute&lt;br /&gt;
!Main &lt;br /&gt;
Parachute&lt;br /&gt;
!WTT&lt;br /&gt;
Model&lt;br /&gt;
|-&lt;br /&gt;
|Re&lt;br /&gt;
|6 • 10&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;&lt;br /&gt;
|2.5 • 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&lt;br /&gt;
|24 • 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&lt;br /&gt;
|100 • 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&lt;br /&gt;
|50 • 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&lt;br /&gt;
|20 • 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&lt;br /&gt;
|2 • 10&amp;lt;sup&amp;gt;6&amp;lt;/sup&amp;gt;&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
=== 4.1.8 Mach Number ===&lt;br /&gt;
Mach number is an important parameter of supersonic flight; it states how much faster than the speed of sound the air vehicle travels.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;Mach\ number,\ M = \frac{flight velocity,\ v}{speed\ of\ sound, c_s}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The speed of sound is the velocity at which a pressure disturbance, such as the sound of the human voice, travels in any medium. The speed of sound varies considerably in different gases, liquids, and metals.&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|Speed of sound in air in MSL&lt;br /&gt;
|C&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt; = 1116.46 ft/s = 340.38 m/s&lt;br /&gt;
|-&lt;br /&gt;
|Speed of sound in water&lt;br /&gt;
|C&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt; = 4749 ft/s = 1461.21 m/s&lt;br /&gt;
|-&lt;br /&gt;
|Speed of sound in iron&lt;br /&gt;
|C&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt; = 16,410 ft/s = 5710.7 m/s&lt;br /&gt;
|}&lt;br /&gt;
The speed of sound depends on temperature and the chemical composition of the medium, A widely used equation for speed of sound in air is&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;C_s = 41.4\sqrt{\gamma\cdot T}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
* &amp;lt;math&amp;gt;C_s&amp;lt;/math&amp;gt; = speed of sound in dry air, ft/s&lt;br /&gt;
* &amp;lt;math&amp;gt;\gamma&amp;lt;/math&amp;gt; = ratio of specific heat, equal to 1.4 for dry air, dimensionless&lt;br /&gt;
* &amp;lt;math&amp;gt;T&amp;lt;/math&amp;gt; = temperature in Fahrenheit absolute, equal to 459.67 + &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F&lt;br /&gt;
&lt;br /&gt;
The speed of sound changes with altitude, as temperature (see Figure 3-1). The drag of streamlined bodies such as missiles, airfoils, and airplanes increases considerably as their velocities approach Mach 1. Depending on the configuration of the body, supersonic compressibility effects may occur in the 0.75 to 0.85 Mach range, causing local supersonic flow, shock waves, flow separation, and concomitant increases in drag and changes in stability.&lt;br /&gt;
&lt;br /&gt;
Parachutes that operate in separated flow over the entire velocity range do not show the typical drag increase when operating close to or beyond Mach 1. Supersonic parachute behavior is discussed in detail in section 5.8.&lt;br /&gt;
&lt;br /&gt;
== '''4.2 CONTINUITY LAW AND BERNOULLI EQUATION''' ==&lt;br /&gt;
4.2.1 Continuity L.aw&lt;br /&gt;
&lt;br /&gt;
Air is thought to flow in layers called streamlines. Figure 4-1 shows streamlines as layers of air without air transfer between individual layers. ne air is shown as being incompressible, a valid assumption for subsonic flow.&lt;br /&gt;
&lt;br /&gt;
  	&lt;br /&gt;
&lt;br /&gt;
If exchange of air does not occur across the streamline boundaries, the amount of air entering the streamline at point 1 must also exit at point 2. as shown in Figure 4*1. Because the cross section at point 2 is smaller than the cross section at point 1, the air must exit at a higher velocity. The following equation defines this condition:&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
this equation which governs the now in and around a body in gases and liquids, is important in aerodynamics and is called the continuity law. For imcompressilble subsonic now, it can be simplified to &lt;br /&gt;
&lt;br /&gt;
Whenever the cross section narrows. the velocity increases; when the cross section widens, the velocity decreases.&lt;br /&gt;
&lt;br /&gt;
4.2.2 Bernoulli Equation&lt;br /&gt;
&lt;br /&gt;
Figure 4-2 illustrates a streamline with the cross section, S, the velocity, v, and the pressure, p. If the air is incompressible, the downstream is v + Av. and the pressure is p + AP. If the air is inviscid, the inertia forces caused by the acceleration of air from v to v + Av must be balanced by differential pressure forces.&lt;br /&gt;
&lt;br /&gt;
    	                                       	&lt;br /&gt;
&lt;br /&gt;
FIGURE 4-2 Pressure and Velocity Distribution in a Streamline Element.&lt;br /&gt;
&lt;br /&gt;
The following equation can be written&lt;br /&gt;
&lt;br /&gt;
Simplified, the above equation yields&lt;br /&gt;
&lt;br /&gt;
'''dp = -pvdv'''&lt;br /&gt;
&lt;br /&gt;
the above equation allows the following consideration: If p is pressure, then 1/2 pv&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; and C must also be pressure. The equation 1/2 pv&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; includes a and is referred to as the dynamic pressure. or sometimes velocity as or impact pressure.&lt;br /&gt;
&lt;br /&gt;
Pressure, p, is defined as static pressure; 1/2 pv&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; as dynamic pressure; and the sum of both, C, as the total pressure or&lt;br /&gt;
&lt;br /&gt;
p + 1/2pv&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; = H&lt;br /&gt;
&lt;br /&gt;
and&lt;br /&gt;
&lt;br /&gt;
where H is the total pressure of the system, lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Dynamic pressure, q, is a frequently used quantity in aerodynamics:&lt;br /&gt;
&lt;br /&gt;
q = 1/2 pv&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
q = dynamic pressure, lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
p =  air density, slugs/ft&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
v =  velocity at a point of undisturbed flow, ft/s&lt;br /&gt;
&lt;br /&gt;
The following formulas are used for calculating the sea-level dynamic pressure if the velocity is given in ft/s, knots, mph, or km/h, respectively:&lt;br /&gt;
&lt;br /&gt;
                                              &lt;br /&gt;
&lt;br /&gt;
'''4.3 NEWTON'S THREE OF MOTION'''&lt;br /&gt;
&lt;br /&gt;
Engineering mechanics are governed by the following three laws of Isaac Newton:&lt;br /&gt;
&lt;br /&gt;
1.  A body remains at rest or in an unaccelerated state of motion unless acted upon.&lt;br /&gt;
&lt;br /&gt;
2.  A force acting upon a body will produce an acceleration in the direction of the force.&lt;br /&gt;
&lt;br /&gt;
3.  An action in one direction will produce an equal reaction in the opposite direction.&lt;br /&gt;
&lt;br /&gt;
The first law is self-explanatory. The second law may be expressed by the equation&lt;br /&gt;
&lt;br /&gt;
F = m * a&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
F = force in pounds acting on the mass, 1b&lt;br /&gt;
&lt;br /&gt;
m = mass of body that the force is acting upon, slugs&lt;br /&gt;
&lt;br /&gt;
a = acceleration in ft/s2 resulting from the force, F&lt;br /&gt;
&lt;br /&gt;
The mass, m, of a body is obtained by&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
W = weight of the body, lb&lt;br /&gt;
&lt;br /&gt;
g = acceleration of gravity, ft/s2&lt;br /&gt;
&lt;br /&gt;
The mass, therefore, has the dimension of&lt;br /&gt;
&lt;br /&gt;
This unit of mass is the slug.&lt;br /&gt;
&lt;br /&gt;
the equation of Newton's second law can now be written&lt;br /&gt;
&lt;br /&gt;
                                        	&lt;br /&gt;
&lt;br /&gt;
The factor a/g is frequently called the load factor, G, and tells how much larger a force is than a force equivalent to the weight of the body. It is customary in parachute work to state that the maximum parachute force allowed is G • W or (a]g) • W. It is appropriate to write&lt;br /&gt;
&lt;br /&gt;
Maximum allowable parachute force,&lt;br /&gt;
&lt;br /&gt;
Figure 4-3 illustrates Newton's third law, explaining the principle of the rocket that can produce thrust in a perfect vacuum.&lt;br /&gt;
&lt;br /&gt;
A mass, m. ejected from a rocket at the velocity, v, per unit time, t, will produce a force, F, which in turn will create a reaction force, R. of equal magnitude but acting in the opposite direction.&lt;br /&gt;
&lt;br /&gt;
=== 4.4 FORCES ACTING ON A BODY MOVING THROUGH AIR ===&lt;br /&gt;
4.4.1 Symmetrical Body&lt;br /&gt;
&lt;br /&gt;
A body moving through air experiences forces caused by air pressure acting on the body. fie same forces if the body moves through air, such as a descending parachute, or if the body is fixed and the air moves against the body, such as a parachute or an airfoil in a wind tunnel (Figure 44).&lt;br /&gt;
&lt;br /&gt;
         	 &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
A stable parachute in a wind tunnel experiences only the force called &amp;quot;drag&amp;quot; in the direction of the airflow. drag force, D, is calculated to&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
D = drag, 1b&lt;br /&gt;
&lt;br /&gt;
Q = dynamic pressure, lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
S = total surface area of the parachute canopy, ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt; = coefficient of drag.  dimensionless&lt;br /&gt;
&lt;br /&gt;
the dynamic pressure, q, can be calculated from section 4.2.2. The surface area of the canopy, S, is selected as a reference area. The drag coefficient  C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, is a form factor that indicates the drag characteristic of a specific shape. Most aerodynamic bodies are designed for low drag or a low drag coefficient. Parachutes, generally, are designed for high drag; therefore, a high drag coefficient is desirable. this difference in drag is demonstrated by the two bodies shown in Figure 4-5.&lt;br /&gt;
&lt;br /&gt;
            	&lt;br /&gt;
&lt;br /&gt;
Both bodies have the same cross section perpendicular to the airflow. The cylindrical. streamlined body has a smooth airflow over its total body length, resulting in a drag coefficient. C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, of 0.05 to 0.1, depending on slenderness ratio, surface roughness, and shape. The drag coefficient of all streamlined bodies is much affected by Reynolds number and Mach number. fie open hemisphere, which is similar to a parachute canopy, has a drag coefficient, C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, of 1.3 to 1.4 for the same body cross section. The difference in drag is explained by the smooth airflow around the streamlined body and a separated. turbulent flow around the open hemisphere. The drag of bodies with separated flow, like parachute canopies, is little affected by Reynolds number.&lt;br /&gt;
&lt;br /&gt;
4.4.2 Airflow Around an Asymmetrical Body (Airfoil)&lt;br /&gt;
&lt;br /&gt;
Figure 4-6 shows an airfoil fixed at an angle of attack, a. against the airflow in a wind tunnel. This airfoil creates a drag force, D, in the direction of the flow; a lift force L perpendicular to the direction of the flow; and a moment, M. around the attachment point of the airfoil. fie sign convention of moments and forces shown are positive. Lift and drag can be combined for the resultant force, R.&lt;br /&gt;
&lt;br /&gt;
FIGURE. 44, Wind-Tunnel Forces Acting on an Airfoil.&lt;br /&gt;
&lt;br /&gt;
The lift, L is calculated&lt;br /&gt;
&lt;br /&gt;
L = q * S * C&amp;lt;sub&amp;gt;L&amp;lt;/sub&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
L = measured lift, 1b&lt;br /&gt;
&lt;br /&gt;
q = dynamic pressure, lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
s = reference area, ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
CL = lift coefficient, dimensionless&lt;br /&gt;
&lt;br /&gt;
The moment is&lt;br /&gt;
&lt;br /&gt;
       M = q * S * c&amp;lt;sub&amp;gt;m&amp;lt;/sub&amp;gt; * c&lt;br /&gt;
&lt;br /&gt;
Where&lt;br /&gt;
&lt;br /&gt;
The reference area, S is defined by agreement, For streamlined bodies, the maximum body cross section is used. Airfoils use the planform of the wing, and parachutes use the canopy surface area. The selection of the wing planform and the parachute surface area as references was made for practical reasons. &amp;lt;sup&amp;gt;e&amp;lt;/sup&amp;gt;me wing planform for a specific wing is fixedt whereas the cross section of the wing in the direction of the flow changes with the angle of attack. Similarly, the surface area of the parachute canopy is fixed; however, the frontal projected area of the inflated parachute canopy changes with airspeed, porosity, line length, and tm of parachute.&lt;br /&gt;
&lt;br /&gt;
Forces and moments acting on an airfoil or a parachute canopy may be presented in several ways. The two most frequently used methods, as shown in Figure 4-7, are with forces oriented to the of flight and with forces oriented to the axis of the airfoil.&lt;br /&gt;
&lt;br /&gt;
me tangential force, and the normal force, N, are calculated&lt;br /&gt;
&lt;br /&gt;
T = C&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; * S * q&lt;br /&gt;
&lt;br /&gt;
        	&lt;br /&gt;
&lt;br /&gt;
and&lt;br /&gt;
&lt;br /&gt;
      	N = C&amp;lt;sub&amp;gt;N&amp;lt;/sub&amp;gt; * S * q&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
C&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; = tangential force coefficient, dimensionless&lt;br /&gt;
&lt;br /&gt;
C&amp;lt;sub&amp;gt;N&amp;lt;/sub&amp;gt; = normal force coefficient, dimensionless&lt;br /&gt;
&lt;br /&gt;
The resultant force, R, and the moment, M, in both presentations have the same direction and the same magnitude. The airflow fixed system is preferred for aerodynamic performance calculations, and the airfoil fixed system for wing stress calculations. me aerodynamic coefficients C&amp;lt;sub&amp;gt;L&amp;lt;/sub&amp;gt;, C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, C&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, C&amp;lt;sub&amp;gt;N&amp;lt;/sub&amp;gt;, and C&amp;lt;sub&amp;gt;m&amp;lt;/sub&amp;gt; can easily be determined in wind•tunnel measurements.&lt;br /&gt;
&lt;br /&gt;
Figure 4-8 shows the relationship of both force systems on a parachute. By definition, a negative moment is stabilizing, as illustrated in Figure 4-8. It is interesting to note that in Europe the stabilizing moment is defined as positive. Wind-tunnel installations frequently measure normal and tangential force instead of lift and drag. If α, T, and N are known, the drag D, can be calculated&lt;br /&gt;
&lt;br /&gt;
D = T*cosα + N * sinα&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
For a parachute with an angle of attack, a, equal to zero, the drag force and the tangential force are synonymous.&lt;br /&gt;
&lt;br /&gt;
Figure 4-9 shows the coefficients C&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, and C&amp;lt;sub&amp;gt;m&amp;lt;/sub&amp;gt; versus angle of attack for stable and unstable parachutes.&lt;br /&gt;
&lt;br /&gt;
The coefficient presentation shows two interesting facts. ne slope of the moment coefficient curve, dC&amp;lt;sub&amp;gt;m&amp;lt;/sub&amp;gt;/dα, for the unstable parachute is positive between -25 degrees and + 25 degrees; this is, by definition, destabilizing. This parachute will oscillate approximately ± 25&lt;br /&gt;
&lt;br /&gt;
FIGURE 4-9. Coefficients C&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, and C&amp;lt;sub&amp;gt;M&amp;lt;/sub&amp;gt; Versus Angle of Attack, α, for a Stable and Unstable Parachute.&lt;br /&gt;
&lt;br /&gt;
degrees. The slope of the moment, dC&amp;lt;sub&amp;gt;m&amp;lt;/sub&amp;gt;/dα, for the stable parachute is negative over the total angle of attack; this is, by definition, stabilizing. The steeper the negative dC&amp;lt;sub&amp;gt;m&amp;lt;/sub&amp;gt;/dα slope, the greater is the stabilizing tendency of the parachute, and the better is its damping capability against unstabilizing forces such as sudden gusts of wind.&lt;br /&gt;
&lt;br /&gt;
Figure 4-10, from Reference 4.1, demonstrates the effect of airflow around a cylinder and an airfoil. The circulation around a rotating cylinder creates lift caused by the increase in velocity on one side of the cylinder and a decrease on the opposite side. This is called the Magnus effect.&lt;br /&gt;
&lt;br /&gt;
= 4.5 EQUILIBRIUM OF FORCES IN STUDY DESCENT OR FLIGHT =&lt;br /&gt;
4.5.1 Parachute in Steady Descent&lt;br /&gt;
&lt;br /&gt;
A stable parachute in unaccelerated descent has an equilibrium between the total drag of the parachute and the load, Dr, and the weight of the load and the parachute assembly, WT (Figure 4-11). For steady descent&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
D&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; = total drag, 1b&lt;br /&gt;
&lt;br /&gt;
D&amp;lt;sub&amp;gt;P&amp;lt;/sub&amp;gt; = drag of parachute, 1b&lt;br /&gt;
&lt;br /&gt;
W&amp;lt;sub&amp;gt;C&amp;lt;/sub&amp;gt; = weight of load. 1b&lt;br /&gt;
&lt;br /&gt;
In most cases, the drag of the load can be neglected in relation to the large drag of the parachute, With drag, D — (C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;S)&amp;lt;sub&amp;gt;p&amp;lt;/sub&amp;gt; • p/2• v&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; and D&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; = W&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;. and solving for v, the important equation for rate of descent, v&amp;lt;sub&amp;gt;e&amp;lt;/sub&amp;gt;, is obtained,&lt;br /&gt;
&lt;br /&gt;
Rate of descent,&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
FIGURE 4-11. Forces Acting on a Parachute in Steady Descent.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
or in parachute terminology for rate of descent at sea level&lt;br /&gt;
&lt;br /&gt;
and rate of descent at any altitude&lt;br /&gt;
&lt;br /&gt;
== For 1/, see column 4 in Table 3-3, ==&lt;br /&gt;
In the equation for rate of descent. V&amp;lt;sub&amp;gt;e&amp;lt;/sub&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
W&amp;lt;sub&amp;gt;T =&amp;lt;/sub&amp;gt; weight of load and parachute assembly, 1b&lt;br /&gt;
&lt;br /&gt;
S&amp;lt;sub&amp;gt;o&amp;lt;/sub&amp;gt; = canopy surface area, ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
C&amp;lt;sub&amp;gt;Do&amp;lt;/sub&amp;gt; = parachute drag coefficient related to S&amp;lt;sub&amp;gt;o&amp;lt;/sub&amp;gt;&lt;br /&gt;
&lt;br /&gt;
p = air density at a specific altitude in slugs/ft&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;, as shown in Table 3-3&lt;br /&gt;
&lt;br /&gt;
During descent from altitude, the parachute system is constantly decelerated because of the increasing air density. This can be ignored for slowly descending main parachutes. However, for drogue chute systems that descend at 200 ft/s or faster, the constant deceleration may result in velocities 3 to 5% higher than the steady rate of descent.&lt;br /&gt;
&lt;br /&gt;
4.5.2 Gliding Parachutes&lt;br /&gt;
&lt;br /&gt;
Figure 4-12 shows the balance of forces on a gliding parachute. The total weight of the system, W&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; . must be balanced by the resultant force. R. However, a lifting force is required for glide. To satisfy the force balance&lt;br /&gt;
&lt;br /&gt;
R = C&amp;lt;sub&amp;gt;R&amp;lt;/sub&amp;gt; * S * p/2 * v&lt;br /&gt;
&lt;br /&gt;
Trajectory velocity, V&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, is calculated&lt;br /&gt;
&lt;br /&gt;
Horizontal velocity is calculated&lt;br /&gt;
&lt;br /&gt;
V&amp;lt;sub&amp;gt;H&amp;lt;/sub&amp;gt; = V&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; • cosø, and vertical velocity, v&amp;lt;sub&amp;gt;v&amp;lt;/sub&amp;gt; = V&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; • sinø&lt;br /&gt;
&lt;br /&gt;
The glide ratio is obtained from&lt;br /&gt;
&lt;br /&gt;
Analysis of Figure 4-12 indicates that the larger the ratio of lift to drag, the better the glide ratio, I./D A high resultant coefficient, C&amp;lt;sub&amp;gt;R&amp;lt;/sub&amp;gt;, results in a low glide or trajectory V&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, desirable for landing. A small C&amp;lt;sub&amp;gt;R&amp;lt;/sub&amp;gt; results in a high glide velocity, V&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, which is desirable for flying toward a target, compensating for head winds, or covering a distance quickly. Generally, gliding parachutes follow the same aerodynamic rules as low-aspect-ratio wings.&lt;br /&gt;
&lt;br /&gt;
           	   	&lt;br /&gt;
&lt;br /&gt;
FIGUR E 4-12, Forces Acting on a Gliding Parachute&lt;br /&gt;
&lt;br /&gt;
4.5-3 Parasite Drag and Induced Drag&lt;br /&gt;
&lt;br /&gt;
The drag acting on a lift-producing air vehicle, such as a gliding parachute or an aircraft, has two primary components: the parasite drag, D&amp;lt;sub&amp;gt;P&amp;lt;/sub&amp;gt; , and the induced drag. D&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Parasite drag is produced by the form drag from individual components such as the suspension lines, canopy, and the jumper of a gliding parachute, and the fuselage, tail sectiora, and control surfaces of an airplane. Large surfaces produce surface friction drag as part of the parasite drag.&lt;br /&gt;
&lt;br /&gt;
Induced drag is caused by the lifting action of the parachute canopy or the aircraft wing. Section 4.7 includes books with detailed discussions of induced drag.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Total drag, D&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, can be defined as&lt;br /&gt;
&lt;br /&gt;
or, in the coefficient form&lt;br /&gt;
&lt;br /&gt;
The parasite drag, D&amp;lt;sub&amp;gt;p&amp;lt;/sub&amp;gt;, and the coefficient, C&amp;lt;sub&amp;gt;DP&amp;lt;/sub&amp;gt;, can be determined in wind-tunnel tests or calculated as the sum of the individual component drags.&lt;br /&gt;
&lt;br /&gt;
The induced drag coefficient, C&amp;lt;sub&amp;gt;Di&amp;lt;/sub&amp;gt; , of a gliding parachute canopy or a wing profile can be calculated&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
C = coefficient of induced drag, dimensionless&lt;br /&gt;
&lt;br /&gt;
The expression b&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;/S is defined as the aspect ratio of a wing or parachute with the notation AR b&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;/S. Therefore&lt;br /&gt;
&lt;br /&gt;
== '''                       ''' 	 ==&lt;br /&gt;
The equation for induced drag indicates that increasing the aspect ratio, AR, reduces the induced drag coefficient,  , and therefore reduces the drag, D. ms, in turn, increases the glide ratio, L/D. Increasing the glide ratio by increasing the aspect ratio is optimized on high-performance sailplanes with aspect ratios higher than 20. Increasing the glide ratio of gliding parachutes by increasing the aspect ratio has limitations, which are discussed in section 5.9.&lt;br /&gt;
&lt;br /&gt;
4.5.4 Aircraft in Horizontal Flight&lt;br /&gt;
&lt;br /&gt;
Figure 4-13 shows forces and moments on an aircraft in steady, horizontal flight. In steady, horizontal flight, an equilibrium exists between all forces and moments acting on the aircraft. Lift on the wing and tail, L&amp;lt;sub&amp;gt;W&amp;lt;/sub&amp;gt; and L&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;. and the weight of the aircraft, W&amp;lt;sub&amp;gt;A&amp;lt;/sub&amp;gt;, balance in the vertical plane. Thrust, T and drag. D, balance each other in the horizontal plane, and the positive or negative moment, M, is balanced by the positive or negative lift of the tail multiplied by the moment arm, L&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
FIGURE 4-13. Forces and Moments Acting on an Aircraft in Steady night,&lt;br /&gt;
&lt;br /&gt;
Any imbalance in these forces results in descent or climb in the vertical plane or faster or slower speed in the horizontal plane. A change in the lift of the elevator initiates climb or descent. Thrust, T, is the prime contributor for climb or descent and faster or slower speed, However, a balance of forces must always be maintained for horizontal flight or steady rate oi climb or descent.&lt;br /&gt;
&lt;br /&gt;
== 4.6 WIND-TUNNEL TESTING OF PARACHUTES ==&lt;br /&gt;
Wind tunnels are an effective tool for testing air vehicles and air-vehicle components and have been used successfully for testing parachutes and parachute systems. Experience has shown that certain rules apply for the wind-tunnel testing of parachutes. Small parachutes manufactured from textiles cannot be made sufficiently similar to large parachutes in geometric design and flexibility, Lightweight material. required to obtain design similarity, is difficult to manufacture or is unobtainable.&lt;br /&gt;
&lt;br /&gt;
One cardinal rule has been established through many years of parachute wind-tunnel testing: A modification that changes the performance of a model parachute in wind-tunnel testing produces the same type and percentage of performance change in a large parachute. This rule is true for drag. stability, and opening-force characteristics.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
4.6.1 Blowers&lt;br /&gt;
&lt;br /&gt;
The simple air blower (Figure 4-14) is a proven tool for preliminary parachute testing of a chiefly qualitative nature. Unless special test conditions prevail, parachutes tested should be a minimum of 1.5 to 2 feet in diameter to obtain meaningful results.&lt;br /&gt;
&lt;br /&gt;
                                                                    &lt;br /&gt;
&lt;br /&gt;
 FIGURE 4-14. Typical Air Blower.&lt;br /&gt;
&lt;br /&gt;
An air blower is a preliminary test too! because it permits quick parachute• configuration changes and excellent visual observation.&lt;br /&gt;
&lt;br /&gt;
4.6.2 Open-Throat, No-Return Wind Tunnels&lt;br /&gt;
&lt;br /&gt;
The open-throat, no-return wind tunnel shown in Figure 4-15 permits exact measurements if parachutes of sufficient size are used. Parachutes 3 feet or more in diameter are well suited for obtaining good, quantitative test results.&lt;br /&gt;
&lt;br /&gt;
              FIGURE 4-15. Open-Throat, No-Return Wind Tunnel&lt;br /&gt;
&lt;br /&gt;
In air blowers and open-throat wind tunnels, the velocity at the skirt of the parachute (Section a-a of Figures 4-14 and 4-15) is lower than the velocity at the nozzle exit of the wind tunnel (Section b&amp;lt;sup&amp;gt;-&amp;lt;/sup&amp;gt;b of Figures 4-14 and 4-15), Care must be taken to measure the parachute test&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
velocity at Section a-a and not at Section b-b, the customary attachment point for airfoils and models.&lt;br /&gt;
&lt;br /&gt;
Wind tunnels frequently cannot test at the descent velocity of most main parachutes of 20 to 30 feet per second. Obtaining proper test results at this low is hampered by a poor velocity distribution in the wind-tunnel-test section, and by the weight of the test parachute. The latter has a tendency to pull the parachute downward, thereby providing a negative angle of attack, lusting unstable parachutes at higher presents the problem that the drag coefficient C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, of unstable parachutes is sensitive. The drag coefficient of unstable parachutes is described in section 5.2.&lt;br /&gt;
&lt;br /&gt;
An open-throat wind tunnel permits quick changes in parachute configuration, such as changing the suspension and reefing line lengths. Large open-throat wind tunnels that are not sealed against outside elements suffer atmospheric problems such as fog formation in the test section.&lt;br /&gt;
&lt;br /&gt;
4.6.3 Closed-Throat, Full-Return Wind Tunnel&lt;br /&gt;
&lt;br /&gt;
Figure 4-16 is a drawing of a full-return, closed-throat wind tunnel. fic full-return, closed-throat wind tunnel is generally considered best suited for obtaining good. qualitative, aerodynamic data, since it has a uniform distribution in the test section. A disadvantage is the difficulty in gaining access to the test section for changing the parachute configuration.&lt;br /&gt;
&lt;br /&gt;
FIGURE 4-16. Closed-Throat, Full-Reuurn Wind Tunnel.&lt;br /&gt;
&lt;br /&gt;
4.6.4 General Comments for Wind-Tunnel Testing of Parachutes&lt;br /&gt;
&lt;br /&gt;
1. Parachute models for wind-tunnel testing should be as large and as similar as possible in geometry and flexibility to full-scale parachutes. Parachutes of less than 1.5 feet in diameter usually lack geometric similarity and material flexibility, which results in inflation characteristics and dissimilar inflated shapes.&lt;br /&gt;
&lt;br /&gt;
2.  The finished dimensions of model parachutes must be measured as accurately as possible to determine the nominal diameter, Do, and the surface area, So. Model parachutes will shrink from 5 to 10% during manufacture because of sewing take-up, which results in a notable difference in the dimensions between the drawing and the completed parachute.&lt;br /&gt;
&lt;br /&gt;
3.  Wind&amp;lt;sup&amp;gt;-&amp;lt;/sup&amp;gt;tunnel tests of parachutes are excellent for comparing different models and modifications: also, they are the most effective means for measuring coefficients of lift, drag. and normal and tangential forces, as well as for determining the load coefficient, for infinite load.&lt;br /&gt;
&lt;br /&gt;
4.  In wind-tunnel tests, velocity decay does not occur during parachute inflation and operation; this is defined as testing under &amp;quot;infinite mass condition. &amp;quot; First-stage drogue chutes and parachutes with a canopy loading, W/C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;S. in excess of 100 lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; approach this condition. Low-canopy-loading main parachutes with rates of descent of 20 to 30 ft/s have a large velocity decay during opening, which requires careful interpretation of the opening-force data obtained in wind-tunnel tests.&lt;br /&gt;
&lt;br /&gt;
5.  In the past, to avoid wind-tunnel blockage and questionable test data. the diameter of a test parachute could not exceed about 5 to 6% of the wind-tunnel test section area. Recent Sandia investigations of single and clustered ribbon parachutes with wind-tunnel blockage ratios of up to 30% have resulted in correction methods that make it possible to test much larger parachutes (Reference 4.2).&lt;br /&gt;
&lt;br /&gt;
= 4.7 REFERENCE MATERIAL =&lt;br /&gt;
4.1 H. H. Hurt. Aerodynamics for Naval Aviators Navy Manual NAVWEPS 00 80T 80. Chief of Naval Operations, Aviation Training Division.&lt;br /&gt;
&lt;br /&gt;
4.2 J, M. Macha and R J. Buffington. &amp;quot;Wall-Interference Corrections for Parachutes in a Closed Wind Tunnel.&amp;quot; AIM Paper, April 1989. (AIM 89-0900-cp.)&lt;br /&gt;
&lt;br /&gt;
For readers interested in a more detailed study of aerodynamics, the following books are recommended.&lt;br /&gt;
&lt;br /&gt;
4.3 J, H, Dwinnel, Principle of Aerodynamics. McGraw-Hill     	Co., New York, 1949.&lt;br /&gt;
&lt;br /&gt;
4.4 J. Morane. Introduction to Theoretical and Computational Aerodynamics. John Wiley &amp;amp; Sons.&lt;br /&gt;
&lt;br /&gt;
4.5 R.S. Shevell. Fundamentals of Flight. Prentice-Hall. 1983.&lt;br /&gt;
&lt;br /&gt;
4.6 J. D. Anderson, Jr. Introduction to Flights, ILS Engineering and History. McGraw-Hill Book co., New York 1978.&lt;br /&gt;
&lt;br /&gt;
4.7 D. J. Cockrell. The Aerodynamics of Parachutes.&amp;quot; AGARDograph No. 6295, available from NASA Langley Research Center, M/S 1M), Hampton, Va., 236.&lt;/div&gt;</summary>
		<author><name>TuanHTruong</name></author>
	</entry>
	<entry>
		<id>https://mediawiki.aerodecelerator.org/index.php?title=Parachute_Aerodynamics&amp;diff=27</id>
		<title>Parachute Aerodynamics</title>
		<link rel="alternate" type="text/html" href="https://mediawiki.aerodecelerator.org/index.php?title=Parachute_Aerodynamics&amp;diff=27"/>
		<updated>2024-05-03T21:08:16Z</updated>

		<summary type="html">&lt;p&gt;TuanHTruong: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&lt;br /&gt;
= CHAPTER 4: AERODYNAMICS AS RELATED TO PARACHUTES =&lt;br /&gt;
== 4.1 PROPERTIES OF THE ATMOSPHERE ==&lt;br /&gt;
All forces acting on parachutes and all movements of parachutes are affected by the atmosphere, or air, surrounding the Earth. The air at the Earth's surface is approximately 78% nitrogen; 21% oxygen; and 1% a mixture of gases such as argon, neon, helium, water vapor, and carbon dioxide. This chemical composition remains relatively constant to an altitude of about 160,000 feet (50 kilometers). The following air qualities are of major significance in the dynamics of bodies moving in the atmosphere:&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
!Air quality&lt;br /&gt;
!Symbol&lt;br /&gt;
!Dimension&lt;br /&gt;
|-&lt;br /&gt;
|Specific weight of air&lt;br /&gt;
|w&lt;br /&gt;
|lb/ft&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;, kg/m&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;&lt;br /&gt;
|-&lt;br /&gt;
|Static pressure&lt;br /&gt;
|p&lt;br /&gt;
|atm, lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;, Pa, bar, torr&lt;br /&gt;
|-&lt;br /&gt;
|Temperature&lt;br /&gt;
|T&lt;br /&gt;
|&amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F, &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;C&lt;br /&gt;
|-&lt;br /&gt;
|Mass density&lt;br /&gt;
|&amp;lt;math&amp;gt;\rho&amp;lt;/math&amp;gt;&lt;br /&gt;
|slugs/ft3, kg s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;/m&amp;lt;sup&amp;gt;4&amp;lt;/sup&amp;gt;&lt;br /&gt;
|-&lt;br /&gt;
|Gravity&lt;br /&gt;
|''g''&lt;br /&gt;
|ft/s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;, m/s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
|-&lt;br /&gt;
|Speed of sound&lt;br /&gt;
|C&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt;&lt;br /&gt;
|ft/s, m/s&lt;br /&gt;
|}&lt;br /&gt;
All of these qualities are altitude-dependent and may vary slightly on the Earth's surface with geographic latitude because of variations of the Earth's radius caused by the centrifugal forces of the rotation of the Earth. All standard data used herein refer to a latitude of 45 degrees. Sea level is defined as mean sea level (MSL). To compare performance data on an equal basis, the United States Bureau of Standards has defined standard day conditions as follows:&lt;br /&gt;
&lt;br /&gt;
Temperature = 15 degrees Celsius (&amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;C) or 59 degrees Fahrenheit (&amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F)&lt;br /&gt;
&lt;br /&gt;
Pressure = 760 millimeters (mm) of mercury (Hg) or 29.9213 inches (in.) Hg&lt;br /&gt;
&lt;br /&gt;
=== 4.1.1 Specific Weight of Air ===&lt;br /&gt;
For standard day conditions of 59 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F temperature and a pressure of 29.9213 in. Hg, the specific weight of air, w, is 0.07648 lb/ft&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt; or 1.2250 kg/m&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;. The specific weight of air changes with pressure, temperature, and humidity. Further data can be found in References 3.4 and 4.1, and in technical handbooks.&lt;br /&gt;
&lt;br /&gt;
=== 4.1.2 Static Pressure ===&lt;br /&gt;
Static pressure depends on geographic latitude, weather conditions, and altitude. The static pressure at any altitude results from the weight of the air above that altitude. For MSL and standard day conditions, the pressure, p&amp;lt;sub&amp;gt;o&amp;lt;/sub&amp;gt;, is 29.9213 in. Hg = 760 mm Hg = 1.0 atmosphere (atm). For conversion to Pascal, torr, or bar, see the conversion tables in section 3.2.&lt;br /&gt;
&lt;br /&gt;
=== 4.1.3 Temperature ===&lt;br /&gt;
Temperatures are defined in the English and metric systems in the so-called absolute and engineering scales. The absolute temperature minimum at 0 degrees, pressure is 0 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;K = -273.16 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;C, and 0 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;R = -459.69 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F. This is also written&lt;br /&gt;
&lt;br /&gt;
Degrees Kelvin = degrees Celsius + 273.16&lt;br /&gt;
&lt;br /&gt;
Degrees Rankine = degrees Fahrenheit + 459.69&lt;br /&gt;
&lt;br /&gt;
The freezing point of water is 32 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F or 0 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;C. The boiling point of water is 212 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F or 100 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;C.&lt;br /&gt;
&lt;br /&gt;
=== 4.1.4 Mass Density of Air ===&lt;br /&gt;
Mass density defines the amount of mass contained in a unit volume of air. The mass density, p, of air is of special importance in aerodynamic calculations.&lt;br /&gt;
&lt;br /&gt;
specific weight of air, w lb/ft3 kg s2&lt;br /&gt;
&lt;br /&gt;
acceleration of gravity, g ft/s2 g 4&lt;br /&gt;
&lt;br /&gt;
slug = weight lb&lt;br /&gt;
&lt;br /&gt;
acceleration of gravity - ft/s 2&lt;br /&gt;
&lt;br /&gt;
Frequently the density ratio, a, is used&lt;br /&gt;
&lt;br /&gt;
ambient air density, p&lt;br /&gt;
&lt;br /&gt;
standard sea-level density, P4,&lt;br /&gt;
&lt;br /&gt;
The factor 1//p/lp determines the increase in parachute rate of descent with altitude. The density at 40,000 feet is ¼ of the MSL density, and the density at 100,000 feet is 1/75 of the MSL density. Therefore, the parachute rate of descent is about twice as high at 40,000 feet and about nine times as high at 100,000 feet. MSL density is 0.00237689 slugs/ft3, or 0.1249 kg s2/m4.&lt;br /&gt;
&lt;br /&gt;
4.1.5 Gravity&lt;br /&gt;
&lt;br /&gt;
Any mass attracts another mass with a force called gravity. If the Earth were surrounded by a vacuum, a body suspended above the Earth and released would fall toward the center of the Earth with increasing velocity caused by the acceleration of gravity, g. In reality, the falling body is decelerated by its air drag until the air drag, D, equals the weight of the body, W, and an equilibrium velocity is reached; for parachutes, this is called the steady-state rate of descent.&lt;br /&gt;
&lt;br /&gt;
The acceleration of gravity, g, at sea lavel is&lt;br /&gt;
&lt;br /&gt;
g = 32.174 ft/s2 or 9.80665 m/s2.&lt;br /&gt;
&lt;br /&gt;
The value g = 9.08665 m/s is standardized internationally but is accurate only for a&lt;br /&gt;
&lt;br /&gt;
latitude of 45 degrees.&lt;br /&gt;
&lt;br /&gt;
With increasing altitude above the Earth's surface, the acceleration of gravity decreases&lt;br /&gt;
&lt;br /&gt;
in accordance with the equation&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
g = acceleration of gravity at any altitude, ft/s 2&lt;br /&gt;
&lt;br /&gt;
-go acceleration of gravity at sea level, ft/s 2&lt;br /&gt;
&lt;br /&gt;
r = average Earth radius = 2.08556 x 107 ft&lt;br /&gt;
&lt;br /&gt;
h = altitude above sea level, ft&lt;br /&gt;
&lt;br /&gt;
For other planets and heavenly bodies, the acceleration of gravity varies with the mass of the body. For example, the acceleration of gravity on Mars is about 1/3 of the acceleration of gravity on Earth. For more details on planets and heavenly bodies, see page XII of Reference 2.1.&lt;br /&gt;
&lt;br /&gt;
4.1.6 Kinematic Viscosity&lt;br /&gt;
&lt;br /&gt;
The coefficient of viscosity, la, defines the shecring stresses in a gas or liquid and is sometimes called the resistance to continuous deformation. In aerodynamics, the coefficient of viscosity is combined with the mass density to form the kinematic viscosity, v, where&lt;br /&gt;
&lt;br /&gt;
coefficient of viscosity, g' 0.0001576 ft2/s at sea level&lt;br /&gt;
&lt;br /&gt;
mass density, P&lt;br /&gt;
&lt;br /&gt;
The kinematic viscosity, v, is altitude dependent and is used to calculate the Reynolds number, Re.&lt;br /&gt;
&lt;br /&gt;
4.1.7 Reynolds Number&lt;br /&gt;
&lt;br /&gt;
The Reynolds number, Re, defines the relationship of mass forces to viscous friction forces in liquids and gases. It is calculated as&lt;br /&gt;
&lt;br /&gt;
Re = v I velocity (ft/s) characteristic length (ft)&lt;br /&gt;
&lt;br /&gt;
V kinematic viscosity (ft2/s)&lt;br /&gt;
&lt;br /&gt;
Reynolds number is an important criterion in subsonic, noncompressible flow, and allows comparison of model tests with full-scale flight tests. A Reynolds number effect on parachutes working in separated, turbulent flow has not yet been established, as shown in section 5.2. The following chart shows the Reynolds numbers for various air vehicles.&lt;br /&gt;
&lt;br /&gt;
Drogue Main WIT&lt;br /&gt;
&lt;br /&gt;
Sbe Ihns=ec t Glider D -4 2 par ute model&lt;br /&gt;
&lt;br /&gt;
Re 6-103 2.5-106 24.106 100&amp;quot;106 50&amp;quot;106 20&amp;quot;106 2.106&lt;br /&gt;
&lt;br /&gt;
4.1.8 Mach Number&lt;br /&gt;
&lt;br /&gt;
Mach number is an important parameter of supersonic flight; it states how much faster than the speed of sound the air vehicle travels.&lt;br /&gt;
&lt;br /&gt;
Mach Number, M= &lt;br /&gt;
&lt;br /&gt;
The speed of sound is the velocity at which a pressure disturbance, such as the sound of the human voice, travels in any medium. The speed of sound varies considerably in different gases, liquids, and metals.&lt;br /&gt;
&lt;br /&gt;
The speed of sound depends on temperature and the chemical composition of the medium, A widely used equation for speed of sound in air is&lt;br /&gt;
&lt;br /&gt;
The speed of sound changes with altitude, as temperature (see Figure 3-1). The drag of streamlined bodies such as missiles, airfoils, and airplanes increases considerably as their velocities approach Mach 1. Depending on the configuration of the body, supersonic compressibility effects may in the 0.75• to 0.85•Mach range, causing local supersonic flow, shock waves, flow separation, and concomitant increases in drag and changes in stability.&lt;br /&gt;
&lt;br /&gt;
Parachutes that operate in separated flow over the entire velocity range do not show the typical drag increase when operating close to or beyond Mach 1. Supersonic parachute behavior is discussed in detail in section 5.8.&lt;br /&gt;
&lt;br /&gt;
== '''4.2 CONTINUITY LAW AND BERNOULLI EQUATION''' ==&lt;br /&gt;
4.2.1 Continuity L.aw&lt;br /&gt;
&lt;br /&gt;
Air is thought to flow in layers called streamlines. Figure 4-1 shows streamlines as layers of air without air transfer between individual layers. ne air is shown as being incompressible, a valid assumption for subsonic flow.&lt;br /&gt;
&lt;br /&gt;
  	&lt;br /&gt;
&lt;br /&gt;
If exchange of air does not occur across the streamline boundaries, the amount of air entering the streamline at point 1 must also exit at point 2. as shown in Figure 4*1. Because the cross section at point 2 is smaller than the cross section at point 1, the air must exit at a higher velocity. The following equation defines this condition:&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
this equation which governs the now in and around a body in gases and liquids, is important in aerodynamics and is called the continuity law. For imcompressilble subsonic now, it can be simplified to &lt;br /&gt;
&lt;br /&gt;
Whenever the cross section narrows. the velocity increases; when the cross section widens, the velocity decreases.&lt;br /&gt;
&lt;br /&gt;
4.2.2 Bernoulli Equation&lt;br /&gt;
&lt;br /&gt;
Figure 4-2 illustrates a streamline with the cross section, S, the velocity, v, and the pressure, p. If the air is incompressible, the downstream is v + Av. and the pressure is p + AP. If the air is inviscid, the inertia forces caused by the acceleration of air from v to v + Av must be balanced by differential pressure forces.&lt;br /&gt;
&lt;br /&gt;
    	                                       	&lt;br /&gt;
&lt;br /&gt;
FIGURE 4-2 Pressure and Velocity Distribution in a Streamline Element.&lt;br /&gt;
&lt;br /&gt;
The following equation can be written&lt;br /&gt;
&lt;br /&gt;
Simplified, the above equation yields&lt;br /&gt;
&lt;br /&gt;
'''dp = -pvdv'''&lt;br /&gt;
&lt;br /&gt;
the above equation allows the following consideration: If p is pressure, then 1/2 pv&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; and C must also be pressure. The equation 1/2 pv&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; includes a and is referred to as the dynamic pressure. or sometimes velocity as or impact pressure.&lt;br /&gt;
&lt;br /&gt;
Pressure, p, is defined as static pressure; 1/2 pv&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; as dynamic pressure; and the sum of both, C, as the total pressure or&lt;br /&gt;
&lt;br /&gt;
p + 1/2pv&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; = H&lt;br /&gt;
&lt;br /&gt;
and&lt;br /&gt;
&lt;br /&gt;
where H is the total pressure of the system, lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Dynamic pressure, q, is a frequently used quantity in aerodynamics:&lt;br /&gt;
&lt;br /&gt;
q = 1/2 pv&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
q = dynamic pressure, lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
p =  air density, slugs/ft&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
v =  velocity at a point of undisturbed flow, ft/s&lt;br /&gt;
&lt;br /&gt;
The following formulas are used for calculating the sea-level dynamic pressure if the velocity is given in ft/s, knots, mph, or km/h, respectively:&lt;br /&gt;
&lt;br /&gt;
                                              &lt;br /&gt;
&lt;br /&gt;
'''4.3 NEWTON'S THREE OF MOTION'''&lt;br /&gt;
&lt;br /&gt;
Engineering mechanics are governed by the following three laws of Isaac Newton:&lt;br /&gt;
&lt;br /&gt;
1.  A body remains at rest or in an unaccelerated state of motion unless acted upon.&lt;br /&gt;
&lt;br /&gt;
2.  A force acting upon a body will produce an acceleration in the direction of the force.&lt;br /&gt;
&lt;br /&gt;
3.  An action in one direction will produce an equal reaction in the opposite direction.&lt;br /&gt;
&lt;br /&gt;
The first law is self-explanatory. The second law may be expressed by the equation&lt;br /&gt;
&lt;br /&gt;
F = m * a&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
F = force in pounds acting on the mass, 1b&lt;br /&gt;
&lt;br /&gt;
m = mass of body that the force is acting upon, slugs&lt;br /&gt;
&lt;br /&gt;
a = acceleration in ft/s2 resulting from the force, F&lt;br /&gt;
&lt;br /&gt;
The mass, m, of a body is obtained by&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
W = weight of the body, lb&lt;br /&gt;
&lt;br /&gt;
g = acceleration of gravity, ft/s2&lt;br /&gt;
&lt;br /&gt;
The mass, therefore, has the dimension of&lt;br /&gt;
&lt;br /&gt;
This unit of mass is the slug.&lt;br /&gt;
&lt;br /&gt;
the equation of Newton's second law can now be written&lt;br /&gt;
&lt;br /&gt;
                                        	&lt;br /&gt;
&lt;br /&gt;
The factor a/g is frequently called the load factor, G, and tells how much larger a force is than a force equivalent to the weight of the body. It is customary in parachute work to state that the maximum parachute force allowed is G • W or (a]g) • W. It is appropriate to write&lt;br /&gt;
&lt;br /&gt;
Maximum allowable parachute force,&lt;br /&gt;
&lt;br /&gt;
Figure 4-3 illustrates Newton's third law, explaining the principle of the rocket that can produce thrust in a perfect vacuum.&lt;br /&gt;
&lt;br /&gt;
A mass, m. ejected from a rocket at the velocity, v, per unit time, t, will produce a force, F, which in turn will create a reaction force, R. of equal magnitude but acting in the opposite direction.&lt;br /&gt;
&lt;br /&gt;
=== 4.4 FORCES ACTING ON A BODY MOVING THROUGH AIR ===&lt;br /&gt;
4.4.1 Symmetrical Body&lt;br /&gt;
&lt;br /&gt;
A body moving through air experiences forces caused by air pressure acting on the body. fie same forces if the body moves through air, such as a descending parachute, or if the body is fixed and the air moves against the body, such as a parachute or an airfoil in a wind tunnel (Figure 44).&lt;br /&gt;
&lt;br /&gt;
         	 &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
A stable parachute in a wind tunnel experiences only the force called &amp;quot;drag&amp;quot; in the direction of the airflow. drag force, D, is calculated to&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
D = drag, 1b&lt;br /&gt;
&lt;br /&gt;
Q = dynamic pressure, lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
S = total surface area of the parachute canopy, ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt; = coefficient of drag.  dimensionless&lt;br /&gt;
&lt;br /&gt;
the dynamic pressure, q, can be calculated from section 4.2.2. The surface area of the canopy, S, is selected as a reference area. The drag coefficient  C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, is a form factor that indicates the drag characteristic of a specific shape. Most aerodynamic bodies are designed for low drag or a low drag coefficient. Parachutes, generally, are designed for high drag; therefore, a high drag coefficient is desirable. this difference in drag is demonstrated by the two bodies shown in Figure 4-5.&lt;br /&gt;
&lt;br /&gt;
            	&lt;br /&gt;
&lt;br /&gt;
Both bodies have the same cross section perpendicular to the airflow. The cylindrical. streamlined body has a smooth airflow over its total body length, resulting in a drag coefficient. C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, of 0.05 to 0.1, depending on slenderness ratio, surface roughness, and shape. The drag coefficient of all streamlined bodies is much affected by Reynolds number and Mach number. fie open hemisphere, which is similar to a parachute canopy, has a drag coefficient, C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, of 1.3 to 1.4 for the same body cross section. The difference in drag is explained by the smooth airflow around the streamlined body and a separated. turbulent flow around the open hemisphere. The drag of bodies with separated flow, like parachute canopies, is little affected by Reynolds number.&lt;br /&gt;
&lt;br /&gt;
4.4.2 Airflow Around an Asymmetrical Body (Airfoil)&lt;br /&gt;
&lt;br /&gt;
Figure 4-6 shows an airfoil fixed at an angle of attack, a. against the airflow in a wind tunnel. This airfoil creates a drag force, D, in the direction of the flow; a lift force L perpendicular to the direction of the flow; and a moment, M. around the attachment point of the airfoil. fie sign convention of moments and forces shown are positive. Lift and drag can be combined for the resultant force, R.&lt;br /&gt;
&lt;br /&gt;
FIGURE. 44, Wind-Tunnel Forces Acting on an Airfoil.&lt;br /&gt;
&lt;br /&gt;
The lift, L is calculated&lt;br /&gt;
&lt;br /&gt;
L = q * S * C&amp;lt;sub&amp;gt;L&amp;lt;/sub&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
L = measured lift, 1b&lt;br /&gt;
&lt;br /&gt;
q = dynamic pressure, lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
s = reference area, ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
CL = lift coefficient, dimensionless&lt;br /&gt;
&lt;br /&gt;
The moment is&lt;br /&gt;
&lt;br /&gt;
       M = q * S * c&amp;lt;sub&amp;gt;m&amp;lt;/sub&amp;gt; * c&lt;br /&gt;
&lt;br /&gt;
Where&lt;br /&gt;
&lt;br /&gt;
The reference area, S is defined by agreement, For streamlined bodies, the maximum body cross section is used. Airfoils use the planform of the wing, and parachutes use the canopy surface area. The selection of the wing planform and the parachute surface area as references was made for practical reasons. &amp;lt;sup&amp;gt;e&amp;lt;/sup&amp;gt;me wing planform for a specific wing is fixedt whereas the cross section of the wing in the direction of the flow changes with the angle of attack. Similarly, the surface area of the parachute canopy is fixed; however, the frontal projected area of the inflated parachute canopy changes with airspeed, porosity, line length, and tm of parachute.&lt;br /&gt;
&lt;br /&gt;
Forces and moments acting on an airfoil or a parachute canopy may be presented in several ways. The two most frequently used methods, as shown in Figure 4-7, are with forces oriented to the of flight and with forces oriented to the axis of the airfoil.&lt;br /&gt;
&lt;br /&gt;
me tangential force, and the normal force, N, are calculated&lt;br /&gt;
&lt;br /&gt;
T = C&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; * S * q&lt;br /&gt;
&lt;br /&gt;
        	&lt;br /&gt;
&lt;br /&gt;
and&lt;br /&gt;
&lt;br /&gt;
      	N = C&amp;lt;sub&amp;gt;N&amp;lt;/sub&amp;gt; * S * q&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
C&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; = tangential force coefficient, dimensionless&lt;br /&gt;
&lt;br /&gt;
C&amp;lt;sub&amp;gt;N&amp;lt;/sub&amp;gt; = normal force coefficient, dimensionless&lt;br /&gt;
&lt;br /&gt;
The resultant force, R, and the moment, M, in both presentations have the same direction and the same magnitude. The airflow fixed system is preferred for aerodynamic performance calculations, and the airfoil fixed system for wing stress calculations. me aerodynamic coefficients C&amp;lt;sub&amp;gt;L&amp;lt;/sub&amp;gt;, C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, C&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, C&amp;lt;sub&amp;gt;N&amp;lt;/sub&amp;gt;, and C&amp;lt;sub&amp;gt;m&amp;lt;/sub&amp;gt; can easily be determined in wind•tunnel measurements.&lt;br /&gt;
&lt;br /&gt;
Figure 4-8 shows the relationship of both force systems on a parachute. By definition, a negative moment is stabilizing, as illustrated in Figure 4-8. It is interesting to note that in Europe the stabilizing moment is defined as positive. Wind-tunnel installations frequently measure normal and tangential force instead of lift and drag. If α, T, and N are known, the drag D, can be calculated&lt;br /&gt;
&lt;br /&gt;
D = T*cosα + N * sinα&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
For a parachute with an angle of attack, a, equal to zero, the drag force and the tangential force are synonymous.&lt;br /&gt;
&lt;br /&gt;
Figure 4-9 shows the coefficients C&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, and C&amp;lt;sub&amp;gt;m&amp;lt;/sub&amp;gt; versus angle of attack for stable and unstable parachutes.&lt;br /&gt;
&lt;br /&gt;
The coefficient presentation shows two interesting facts. ne slope of the moment coefficient curve, dC&amp;lt;sub&amp;gt;m&amp;lt;/sub&amp;gt;/dα, for the unstable parachute is positive between -25 degrees and + 25 degrees; this is, by definition, destabilizing. This parachute will oscillate approximately ± 25&lt;br /&gt;
&lt;br /&gt;
FIGURE 4-9. Coefficients C&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, and C&amp;lt;sub&amp;gt;M&amp;lt;/sub&amp;gt; Versus Angle of Attack, α, for a Stable and Unstable Parachute.&lt;br /&gt;
&lt;br /&gt;
degrees. The slope of the moment, dC&amp;lt;sub&amp;gt;m&amp;lt;/sub&amp;gt;/dα, for the stable parachute is negative over the total angle of attack; this is, by definition, stabilizing. The steeper the negative dC&amp;lt;sub&amp;gt;m&amp;lt;/sub&amp;gt;/dα slope, the greater is the stabilizing tendency of the parachute, and the better is its damping capability against unstabilizing forces such as sudden gusts of wind.&lt;br /&gt;
&lt;br /&gt;
Figure 4-10, from Reference 4.1, demonstrates the effect of airflow around a cylinder and an airfoil. The circulation around a rotating cylinder creates lift caused by the increase in velocity on one side of the cylinder and a decrease on the opposite side. This is called the Magnus effect.&lt;br /&gt;
&lt;br /&gt;
= 4.5 EQUILIBRIUM OF FORCES IN STUDY DESCENT OR FLIGHT =&lt;br /&gt;
4.5.1 Parachute in Steady Descent&lt;br /&gt;
&lt;br /&gt;
A stable parachute in unaccelerated descent has an equilibrium between the total drag of the parachute and the load, Dr, and the weight of the load and the parachute assembly, WT (Figure 4-11). For steady descent&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
D&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; = total drag, 1b&lt;br /&gt;
&lt;br /&gt;
D&amp;lt;sub&amp;gt;P&amp;lt;/sub&amp;gt; = drag of parachute, 1b&lt;br /&gt;
&lt;br /&gt;
W&amp;lt;sub&amp;gt;C&amp;lt;/sub&amp;gt; = weight of load. 1b&lt;br /&gt;
&lt;br /&gt;
In most cases, the drag of the load can be neglected in relation to the large drag of the parachute, With drag, D — (C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;S)&amp;lt;sub&amp;gt;p&amp;lt;/sub&amp;gt; • p/2• v&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; and D&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; = W&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;. and solving for v, the important equation for rate of descent, v&amp;lt;sub&amp;gt;e&amp;lt;/sub&amp;gt;, is obtained,&lt;br /&gt;
&lt;br /&gt;
Rate of descent,&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
FIGURE 4-11. Forces Acting on a Parachute in Steady Descent.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
or in parachute terminology for rate of descent at sea level&lt;br /&gt;
&lt;br /&gt;
and rate of descent at any altitude&lt;br /&gt;
&lt;br /&gt;
== For 1/, see column 4 in Table 3-3, ==&lt;br /&gt;
In the equation for rate of descent. V&amp;lt;sub&amp;gt;e&amp;lt;/sub&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
W&amp;lt;sub&amp;gt;T =&amp;lt;/sub&amp;gt; weight of load and parachute assembly, 1b&lt;br /&gt;
&lt;br /&gt;
S&amp;lt;sub&amp;gt;o&amp;lt;/sub&amp;gt; = canopy surface area, ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
C&amp;lt;sub&amp;gt;Do&amp;lt;/sub&amp;gt; = parachute drag coefficient related to S&amp;lt;sub&amp;gt;o&amp;lt;/sub&amp;gt;&lt;br /&gt;
&lt;br /&gt;
p = air density at a specific altitude in slugs/ft&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;, as shown in Table 3-3&lt;br /&gt;
&lt;br /&gt;
During descent from altitude, the parachute system is constantly decelerated because of the increasing air density. This can be ignored for slowly descending main parachutes. However, for drogue chute systems that descend at 200 ft/s or faster, the constant deceleration may result in velocities 3 to 5% higher than the steady rate of descent.&lt;br /&gt;
&lt;br /&gt;
4.5.2 Gliding Parachutes&lt;br /&gt;
&lt;br /&gt;
Figure 4-12 shows the balance of forces on a gliding parachute. The total weight of the system, W&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; . must be balanced by the resultant force. R. However, a lifting force is required for glide. To satisfy the force balance&lt;br /&gt;
&lt;br /&gt;
R = C&amp;lt;sub&amp;gt;R&amp;lt;/sub&amp;gt; * S * p/2 * v&lt;br /&gt;
&lt;br /&gt;
Trajectory velocity, V&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, is calculated&lt;br /&gt;
&lt;br /&gt;
Horizontal velocity is calculated&lt;br /&gt;
&lt;br /&gt;
V&amp;lt;sub&amp;gt;H&amp;lt;/sub&amp;gt; = V&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; • cosø, and vertical velocity, v&amp;lt;sub&amp;gt;v&amp;lt;/sub&amp;gt; = V&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; • sinø&lt;br /&gt;
&lt;br /&gt;
The glide ratio is obtained from&lt;br /&gt;
&lt;br /&gt;
Analysis of Figure 4-12 indicates that the larger the ratio of lift to drag, the better the glide ratio, I./D A high resultant coefficient, C&amp;lt;sub&amp;gt;R&amp;lt;/sub&amp;gt;, results in a low glide or trajectory V&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, desirable for landing. A small C&amp;lt;sub&amp;gt;R&amp;lt;/sub&amp;gt; results in a high glide velocity, V&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, which is desirable for flying toward a target, compensating for head winds, or covering a distance quickly. Generally, gliding parachutes follow the same aerodynamic rules as low-aspect-ratio wings.&lt;br /&gt;
&lt;br /&gt;
           	   	&lt;br /&gt;
&lt;br /&gt;
FIGUR E 4-12, Forces Acting on a Gliding Parachute&lt;br /&gt;
&lt;br /&gt;
4.5-3 Parasite Drag and Induced Drag&lt;br /&gt;
&lt;br /&gt;
The drag acting on a lift-producing air vehicle, such as a gliding parachute or an aircraft, has two primary components: the parasite drag, D&amp;lt;sub&amp;gt;P&amp;lt;/sub&amp;gt; , and the induced drag. D&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Parasite drag is produced by the form drag from individual components such as the suspension lines, canopy, and the jumper of a gliding parachute, and the fuselage, tail sectiora, and control surfaces of an airplane. Large surfaces produce surface friction drag as part of the parasite drag.&lt;br /&gt;
&lt;br /&gt;
Induced drag is caused by the lifting action of the parachute canopy or the aircraft wing. Section 4.7 includes books with detailed discussions of induced drag.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Total drag, D&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, can be defined as&lt;br /&gt;
&lt;br /&gt;
or, in the coefficient form&lt;br /&gt;
&lt;br /&gt;
The parasite drag, D&amp;lt;sub&amp;gt;p&amp;lt;/sub&amp;gt;, and the coefficient, C&amp;lt;sub&amp;gt;DP&amp;lt;/sub&amp;gt;, can be determined in wind-tunnel tests or calculated as the sum of the individual component drags.&lt;br /&gt;
&lt;br /&gt;
The induced drag coefficient, C&amp;lt;sub&amp;gt;Di&amp;lt;/sub&amp;gt; , of a gliding parachute canopy or a wing profile can be calculated&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
C = coefficient of induced drag, dimensionless&lt;br /&gt;
&lt;br /&gt;
The expression b&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;/S is defined as the aspect ratio of a wing or parachute with the notation AR b&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;/S. Therefore&lt;br /&gt;
&lt;br /&gt;
== '''                       ''' 	 ==&lt;br /&gt;
The equation for induced drag indicates that increasing the aspect ratio, AR, reduces the induced drag coefficient,  , and therefore reduces the drag, D. ms, in turn, increases the glide ratio, L/D. Increasing the glide ratio by increasing the aspect ratio is optimized on high-performance sailplanes with aspect ratios higher than 20. Increasing the glide ratio of gliding parachutes by increasing the aspect ratio has limitations, which are discussed in section 5.9.&lt;br /&gt;
&lt;br /&gt;
4.5.4 Aircraft in Horizontal Flight&lt;br /&gt;
&lt;br /&gt;
Figure 4-13 shows forces and moments on an aircraft in steady, horizontal flight. In steady, horizontal flight, an equilibrium exists between all forces and moments acting on the aircraft. Lift on the wing and tail, L&amp;lt;sub&amp;gt;W&amp;lt;/sub&amp;gt; and L&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;. and the weight of the aircraft, W&amp;lt;sub&amp;gt;A&amp;lt;/sub&amp;gt;, balance in the vertical plane. Thrust, T and drag. D, balance each other in the horizontal plane, and the positive or negative moment, M, is balanced by the positive or negative lift of the tail multiplied by the moment arm, L&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
FIGURE 4-13. Forces and Moments Acting on an Aircraft in Steady night,&lt;br /&gt;
&lt;br /&gt;
Any imbalance in these forces results in descent or climb in the vertical plane or faster or slower speed in the horizontal plane. A change in the lift of the elevator initiates climb or descent. Thrust, T, is the prime contributor for climb or descent and faster or slower speed, However, a balance of forces must always be maintained for horizontal flight or steady rate oi climb or descent.&lt;br /&gt;
&lt;br /&gt;
== 4.6 WIND-TUNNEL TESTING OF PARACHUTES ==&lt;br /&gt;
Wind tunnels are an effective tool for testing air vehicles and air-vehicle components and have been used successfully for testing parachutes and parachute systems. Experience has shown that certain rules apply for the wind-tunnel testing of parachutes. Small parachutes manufactured from textiles cannot be made sufficiently similar to large parachutes in geometric design and flexibility, Lightweight material. required to obtain design similarity, is difficult to manufacture or is unobtainable.&lt;br /&gt;
&lt;br /&gt;
One cardinal rule has been established through many years of parachute wind-tunnel testing: A modification that changes the performance of a model parachute in wind-tunnel testing produces the same type and percentage of performance change in a large parachute. This rule is true for drag. stability, and opening-force characteristics.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
4.6.1 Blowers&lt;br /&gt;
&lt;br /&gt;
The simple air blower (Figure 4-14) is a proven tool for preliminary parachute testing of a chiefly qualitative nature. Unless special test conditions prevail, parachutes tested should be a minimum of 1.5 to 2 feet in diameter to obtain meaningful results.&lt;br /&gt;
&lt;br /&gt;
                                                                    &lt;br /&gt;
&lt;br /&gt;
 FIGURE 4-14. Typical Air Blower.&lt;br /&gt;
&lt;br /&gt;
An air blower is a preliminary test too! because it permits quick parachute• configuration changes and excellent visual observation.&lt;br /&gt;
&lt;br /&gt;
4.6.2 Open-Throat, No-Return Wind Tunnels&lt;br /&gt;
&lt;br /&gt;
The open-throat, no-return wind tunnel shown in Figure 4-15 permits exact measurements if parachutes of sufficient size are used. Parachutes 3 feet or more in diameter are well suited for obtaining good, quantitative test results.&lt;br /&gt;
&lt;br /&gt;
              FIGURE 4-15. Open-Throat, No-Return Wind Tunnel&lt;br /&gt;
&lt;br /&gt;
In air blowers and open-throat wind tunnels, the velocity at the skirt of the parachute (Section a-a of Figures 4-14 and 4-15) is lower than the velocity at the nozzle exit of the wind tunnel (Section b&amp;lt;sup&amp;gt;-&amp;lt;/sup&amp;gt;b of Figures 4-14 and 4-15), Care must be taken to measure the parachute test&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
velocity at Section a-a and not at Section b-b, the customary attachment point for airfoils and models.&lt;br /&gt;
&lt;br /&gt;
Wind tunnels frequently cannot test at the descent velocity of most main parachutes of 20 to 30 feet per second. Obtaining proper test results at this low is hampered by a poor velocity distribution in the wind-tunnel-test section, and by the weight of the test parachute. The latter has a tendency to pull the parachute downward, thereby providing a negative angle of attack, lusting unstable parachutes at higher presents the problem that the drag coefficient C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, of unstable parachutes is sensitive. The drag coefficient of unstable parachutes is described in section 5.2.&lt;br /&gt;
&lt;br /&gt;
An open-throat wind tunnel permits quick changes in parachute configuration, such as changing the suspension and reefing line lengths. Large open-throat wind tunnels that are not sealed against outside elements suffer atmospheric problems such as fog formation in the test section.&lt;br /&gt;
&lt;br /&gt;
4.6.3 Closed-Throat, Full-Return Wind Tunnel&lt;br /&gt;
&lt;br /&gt;
Figure 4-16 is a drawing of a full-return, closed-throat wind tunnel. fic full-return, closed-throat wind tunnel is generally considered best suited for obtaining good. qualitative, aerodynamic data, since it has a uniform distribution in the test section. A disadvantage is the difficulty in gaining access to the test section for changing the parachute configuration.&lt;br /&gt;
&lt;br /&gt;
FIGURE 4-16. Closed-Throat, Full-Reuurn Wind Tunnel.&lt;br /&gt;
&lt;br /&gt;
4.6.4 General Comments for Wind-Tunnel Testing of Parachutes&lt;br /&gt;
&lt;br /&gt;
1. Parachute models for wind-tunnel testing should be as large and as similar as possible in geometry and flexibility to full-scale parachutes. Parachutes of less than 1.5 feet in diameter usually lack geometric similarity and material flexibility, which results in inflation characteristics and dissimilar inflated shapes.&lt;br /&gt;
&lt;br /&gt;
2.  The finished dimensions of model parachutes must be measured as accurately as possible to determine the nominal diameter, Do, and the surface area, So. Model parachutes will shrink from 5 to 10% during manufacture because of sewing take-up, which results in a notable difference in the dimensions between the drawing and the completed parachute.&lt;br /&gt;
&lt;br /&gt;
3.  Wind&amp;lt;sup&amp;gt;-&amp;lt;/sup&amp;gt;tunnel tests of parachutes are excellent for comparing different models and modifications: also, they are the most effective means for measuring coefficients of lift, drag. and normal and tangential forces, as well as for determining the load coefficient, for infinite load.&lt;br /&gt;
&lt;br /&gt;
4.  In wind-tunnel tests, velocity decay does not occur during parachute inflation and operation; this is defined as testing under &amp;quot;infinite mass condition. &amp;quot; First-stage drogue chutes and parachutes with a canopy loading, W/C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;S. in excess of 100 lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; approach this condition. Low-canopy-loading main parachutes with rates of descent of 20 to 30 ft/s have a large velocity decay during opening, which requires careful interpretation of the opening-force data obtained in wind-tunnel tests.&lt;br /&gt;
&lt;br /&gt;
5.  In the past, to avoid wind-tunnel blockage and questionable test data. the diameter of a test parachute could not exceed about 5 to 6% of the wind-tunnel test section area. Recent Sandia investigations of single and clustered ribbon parachutes with wind-tunnel blockage ratios of up to 30% have resulted in correction methods that make it possible to test much larger parachutes (Reference 4.2).&lt;br /&gt;
&lt;br /&gt;
= 4.7 REFERENCE MATERIAL =&lt;br /&gt;
4.1 H. H. Hurt. Aerodynamics for Naval Aviators Navy Manual NAVWEPS 00 80T 80. Chief of Naval Operations, Aviation Training Division.&lt;br /&gt;
&lt;br /&gt;
4.2 J, M. Macha and R J. Buffington. &amp;quot;Wall-Interference Corrections for Parachutes in a Closed Wind Tunnel.&amp;quot; AIM Paper, April 1989. (AIM 89-0900-cp.)&lt;br /&gt;
&lt;br /&gt;
For readers interested in a more detailed study of aerodynamics, the following books are recommended.&lt;br /&gt;
&lt;br /&gt;
4.3 J, H, Dwinnel, Principle of Aerodynamics. McGraw-Hill     	Co., New York, 1949.&lt;br /&gt;
&lt;br /&gt;
4.4 J. Morane. Introduction to Theoretical and Computational Aerodynamics. John Wiley &amp;amp; Sons.&lt;br /&gt;
&lt;br /&gt;
4.5 R.S. Shevell. Fundamentals of Flight. Prentice-Hall. 1983.&lt;br /&gt;
&lt;br /&gt;
4.6 J. D. Anderson, Jr. Introduction to Flights, ILS Engineering and History. McGraw-Hill Book co., New York 1978.&lt;br /&gt;
&lt;br /&gt;
4.7 D. J. Cockrell. The Aerodynamics of Parachutes.&amp;quot; AGARDograph No. 6295, available from NASA Langley Research Center, M/S 1M), Hampton, Va., 236.&lt;/div&gt;</summary>
		<author><name>TuanHTruong</name></author>
	</entry>
	<entry>
		<id>https://mediawiki.aerodecelerator.org/index.php?title=Parachute_Aerodynamics&amp;diff=26</id>
		<title>Parachute Aerodynamics</title>
		<link rel="alternate" type="text/html" href="https://mediawiki.aerodecelerator.org/index.php?title=Parachute_Aerodynamics&amp;diff=26"/>
		<updated>2024-05-03T21:05:44Z</updated>

		<summary type="html">&lt;p&gt;TuanHTruong: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&lt;br /&gt;
= CHAPTER 4: AERODYNAMICS AS RELATED TO PARACHUTES =&lt;br /&gt;
== 4.1 PROPERTIES OF THE ATMOSPHERE ==&lt;br /&gt;
All forces acting on parachutes and all movements of parachutes are affected by the atmosphere, or air, surrounding the Earth. The air at the Earth's surface is approximately 78% nitrogen; 21% oxygen; and 1% a mixture of gases such as argon, neon, helium, water vapor, and carbon dioxide. This chemical composition remains relatively constant to an altitude of about 160,000 feet (50 kilometers). The following air qualities are of major significance in the dynamics of bodies moving in the atmosphere:&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
!Air quality&lt;br /&gt;
!Symbol&lt;br /&gt;
!Dimension&lt;br /&gt;
|-&lt;br /&gt;
|Specific weight of air&lt;br /&gt;
|w&lt;br /&gt;
|lb/ft&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;, kg/m&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;&lt;br /&gt;
|-&lt;br /&gt;
|Static pressure&lt;br /&gt;
|p&lt;br /&gt;
|atm, lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;, Pa, bar, torr&lt;br /&gt;
|-&lt;br /&gt;
|Temperature&lt;br /&gt;
|T&lt;br /&gt;
|&amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F, &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;C&lt;br /&gt;
|-&lt;br /&gt;
|Mass density&lt;br /&gt;
|&amp;lt;math&amp;gt;\rho&amp;lt;/math&amp;gt;&lt;br /&gt;
|slugs/ft3, kg s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;/m&amp;lt;sup&amp;gt;4&amp;lt;/sup&amp;gt;&lt;br /&gt;
|-&lt;br /&gt;
|Gravity&lt;br /&gt;
|''g''&lt;br /&gt;
|ft/s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;, m/s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
|-&lt;br /&gt;
|Speed of sound&lt;br /&gt;
|C&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt;&lt;br /&gt;
|ft/s, m/s&lt;br /&gt;
|}&lt;br /&gt;
All of these qualities are altitude-dependent and may vary slightly on the Earth's surface with geographic latitude because of variations of the Earth's radius caused by the centrifugal forces of the rotation of the Earth. All standard data used herein refer to a latitude of 45 degrees. Sea level is defined as mean sea level (MSL). To compare performance data on an equal basis, the United States Bureau of Standards has defined standard day conditions as follows:&lt;br /&gt;
&lt;br /&gt;
Temperature = 15 degrees Celsius (&amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;C) or 59 degrees Fahrenheit (&amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F)&lt;br /&gt;
&lt;br /&gt;
Pressure - 760 millimeters (mm) of mercury (Hg) or 29.9213 inches (in.) Hg&lt;br /&gt;
&lt;br /&gt;
=== 4.1.1 Specific Weight of Air ===&lt;br /&gt;
For standard day conditions of 59 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F temperature and a pressure of 29.9213 in. Hg, the specific weight of air, w, is 0.07648 lb/ft&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt; or 1.2250 kg/m&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;. The specific weight of air changes with pressure, temperature, and humidity. Further data can be found in References 3.4 and 4.1, and in technical handbooks.&lt;br /&gt;
&lt;br /&gt;
=== 4.1.2 Static Pressure ===&lt;br /&gt;
Static pressure depends on geographic latitude, weather conditions, and altitude. The static pressure at any altitude results from the weight of the air above that altitude. For MSL and standard day conditions, the pressure, p&amp;lt;sub&amp;gt;o&amp;lt;/sub&amp;gt;, is 29.9213 in. Hg = 760 mm Hg = 1.0 atmosphere (atm). For conversion to Pascal, torr, or bar, see the conversion tables in section 3.2.&lt;br /&gt;
&lt;br /&gt;
=== 4.1.3 Temperature ===&lt;br /&gt;
Temperatures are defined in the English and metric systems in the so-called absolute and engineering scales. The absolute temperature minimum at 0 degrees, pressure is 0 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;K = -273.16 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;C, and 0 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;R = -459.69 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F. This is also written&lt;br /&gt;
&lt;br /&gt;
Degrees Kelvin = degrees Celsius + 273.16&lt;br /&gt;
&lt;br /&gt;
Degrees Rankine = degrees Fahrenheit + 459.69&lt;br /&gt;
&lt;br /&gt;
The freezing point of water is 32 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F or 0 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;C. The boiling point of water is 212 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F or 100 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;C.&lt;br /&gt;
&lt;br /&gt;
=== 4.1.4 Mass Density of Air ===&lt;br /&gt;
Mass density defines the amount of mass contained in a unit volume of air. The mass density, p, of air is of special importance in aerodynamic calculations.&lt;br /&gt;
&lt;br /&gt;
specific weight of air, w lb/ft3 kg s2&lt;br /&gt;
&lt;br /&gt;
acceleration of gravity, g ft/s2 g 4&lt;br /&gt;
&lt;br /&gt;
slug = weight lb&lt;br /&gt;
&lt;br /&gt;
acceleration of gravity - ft/s 2&lt;br /&gt;
&lt;br /&gt;
Frequently the density ratio, a, is used&lt;br /&gt;
&lt;br /&gt;
ambient air density, p&lt;br /&gt;
&lt;br /&gt;
standard sea-level density, P4,&lt;br /&gt;
&lt;br /&gt;
The factor 1//p/lp determines the increase in parachute rate of descent with altitude. The density at 40,000 feet is ¼ of the MSL density, and the density at 100,000 feet is 1/75 of the MSL density. Therefore, the parachute rate of descent is about twice as high at 40,000 feet and about nine times as high at 100,000 feet. MSL density is 0.00237689 slugs/ft3, or 0.1249 kg s2/m4.&lt;br /&gt;
&lt;br /&gt;
4.1.5 Gravity&lt;br /&gt;
&lt;br /&gt;
Any mass attracts another mass with a force called gravity. If the Earth were surrounded by a vacuum, a body suspended above the Earth and released would fall toward the center of the Earth with increasing velocity caused by the acceleration of gravity, g. In reality, the falling body is decelerated by its air drag until the air drag, D, equals the weight of the body, W, and an equilibrium velocity is reached; for parachutes, this is called the steady-state rate of descent.&lt;br /&gt;
&lt;br /&gt;
The acceleration of gravity, g, at sea lavel is&lt;br /&gt;
&lt;br /&gt;
g = 32.174 ft/s2 or 9.80665 m/s2.&lt;br /&gt;
&lt;br /&gt;
The value g = 9.08665 m/s is standardized internationally but is accurate only for a&lt;br /&gt;
&lt;br /&gt;
latitude of 45 degrees.&lt;br /&gt;
&lt;br /&gt;
With increasing altitude above the Earth's surface, the acceleration of gravity decreases&lt;br /&gt;
&lt;br /&gt;
in accordance with the equation&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
g = acceleration of gravity at any altitude, ft/s 2&lt;br /&gt;
&lt;br /&gt;
-go acceleration of gravity at sea level, ft/s 2&lt;br /&gt;
&lt;br /&gt;
r = average Earth radius = 2.08556 x 107 ft&lt;br /&gt;
&lt;br /&gt;
h = altitude above sea level, ft&lt;br /&gt;
&lt;br /&gt;
For other planets and heavenly bodies, the acceleration of gravity varies with the mass of the body. For example, the acceleration of gravity on Mars is about 1/3 of the acceleration of gravity on Earth. For more details on planets and heavenly bodies, see page XII of Reference 2.1.&lt;br /&gt;
&lt;br /&gt;
4.1.6 Kinematic Viscosity&lt;br /&gt;
&lt;br /&gt;
The coefficient of viscosity, la, defines the shecring stresses in a gas or liquid and is sometimes called the resistance to continuous deformation. In aerodynamics, the coefficient of viscosity is combined with the mass density to form the kinematic viscosity, v, where&lt;br /&gt;
&lt;br /&gt;
coefficient of viscosity, g' 0.0001576 ft2/s at sea level&lt;br /&gt;
&lt;br /&gt;
mass density, P&lt;br /&gt;
&lt;br /&gt;
The kinematic viscosity, v, is altitude dependent and is used to calculate the Reynolds number, Re.&lt;br /&gt;
&lt;br /&gt;
4.1.7 Reynolds Number&lt;br /&gt;
&lt;br /&gt;
The Reynolds number, Re, defines the relationship of mass forces to viscous friction forces in liquids and gases. It is calculated as&lt;br /&gt;
&lt;br /&gt;
Re = v I velocity (ft/s) characteristic length (ft)&lt;br /&gt;
&lt;br /&gt;
V kinematic viscosity (ft2/s)&lt;br /&gt;
&lt;br /&gt;
Reynolds number is an important criterion in subsonic, noncompressible flow, and allows comparison of model tests with full-scale flight tests. A Reynolds number effect on parachutes working in separated, turbulent flow has not yet been established, as shown in section 5.2. The following chart shows the Reynolds numbers for various air vehicles.&lt;br /&gt;
&lt;br /&gt;
Drogue Main WIT&lt;br /&gt;
&lt;br /&gt;
Sbe Ihns=ec t Glider D -4 2 par ute model&lt;br /&gt;
&lt;br /&gt;
Re 6-103 2.5-106 24.106 100&amp;quot;106 50&amp;quot;106 20&amp;quot;106 2.106&lt;br /&gt;
&lt;br /&gt;
4.1.8 Mach Number&lt;br /&gt;
&lt;br /&gt;
Mach number is an important parameter of supersonic flight; it states how much faster than the speed of sound the air vehicle travels.&lt;br /&gt;
&lt;br /&gt;
Mach Number, M= &lt;br /&gt;
&lt;br /&gt;
The speed of sound is the velocity at which a pressure disturbance, such as the sound of the human voice, travels in any medium. The speed of sound varies considerably in different gases, liquids, and metals.&lt;br /&gt;
&lt;br /&gt;
The speed of sound depends on temperature and the chemical composition of the medium, A widely used equation for speed of sound in air is&lt;br /&gt;
&lt;br /&gt;
The speed of sound changes with altitude, as temperature (see Figure 3-1). The drag of streamlined bodies such as missiles, airfoils, and airplanes increases considerably as their velocities approach Mach 1. Depending on the configuration of the body, supersonic compressibility effects may in the 0.75• to 0.85•Mach range, causing local supersonic flow, shock waves, flow separation, and concomitant increases in drag and changes in stability.&lt;br /&gt;
&lt;br /&gt;
Parachutes that operate in separated flow over the entire velocity range do not show the typical drag increase when operating close to or beyond Mach 1. Supersonic parachute behavior is discussed in detail in section 5.8.&lt;br /&gt;
&lt;br /&gt;
== '''4.2 CONTINUITY LAW AND BERNOULLI EQUATION''' ==&lt;br /&gt;
4.2.1 Continuity L.aw&lt;br /&gt;
&lt;br /&gt;
Air is thought to flow in layers called streamlines. Figure 4-1 shows streamlines as layers of air without air transfer between individual layers. ne air is shown as being incompressible, a valid assumption for subsonic flow.&lt;br /&gt;
&lt;br /&gt;
  	&lt;br /&gt;
&lt;br /&gt;
If exchange of air does not occur across the streamline boundaries, the amount of air entering the streamline at point 1 must also exit at point 2. as shown in Figure 4*1. Because the cross section at point 2 is smaller than the cross section at point 1, the air must exit at a higher velocity. The following equation defines this condition:&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
this equation which governs the now in and around a body in gases and liquids, is important in aerodynamics and is called the continuity law. For imcompressilble subsonic now, it can be simplified to &lt;br /&gt;
&lt;br /&gt;
Whenever the cross section narrows. the velocity increases; when the cross section widens, the velocity decreases.&lt;br /&gt;
&lt;br /&gt;
4.2.2 Bernoulli Equation&lt;br /&gt;
&lt;br /&gt;
Figure 4-2 illustrates a streamline with the cross section, S, the velocity, v, and the pressure, p. If the air is incompressible, the downstream is v + Av. and the pressure is p + AP. If the air is inviscid, the inertia forces caused by the acceleration of air from v to v + Av must be balanced by differential pressure forces.&lt;br /&gt;
&lt;br /&gt;
    	                                       	&lt;br /&gt;
&lt;br /&gt;
FIGURE 4-2 Pressure and Velocity Distribution in a Streamline Element.&lt;br /&gt;
&lt;br /&gt;
The following equation can be written&lt;br /&gt;
&lt;br /&gt;
Simplified, the above equation yields&lt;br /&gt;
&lt;br /&gt;
'''dp = -pvdv'''&lt;br /&gt;
&lt;br /&gt;
the above equation allows the following consideration: If p is pressure, then 1/2 pv&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; and C must also be pressure. The equation 1/2 pv&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; includes a and is referred to as the dynamic pressure. or sometimes velocity as or impact pressure.&lt;br /&gt;
&lt;br /&gt;
Pressure, p, is defined as static pressure; 1/2 pv&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; as dynamic pressure; and the sum of both, C, as the total pressure or&lt;br /&gt;
&lt;br /&gt;
p + 1/2pv&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; = H&lt;br /&gt;
&lt;br /&gt;
and&lt;br /&gt;
&lt;br /&gt;
where H is the total pressure of the system, lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Dynamic pressure, q, is a frequently used quantity in aerodynamics:&lt;br /&gt;
&lt;br /&gt;
q = 1/2 pv&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
q = dynamic pressure, lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
p =  air density, slugs/ft&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
v =  velocity at a point of undisturbed flow, ft/s&lt;br /&gt;
&lt;br /&gt;
The following formulas are used for calculating the sea-level dynamic pressure if the velocity is given in ft/s, knots, mph, or km/h, respectively:&lt;br /&gt;
&lt;br /&gt;
                                              &lt;br /&gt;
&lt;br /&gt;
'''4.3 NEWTON'S THREE OF MOTION'''&lt;br /&gt;
&lt;br /&gt;
Engineering mechanics are governed by the following three laws of Isaac Newton:&lt;br /&gt;
&lt;br /&gt;
1.  A body remains at rest or in an unaccelerated state of motion unless acted upon.&lt;br /&gt;
&lt;br /&gt;
2.  A force acting upon a body will produce an acceleration in the direction of the force.&lt;br /&gt;
&lt;br /&gt;
3.  An action in one direction will produce an equal reaction in the opposite direction.&lt;br /&gt;
&lt;br /&gt;
The first law is self-explanatory. The second law may be expressed by the equation&lt;br /&gt;
&lt;br /&gt;
F = m * a&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
F = force in pounds acting on the mass, 1b&lt;br /&gt;
&lt;br /&gt;
m = mass of body that the force is acting upon, slugs&lt;br /&gt;
&lt;br /&gt;
a = acceleration in ft/s2 resulting from the force, F&lt;br /&gt;
&lt;br /&gt;
The mass, m, of a body is obtained by&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
W = weight of the body, lb&lt;br /&gt;
&lt;br /&gt;
g = acceleration of gravity, ft/s2&lt;br /&gt;
&lt;br /&gt;
The mass, therefore, has the dimension of&lt;br /&gt;
&lt;br /&gt;
This unit of mass is the slug.&lt;br /&gt;
&lt;br /&gt;
the equation of Newton's second law can now be written&lt;br /&gt;
&lt;br /&gt;
                                        	&lt;br /&gt;
&lt;br /&gt;
The factor a/g is frequently called the load factor, G, and tells how much larger a force is than a force equivalent to the weight of the body. It is customary in parachute work to state that the maximum parachute force allowed is G • W or (a]g) • W. It is appropriate to write&lt;br /&gt;
&lt;br /&gt;
Maximum allowable parachute force,&lt;br /&gt;
&lt;br /&gt;
Figure 4-3 illustrates Newton's third law, explaining the principle of the rocket that can produce thrust in a perfect vacuum.&lt;br /&gt;
&lt;br /&gt;
A mass, m. ejected from a rocket at the velocity, v, per unit time, t, will produce a force, F, which in turn will create a reaction force, R. of equal magnitude but acting in the opposite direction.&lt;br /&gt;
&lt;br /&gt;
=== 4.4 FORCES ACTING ON A BODY MOVING THROUGH AIR ===&lt;br /&gt;
4.4.1 Symmetrical Body&lt;br /&gt;
&lt;br /&gt;
A body moving through air experiences forces caused by air pressure acting on the body. fie same forces if the body moves through air, such as a descending parachute, or if the body is fixed and the air moves against the body, such as a parachute or an airfoil in a wind tunnel (Figure 44).&lt;br /&gt;
&lt;br /&gt;
         	 &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
A stable parachute in a wind tunnel experiences only the force called &amp;quot;drag&amp;quot; in the direction of the airflow. drag force, D, is calculated to&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
D = drag, 1b&lt;br /&gt;
&lt;br /&gt;
Q = dynamic pressure, lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
S = total surface area of the parachute canopy, ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt; = coefficient of drag.  dimensionless&lt;br /&gt;
&lt;br /&gt;
the dynamic pressure, q, can be calculated from section 4.2.2. The surface area of the canopy, S, is selected as a reference area. The drag coefficient  C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, is a form factor that indicates the drag characteristic of a specific shape. Most aerodynamic bodies are designed for low drag or a low drag coefficient. Parachutes, generally, are designed for high drag; therefore, a high drag coefficient is desirable. this difference in drag is demonstrated by the two bodies shown in Figure 4-5.&lt;br /&gt;
&lt;br /&gt;
            	&lt;br /&gt;
&lt;br /&gt;
Both bodies have the same cross section perpendicular to the airflow. The cylindrical. streamlined body has a smooth airflow over its total body length, resulting in a drag coefficient. C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, of 0.05 to 0.1, depending on slenderness ratio, surface roughness, and shape. The drag coefficient of all streamlined bodies is much affected by Reynolds number and Mach number. fie open hemisphere, which is similar to a parachute canopy, has a drag coefficient, C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, of 1.3 to 1.4 for the same body cross section. The difference in drag is explained by the smooth airflow around the streamlined body and a separated. turbulent flow around the open hemisphere. The drag of bodies with separated flow, like parachute canopies, is little affected by Reynolds number.&lt;br /&gt;
&lt;br /&gt;
4.4.2 Airflow Around an Asymmetrical Body (Airfoil)&lt;br /&gt;
&lt;br /&gt;
Figure 4-6 shows an airfoil fixed at an angle of attack, a. against the airflow in a wind tunnel. This airfoil creates a drag force, D, in the direction of the flow; a lift force L perpendicular to the direction of the flow; and a moment, M. around the attachment point of the airfoil. fie sign convention of moments and forces shown are positive. Lift and drag can be combined for the resultant force, R.&lt;br /&gt;
&lt;br /&gt;
FIGURE. 44, Wind-Tunnel Forces Acting on an Airfoil.&lt;br /&gt;
&lt;br /&gt;
The lift, L is calculated&lt;br /&gt;
&lt;br /&gt;
L = q * S * C&amp;lt;sub&amp;gt;L&amp;lt;/sub&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
L = measured lift, 1b&lt;br /&gt;
&lt;br /&gt;
q = dynamic pressure, lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
s = reference area, ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
CL = lift coefficient, dimensionless&lt;br /&gt;
&lt;br /&gt;
The moment is&lt;br /&gt;
&lt;br /&gt;
       M = q * S * c&amp;lt;sub&amp;gt;m&amp;lt;/sub&amp;gt; * c&lt;br /&gt;
&lt;br /&gt;
Where&lt;br /&gt;
&lt;br /&gt;
The reference area, S is defined by agreement, For streamlined bodies, the maximum body cross section is used. Airfoils use the planform of the wing, and parachutes use the canopy surface area. The selection of the wing planform and the parachute surface area as references was made for practical reasons. &amp;lt;sup&amp;gt;e&amp;lt;/sup&amp;gt;me wing planform for a specific wing is fixedt whereas the cross section of the wing in the direction of the flow changes with the angle of attack. Similarly, the surface area of the parachute canopy is fixed; however, the frontal projected area of the inflated parachute canopy changes with airspeed, porosity, line length, and tm of parachute.&lt;br /&gt;
&lt;br /&gt;
Forces and moments acting on an airfoil or a parachute canopy may be presented in several ways. The two most frequently used methods, as shown in Figure 4-7, are with forces oriented to the of flight and with forces oriented to the axis of the airfoil.&lt;br /&gt;
&lt;br /&gt;
me tangential force, and the normal force, N, are calculated&lt;br /&gt;
&lt;br /&gt;
T = C&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; * S * q&lt;br /&gt;
&lt;br /&gt;
        	&lt;br /&gt;
&lt;br /&gt;
and&lt;br /&gt;
&lt;br /&gt;
      	N = C&amp;lt;sub&amp;gt;N&amp;lt;/sub&amp;gt; * S * q&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
C&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; = tangential force coefficient, dimensionless&lt;br /&gt;
&lt;br /&gt;
C&amp;lt;sub&amp;gt;N&amp;lt;/sub&amp;gt; = normal force coefficient, dimensionless&lt;br /&gt;
&lt;br /&gt;
The resultant force, R, and the moment, M, in both presentations have the same direction and the same magnitude. The airflow fixed system is preferred for aerodynamic performance calculations, and the airfoil fixed system for wing stress calculations. me aerodynamic coefficients C&amp;lt;sub&amp;gt;L&amp;lt;/sub&amp;gt;, C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, C&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, C&amp;lt;sub&amp;gt;N&amp;lt;/sub&amp;gt;, and C&amp;lt;sub&amp;gt;m&amp;lt;/sub&amp;gt; can easily be determined in wind•tunnel measurements.&lt;br /&gt;
&lt;br /&gt;
Figure 4-8 shows the relationship of both force systems on a parachute. By definition, a negative moment is stabilizing, as illustrated in Figure 4-8. It is interesting to note that in Europe the stabilizing moment is defined as positive. Wind-tunnel installations frequently measure normal and tangential force instead of lift and drag. If α, T, and N are known, the drag D, can be calculated&lt;br /&gt;
&lt;br /&gt;
D = T*cosα + N * sinα&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
For a parachute with an angle of attack, a, equal to zero, the drag force and the tangential force are synonymous.&lt;br /&gt;
&lt;br /&gt;
Figure 4-9 shows the coefficients C&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, and C&amp;lt;sub&amp;gt;m&amp;lt;/sub&amp;gt; versus angle of attack for stable and unstable parachutes.&lt;br /&gt;
&lt;br /&gt;
The coefficient presentation shows two interesting facts. ne slope of the moment coefficient curve, dC&amp;lt;sub&amp;gt;m&amp;lt;/sub&amp;gt;/dα, for the unstable parachute is positive between -25 degrees and + 25 degrees; this is, by definition, destabilizing. This parachute will oscillate approximately ± 25&lt;br /&gt;
&lt;br /&gt;
FIGURE 4-9. Coefficients C&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, and C&amp;lt;sub&amp;gt;M&amp;lt;/sub&amp;gt; Versus Angle of Attack, α, for a Stable and Unstable Parachute.&lt;br /&gt;
&lt;br /&gt;
degrees. The slope of the moment, dC&amp;lt;sub&amp;gt;m&amp;lt;/sub&amp;gt;/dα, for the stable parachute is negative over the total angle of attack; this is, by definition, stabilizing. The steeper the negative dC&amp;lt;sub&amp;gt;m&amp;lt;/sub&amp;gt;/dα slope, the greater is the stabilizing tendency of the parachute, and the better is its damping capability against unstabilizing forces such as sudden gusts of wind.&lt;br /&gt;
&lt;br /&gt;
Figure 4-10, from Reference 4.1, demonstrates the effect of airflow around a cylinder and an airfoil. The circulation around a rotating cylinder creates lift caused by the increase in velocity on one side of the cylinder and a decrease on the opposite side. This is called the Magnus effect.&lt;br /&gt;
&lt;br /&gt;
= 4.5 EQUILIBRIUM OF FORCES IN STUDY DESCENT OR FLIGHT =&lt;br /&gt;
4.5.1 Parachute in Steady Descent&lt;br /&gt;
&lt;br /&gt;
A stable parachute in unaccelerated descent has an equilibrium between the total drag of the parachute and the load, Dr, and the weight of the load and the parachute assembly, WT (Figure 4-11). For steady descent&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
D&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; = total drag, 1b&lt;br /&gt;
&lt;br /&gt;
D&amp;lt;sub&amp;gt;P&amp;lt;/sub&amp;gt; = drag of parachute, 1b&lt;br /&gt;
&lt;br /&gt;
W&amp;lt;sub&amp;gt;C&amp;lt;/sub&amp;gt; = weight of load. 1b&lt;br /&gt;
&lt;br /&gt;
In most cases, the drag of the load can be neglected in relation to the large drag of the parachute, With drag, D — (C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;S)&amp;lt;sub&amp;gt;p&amp;lt;/sub&amp;gt; • p/2• v&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; and D&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; = W&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;. and solving for v, the important equation for rate of descent, v&amp;lt;sub&amp;gt;e&amp;lt;/sub&amp;gt;, is obtained,&lt;br /&gt;
&lt;br /&gt;
Rate of descent,&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
FIGURE 4-11. Forces Acting on a Parachute in Steady Descent.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
or in parachute terminology for rate of descent at sea level&lt;br /&gt;
&lt;br /&gt;
and rate of descent at any altitude&lt;br /&gt;
&lt;br /&gt;
== For 1/, see column 4 in Table 3-3, ==&lt;br /&gt;
In the equation for rate of descent. V&amp;lt;sub&amp;gt;e&amp;lt;/sub&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
W&amp;lt;sub&amp;gt;T =&amp;lt;/sub&amp;gt; weight of load and parachute assembly, 1b&lt;br /&gt;
&lt;br /&gt;
S&amp;lt;sub&amp;gt;o&amp;lt;/sub&amp;gt; = canopy surface area, ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
C&amp;lt;sub&amp;gt;Do&amp;lt;/sub&amp;gt; = parachute drag coefficient related to S&amp;lt;sub&amp;gt;o&amp;lt;/sub&amp;gt;&lt;br /&gt;
&lt;br /&gt;
p = air density at a specific altitude in slugs/ft&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;, as shown in Table 3-3&lt;br /&gt;
&lt;br /&gt;
During descent from altitude, the parachute system is constantly decelerated because of the increasing air density. This can be ignored for slowly descending main parachutes. However, for drogue chute systems that descend at 200 ft/s or faster, the constant deceleration may result in velocities 3 to 5% higher than the steady rate of descent.&lt;br /&gt;
&lt;br /&gt;
4.5.2 Gliding Parachutes&lt;br /&gt;
&lt;br /&gt;
Figure 4-12 shows the balance of forces on a gliding parachute. The total weight of the system, W&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; . must be balanced by the resultant force. R. However, a lifting force is required for glide. To satisfy the force balance&lt;br /&gt;
&lt;br /&gt;
R = C&amp;lt;sub&amp;gt;R&amp;lt;/sub&amp;gt; * S * p/2 * v&lt;br /&gt;
&lt;br /&gt;
Trajectory velocity, V&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, is calculated&lt;br /&gt;
&lt;br /&gt;
Horizontal velocity is calculated&lt;br /&gt;
&lt;br /&gt;
V&amp;lt;sub&amp;gt;H&amp;lt;/sub&amp;gt; = V&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; • cosø, and vertical velocity, v&amp;lt;sub&amp;gt;v&amp;lt;/sub&amp;gt; = V&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; • sinø&lt;br /&gt;
&lt;br /&gt;
The glide ratio is obtained from&lt;br /&gt;
&lt;br /&gt;
Analysis of Figure 4-12 indicates that the larger the ratio of lift to drag, the better the glide ratio, I./D A high resultant coefficient, C&amp;lt;sub&amp;gt;R&amp;lt;/sub&amp;gt;, results in a low glide or trajectory V&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, desirable for landing. A small C&amp;lt;sub&amp;gt;R&amp;lt;/sub&amp;gt; results in a high glide velocity, V&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, which is desirable for flying toward a target, compensating for head winds, or covering a distance quickly. Generally, gliding parachutes follow the same aerodynamic rules as low-aspect-ratio wings.&lt;br /&gt;
&lt;br /&gt;
           	   	&lt;br /&gt;
&lt;br /&gt;
FIGUR E 4-12, Forces Acting on a Gliding Parachute&lt;br /&gt;
&lt;br /&gt;
4.5-3 Parasite Drag and Induced Drag&lt;br /&gt;
&lt;br /&gt;
The drag acting on a lift-producing air vehicle, such as a gliding parachute or an aircraft, has two primary components: the parasite drag, D&amp;lt;sub&amp;gt;P&amp;lt;/sub&amp;gt; , and the induced drag. D&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Parasite drag is produced by the form drag from individual components such as the suspension lines, canopy, and the jumper of a gliding parachute, and the fuselage, tail sectiora, and control surfaces of an airplane. Large surfaces produce surface friction drag as part of the parasite drag.&lt;br /&gt;
&lt;br /&gt;
Induced drag is caused by the lifting action of the parachute canopy or the aircraft wing. Section 4.7 includes books with detailed discussions of induced drag.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Total drag, D&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, can be defined as&lt;br /&gt;
&lt;br /&gt;
or, in the coefficient form&lt;br /&gt;
&lt;br /&gt;
The parasite drag, D&amp;lt;sub&amp;gt;p&amp;lt;/sub&amp;gt;, and the coefficient, C&amp;lt;sub&amp;gt;DP&amp;lt;/sub&amp;gt;, can be determined in wind-tunnel tests or calculated as the sum of the individual component drags.&lt;br /&gt;
&lt;br /&gt;
The induced drag coefficient, C&amp;lt;sub&amp;gt;Di&amp;lt;/sub&amp;gt; , of a gliding parachute canopy or a wing profile can be calculated&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
C = coefficient of induced drag, dimensionless&lt;br /&gt;
&lt;br /&gt;
The expression b&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;/S is defined as the aspect ratio of a wing or parachute with the notation AR b&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;/S. Therefore&lt;br /&gt;
&lt;br /&gt;
== '''                       ''' 	 ==&lt;br /&gt;
The equation for induced drag indicates that increasing the aspect ratio, AR, reduces the induced drag coefficient,  , and therefore reduces the drag, D. ms, in turn, increases the glide ratio, L/D. Increasing the glide ratio by increasing the aspect ratio is optimized on high-performance sailplanes with aspect ratios higher than 20. Increasing the glide ratio of gliding parachutes by increasing the aspect ratio has limitations, which are discussed in section 5.9.&lt;br /&gt;
&lt;br /&gt;
4.5.4 Aircraft in Horizontal Flight&lt;br /&gt;
&lt;br /&gt;
Figure 4-13 shows forces and moments on an aircraft in steady, horizontal flight. In steady, horizontal flight, an equilibrium exists between all forces and moments acting on the aircraft. Lift on the wing and tail, L&amp;lt;sub&amp;gt;W&amp;lt;/sub&amp;gt; and L&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;. and the weight of the aircraft, W&amp;lt;sub&amp;gt;A&amp;lt;/sub&amp;gt;, balance in the vertical plane. Thrust, T and drag. D, balance each other in the horizontal plane, and the positive or negative moment, M, is balanced by the positive or negative lift of the tail multiplied by the moment arm, L&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
FIGURE 4-13. Forces and Moments Acting on an Aircraft in Steady night,&lt;br /&gt;
&lt;br /&gt;
Any imbalance in these forces results in descent or climb in the vertical plane or faster or slower speed in the horizontal plane. A change in the lift of the elevator initiates climb or descent. Thrust, T, is the prime contributor for climb or descent and faster or slower speed, However, a balance of forces must always be maintained for horizontal flight or steady rate oi climb or descent.&lt;br /&gt;
&lt;br /&gt;
== 4.6 WIND-TUNNEL TESTING OF PARACHUTES ==&lt;br /&gt;
Wind tunnels are an effective tool for testing air vehicles and air-vehicle components and have been used successfully for testing parachutes and parachute systems. Experience has shown that certain rules apply for the wind-tunnel testing of parachutes. Small parachutes manufactured from textiles cannot be made sufficiently similar to large parachutes in geometric design and flexibility, Lightweight material. required to obtain design similarity, is difficult to manufacture or is unobtainable.&lt;br /&gt;
&lt;br /&gt;
One cardinal rule has been established through many years of parachute wind-tunnel testing: A modification that changes the performance of a model parachute in wind-tunnel testing produces the same type and percentage of performance change in a large parachute. This rule is true for drag. stability, and opening-force characteristics.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
4.6.1 Blowers&lt;br /&gt;
&lt;br /&gt;
The simple air blower (Figure 4-14) is a proven tool for preliminary parachute testing of a chiefly qualitative nature. Unless special test conditions prevail, parachutes tested should be a minimum of 1.5 to 2 feet in diameter to obtain meaningful results.&lt;br /&gt;
&lt;br /&gt;
                                                                    &lt;br /&gt;
&lt;br /&gt;
 FIGURE 4-14. Typical Air Blower.&lt;br /&gt;
&lt;br /&gt;
An air blower is a preliminary test too! because it permits quick parachute• configuration changes and excellent visual observation.&lt;br /&gt;
&lt;br /&gt;
4.6.2 Open-Throat, No-Return Wind Tunnels&lt;br /&gt;
&lt;br /&gt;
The open-throat, no-return wind tunnel shown in Figure 4-15 permits exact measurements if parachutes of sufficient size are used. Parachutes 3 feet or more in diameter are well suited for obtaining good, quantitative test results.&lt;br /&gt;
&lt;br /&gt;
              FIGURE 4-15. Open-Throat, No-Return Wind Tunnel&lt;br /&gt;
&lt;br /&gt;
In air blowers and open-throat wind tunnels, the velocity at the skirt of the parachute (Section a-a of Figures 4-14 and 4-15) is lower than the velocity at the nozzle exit of the wind tunnel (Section b&amp;lt;sup&amp;gt;-&amp;lt;/sup&amp;gt;b of Figures 4-14 and 4-15), Care must be taken to measure the parachute test&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
velocity at Section a-a and not at Section b-b, the customary attachment point for airfoils and models.&lt;br /&gt;
&lt;br /&gt;
Wind tunnels frequently cannot test at the descent velocity of most main parachutes of 20 to 30 feet per second. Obtaining proper test results at this low is hampered by a poor velocity distribution in the wind-tunnel-test section, and by the weight of the test parachute. The latter has a tendency to pull the parachute downward, thereby providing a negative angle of attack, lusting unstable parachutes at higher presents the problem that the drag coefficient C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, of unstable parachutes is sensitive. The drag coefficient of unstable parachutes is described in section 5.2.&lt;br /&gt;
&lt;br /&gt;
An open-throat wind tunnel permits quick changes in parachute configuration, such as changing the suspension and reefing line lengths. Large open-throat wind tunnels that are not sealed against outside elements suffer atmospheric problems such as fog formation in the test section.&lt;br /&gt;
&lt;br /&gt;
4.6.3 Closed-Throat, Full-Return Wind Tunnel&lt;br /&gt;
&lt;br /&gt;
Figure 4-16 is a drawing of a full-return, closed-throat wind tunnel. fic full-return, closed-throat wind tunnel is generally considered best suited for obtaining good. qualitative, aerodynamic data, since it has a uniform distribution in the test section. A disadvantage is the difficulty in gaining access to the test section for changing the parachute configuration.&lt;br /&gt;
&lt;br /&gt;
FIGURE 4-16. Closed-Throat, Full-Reuurn Wind Tunnel.&lt;br /&gt;
&lt;br /&gt;
4.6.4 General Comments for Wind-Tunnel Testing of Parachutes&lt;br /&gt;
&lt;br /&gt;
1. Parachute models for wind-tunnel testing should be as large and as similar as possible in geometry and flexibility to full-scale parachutes. Parachutes of less than 1.5 feet in diameter usually lack geometric similarity and material flexibility, which results in inflation characteristics and dissimilar inflated shapes.&lt;br /&gt;
&lt;br /&gt;
2.  The finished dimensions of model parachutes must be measured as accurately as possible to determine the nominal diameter, Do, and the surface area, So. Model parachutes will shrink from 5 to 10% during manufacture because of sewing take-up, which results in a notable difference in the dimensions between the drawing and the completed parachute.&lt;br /&gt;
&lt;br /&gt;
3.  Wind&amp;lt;sup&amp;gt;-&amp;lt;/sup&amp;gt;tunnel tests of parachutes are excellent for comparing different models and modifications: also, they are the most effective means for measuring coefficients of lift, drag. and normal and tangential forces, as well as for determining the load coefficient, for infinite load.&lt;br /&gt;
&lt;br /&gt;
4.  In wind-tunnel tests, velocity decay does not occur during parachute inflation and operation; this is defined as testing under &amp;quot;infinite mass condition. &amp;quot; First-stage drogue chutes and parachutes with a canopy loading, W/C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;S. in excess of 100 lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; approach this condition. Low-canopy-loading main parachutes with rates of descent of 20 to 30 ft/s have a large velocity decay during opening, which requires careful interpretation of the opening-force data obtained in wind-tunnel tests.&lt;br /&gt;
&lt;br /&gt;
5.  In the past, to avoid wind-tunnel blockage and questionable test data. the diameter of a test parachute could not exceed about 5 to 6% of the wind-tunnel test section area. Recent Sandia investigations of single and clustered ribbon parachutes with wind-tunnel blockage ratios of up to 30% have resulted in correction methods that make it possible to test much larger parachutes (Reference 4.2).&lt;br /&gt;
&lt;br /&gt;
= 4.7 REFERENCE MATERIAL =&lt;br /&gt;
4.1 H. H. Hurt. Aerodynamics for Naval Aviators Navy Manual NAVWEPS 00 80T 80. Chief of Naval Operations, Aviation Training Division.&lt;br /&gt;
&lt;br /&gt;
4.2 J, M. Macha and R J. Buffington. &amp;quot;Wall-Interference Corrections for Parachutes in a Closed Wind Tunnel.&amp;quot; AIM Paper, April 1989. (AIM 89-0900-cp.)&lt;br /&gt;
&lt;br /&gt;
For readers interested in a more detailed study of aerodynamics, the following books are recommended.&lt;br /&gt;
&lt;br /&gt;
4.3 J, H, Dwinnel, Principle of Aerodynamics. McGraw-Hill     	Co., New York, 1949.&lt;br /&gt;
&lt;br /&gt;
4.4 J. Morane. Introduction to Theoretical and Computational Aerodynamics. John Wiley &amp;amp; Sons.&lt;br /&gt;
&lt;br /&gt;
4.5 R.S. Shevell. Fundamentals of Flight. Prentice-Hall. 1983.&lt;br /&gt;
&lt;br /&gt;
4.6 J. D. Anderson, Jr. Introduction to Flights, ILS Engineering and History. McGraw-Hill Book co., New York 1978.&lt;br /&gt;
&lt;br /&gt;
4.7 D. J. Cockrell. The Aerodynamics of Parachutes.&amp;quot; AGARDograph No. 6295, available from NASA Langley Research Center, M/S 1M), Hampton, Va., 236.&lt;/div&gt;</summary>
		<author><name>TuanHTruong</name></author>
	</entry>
	<entry>
		<id>https://mediawiki.aerodecelerator.org/index.php?title=Parachute_Aerodynamics&amp;diff=25</id>
		<title>Parachute Aerodynamics</title>
		<link rel="alternate" type="text/html" href="https://mediawiki.aerodecelerator.org/index.php?title=Parachute_Aerodynamics&amp;diff=25"/>
		<updated>2024-05-03T21:04:56Z</updated>

		<summary type="html">&lt;p&gt;TuanHTruong: Equations and tables will be laborious! Chipping away.&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&lt;br /&gt;
= CHAPTER 4 =&lt;br /&gt;
= AERODYNAMICS AS RELATED TO PARACHUTES =&lt;br /&gt;
&lt;br /&gt;
== 4.1 PROPERTIES OF THE ATMOSPHERE ==&lt;br /&gt;
All forces acting on parachutes and all movements of parachutes are affected by the atmosphere, or air, surrounding the Earth. The air at the Earth's surface is approximately 78% nitrogen; 21% oxygen; and 1% a mixture of gases such as argon, neon, helium, water vapor, and carbon dioxide. This chemical composition remains relatively constant to an altitude of about 160,000 feet (50 kilometers). The following air qualities are of major significance in the dynamics of bodies moving in the atmosphere:&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
!Air quality&lt;br /&gt;
!Symbol&lt;br /&gt;
!Dimension&lt;br /&gt;
|-&lt;br /&gt;
|Specific weight of air&lt;br /&gt;
|w&lt;br /&gt;
|lb/ft&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;, kg/m&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;&lt;br /&gt;
|-&lt;br /&gt;
|Static pressure&lt;br /&gt;
|p&lt;br /&gt;
|atm, lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;, Pa, bar, torr&lt;br /&gt;
|-&lt;br /&gt;
|Temperature&lt;br /&gt;
|T&lt;br /&gt;
|&amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F, &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;C&lt;br /&gt;
|-&lt;br /&gt;
|Mass density&lt;br /&gt;
|&amp;lt;math&amp;gt;\rho&amp;lt;/math&amp;gt;&lt;br /&gt;
|slugs/ft3, kg s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;/m&amp;lt;sup&amp;gt;4&amp;lt;/sup&amp;gt;&lt;br /&gt;
|-&lt;br /&gt;
|Gravity&lt;br /&gt;
|''g''&lt;br /&gt;
|ft/s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;, m/s&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
|-&lt;br /&gt;
|Speed of sound&lt;br /&gt;
|C&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt;&lt;br /&gt;
|ft/s, m/s&lt;br /&gt;
|}&lt;br /&gt;
All of these qualities are altitude-dependent and may vary slightly on the Earth's surface with geographic latitude because of variations of the Earth's radius caused by the centrifugal forces of the rotation of the Earth. All standard data used herein refer to a latitude of 45 degrees. Sea level is defined as mean sea level (MSL). To compare performance data on an equal basis, the United States Bureau of Standards has defined standard day conditions as follows:&lt;br /&gt;
&lt;br /&gt;
Temperature = 15 degrees Celsius (&amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;C) or 59 degrees Fahrenheit (&amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F)&lt;br /&gt;
&lt;br /&gt;
Pressure - 760 millimeters (mm) of mercury (Hg) or 29.9213 inches (in.) Hg&lt;br /&gt;
&lt;br /&gt;
=== 4.1.1 Specific Weight of Air ===&lt;br /&gt;
For standard day conditions of 59 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F temperature and a pressure of 29.9213 in. Hg, the specific weight of air, w, is 0.07648 lb/ft&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt; or 1.2250 kg/m&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;. The specific weight of air changes with pressure, temperature, and humidity. Further data can be found in References 3.4 and 4.1, and in technical handbooks.&lt;br /&gt;
&lt;br /&gt;
=== 4.1.2 Static Pressure ===&lt;br /&gt;
Static pressure depends on geographic latitude, weather conditions, and altitude. The static pressure at any altitude results from the weight of the air above that altitude. For MSL and standard day conditions, the pressure, p&amp;lt;sub&amp;gt;o&amp;lt;/sub&amp;gt;, is 29.9213 in. Hg = 760 mm Hg = 1.0 atmosphere (atm). For conversion to Pascal, torr, or bar, see the conversion tables in section 3.2.&lt;br /&gt;
&lt;br /&gt;
=== 4.1.3 Temperature ===&lt;br /&gt;
Temperatures are defined in the English and metric systems in the so-called absolute and engineering scales. The absolute temperature minimum at 0 degrees, pressure is 0 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;K = -273.16 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;C, and 0 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;R = -459.69 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F. This is also written&lt;br /&gt;
&lt;br /&gt;
Degrees Kelvin = degrees Celsius + 273.16&lt;br /&gt;
&lt;br /&gt;
Degrees Rankine = degrees Fahrenheit + 459.69&lt;br /&gt;
&lt;br /&gt;
The freezing point of water is 32 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F or 0 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;C. The boiling point of water is 212 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;F or 100 &amp;lt;sup&amp;gt;&amp;lt;small&amp;gt;o&amp;lt;/small&amp;gt;&amp;lt;/sup&amp;gt;C.&lt;br /&gt;
&lt;br /&gt;
=== 4.1.4 Mass Density of Air ===&lt;br /&gt;
Mass density defines the amount of mass contained in a unit volume of air. The mass density, p, of air is of special importance in aerodynamic calculations.&lt;br /&gt;
&lt;br /&gt;
specific weight of air, w lb/ft3 kg s2&lt;br /&gt;
&lt;br /&gt;
acceleration of gravity, g ft/s2 g 4&lt;br /&gt;
&lt;br /&gt;
slug = weight lb&lt;br /&gt;
&lt;br /&gt;
acceleration of gravity - ft/s 2&lt;br /&gt;
&lt;br /&gt;
Frequently the density ratio, a, is used&lt;br /&gt;
&lt;br /&gt;
ambient air density, p&lt;br /&gt;
&lt;br /&gt;
standard sea-level density, P4,&lt;br /&gt;
&lt;br /&gt;
The factor 1//p/lp determines the increase in parachute rate of descent with altitude. The density at 40,000 feet is ¼ of the MSL density, and the density at 100,000 feet is 1/75 of the MSL density. Therefore, the parachute rate of descent is about twice as high at 40,000 feet and about nine times as high at 100,000 feet. MSL density is 0.00237689 slugs/ft3, or 0.1249 kg s2/m4.&lt;br /&gt;
&lt;br /&gt;
4.1.5 Gravity&lt;br /&gt;
&lt;br /&gt;
Any mass attracts another mass with a force called gravity. If the Earth were surrounded by a vacuum, a body suspended above the Earth and released would fall toward the center of the Earth with increasing velocity caused by the acceleration of gravity, g. In reality, the falling body is decelerated by its air drag until the air drag, D, equals the weight of the body, W, and an equilibrium velocity is reached; for parachutes, this is called the steady-state rate of descent.&lt;br /&gt;
&lt;br /&gt;
The acceleration of gravity, g, at sea lavel is&lt;br /&gt;
&lt;br /&gt;
g = 32.174 ft/s2 or 9.80665 m/s2.&lt;br /&gt;
&lt;br /&gt;
The value g = 9.08665 m/s is standardized internationally but is accurate only for a&lt;br /&gt;
&lt;br /&gt;
latitude of 45 degrees.&lt;br /&gt;
&lt;br /&gt;
With increasing altitude above the Earth's surface, the acceleration of gravity decreases&lt;br /&gt;
&lt;br /&gt;
in accordance with the equation&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
g = acceleration of gravity at any altitude, ft/s 2&lt;br /&gt;
&lt;br /&gt;
-go acceleration of gravity at sea level, ft/s 2&lt;br /&gt;
&lt;br /&gt;
r = average Earth radius = 2.08556 x 107 ft&lt;br /&gt;
&lt;br /&gt;
h = altitude above sea level, ft&lt;br /&gt;
&lt;br /&gt;
For other planets and heavenly bodies, the acceleration of gravity varies with the mass of the body. For example, the acceleration of gravity on Mars is about 1/3 of the acceleration of gravity on Earth. For more details on planets and heavenly bodies, see page XII of Reference 2.1.&lt;br /&gt;
&lt;br /&gt;
4.1.6 Kinematic Viscosity&lt;br /&gt;
&lt;br /&gt;
The coefficient of viscosity, la, defines the shecring stresses in a gas or liquid and is sometimes called the resistance to continuous deformation. In aerodynamics, the coefficient of viscosity is combined with the mass density to form the kinematic viscosity, v, where&lt;br /&gt;
&lt;br /&gt;
coefficient of viscosity, g' 0.0001576 ft2/s at sea level&lt;br /&gt;
&lt;br /&gt;
mass density, P&lt;br /&gt;
&lt;br /&gt;
The kinematic viscosity, v, is altitude dependent and is used to calculate the Reynolds number, Re.&lt;br /&gt;
&lt;br /&gt;
4.1.7 Reynolds Number&lt;br /&gt;
&lt;br /&gt;
The Reynolds number, Re, defines the relationship of mass forces to viscous friction forces in liquids and gases. It is calculated as&lt;br /&gt;
&lt;br /&gt;
Re = v I velocity (ft/s) characteristic length (ft)&lt;br /&gt;
&lt;br /&gt;
V kinematic viscosity (ft2/s)&lt;br /&gt;
&lt;br /&gt;
Reynolds number is an important criterion in subsonic, noncompressible flow, and allows comparison of model tests with full-scale flight tests. A Reynolds number effect on parachutes working in separated, turbulent flow has not yet been established, as shown in section 5.2. The following chart shows the Reynolds numbers for various air vehicles.&lt;br /&gt;
&lt;br /&gt;
Drogue Main WIT&lt;br /&gt;
&lt;br /&gt;
Sbe Ihns=ec t Glider D -4 2 par ute model&lt;br /&gt;
&lt;br /&gt;
Re 6-103 2.5-106 24.106 100&amp;quot;106 50&amp;quot;106 20&amp;quot;106 2.106&lt;br /&gt;
&lt;br /&gt;
4.1.8 Mach Number&lt;br /&gt;
&lt;br /&gt;
Mach number is an important parameter of supersonic flight; it states how much faster than the speed of sound the air vehicle travels.&lt;br /&gt;
&lt;br /&gt;
Mach Number, M= &lt;br /&gt;
&lt;br /&gt;
The speed of sound is the velocity at which a pressure disturbance, such as the sound of the human voice, travels in any medium. The speed of sound varies considerably in different gases, liquids, and metals.&lt;br /&gt;
&lt;br /&gt;
The speed of sound depends on temperature and the chemical composition of the medium, A widely used equation for speed of sound in air is&lt;br /&gt;
&lt;br /&gt;
The speed of sound changes with altitude, as temperature (see Figure 3-1). The drag of streamlined bodies such as missiles, airfoils, and airplanes increases considerably as their velocities approach Mach 1. Depending on the configuration of the body, supersonic compressibility effects may in the 0.75• to 0.85•Mach range, causing local supersonic flow, shock waves, flow separation, and concomitant increases in drag and changes in stability.&lt;br /&gt;
&lt;br /&gt;
Parachutes that operate in separated flow over the entire velocity range do not show the typical drag increase when operating close to or beyond Mach 1. Supersonic parachute behavior is discussed in detail in section 5.8.&lt;br /&gt;
&lt;br /&gt;
== '''4.2 CONTINUITY LAW AND BERNOULLI EQUATION''' ==&lt;br /&gt;
4.2.1 Continuity L.aw&lt;br /&gt;
&lt;br /&gt;
Air is thought to flow in layers called streamlines. Figure 4-1 shows streamlines as layers of air without air transfer between individual layers. ne air is shown as being incompressible, a valid assumption for subsonic flow.&lt;br /&gt;
&lt;br /&gt;
  	&lt;br /&gt;
&lt;br /&gt;
If exchange of air does not occur across the streamline boundaries, the amount of air entering the streamline at point 1 must also exit at point 2. as shown in Figure 4*1. Because the cross section at point 2 is smaller than the cross section at point 1, the air must exit at a higher velocity. The following equation defines this condition:&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
this equation which governs the now in and around a body in gases and liquids, is important in aerodynamics and is called the continuity law. For imcompressilble subsonic now, it can be simplified to &lt;br /&gt;
&lt;br /&gt;
Whenever the cross section narrows. the velocity increases; when the cross section widens, the velocity decreases.&lt;br /&gt;
&lt;br /&gt;
4.2.2 Bernoulli Equation&lt;br /&gt;
&lt;br /&gt;
Figure 4-2 illustrates a streamline with the cross section, S, the velocity, v, and the pressure, p. If the air is incompressible, the downstream is v + Av. and the pressure is p + AP. If the air is inviscid, the inertia forces caused by the acceleration of air from v to v + Av must be balanced by differential pressure forces.&lt;br /&gt;
&lt;br /&gt;
    	                                       	&lt;br /&gt;
&lt;br /&gt;
FIGURE 4-2 Pressure and Velocity Distribution in a Streamline Element.&lt;br /&gt;
&lt;br /&gt;
The following equation can be written&lt;br /&gt;
&lt;br /&gt;
Simplified, the above equation yields&lt;br /&gt;
&lt;br /&gt;
'''dp = -pvdv'''&lt;br /&gt;
&lt;br /&gt;
the above equation allows the following consideration: If p is pressure, then 1/2 pv&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; and C must also be pressure. The equation 1/2 pv&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; includes a and is referred to as the dynamic pressure. or sometimes velocity as or impact pressure.&lt;br /&gt;
&lt;br /&gt;
Pressure, p, is defined as static pressure; 1/2 pv&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; as dynamic pressure; and the sum of both, C, as the total pressure or&lt;br /&gt;
&lt;br /&gt;
p + 1/2pv&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; = H&lt;br /&gt;
&lt;br /&gt;
and&lt;br /&gt;
&lt;br /&gt;
where H is the total pressure of the system, lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Dynamic pressure, q, is a frequently used quantity in aerodynamics:&lt;br /&gt;
&lt;br /&gt;
q = 1/2 pv&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
q = dynamic pressure, lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
p =  air density, slugs/ft&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
v =  velocity at a point of undisturbed flow, ft/s&lt;br /&gt;
&lt;br /&gt;
The following formulas are used for calculating the sea-level dynamic pressure if the velocity is given in ft/s, knots, mph, or km/h, respectively:&lt;br /&gt;
&lt;br /&gt;
                                              &lt;br /&gt;
&lt;br /&gt;
'''4.3 NEWTON'S THREE OF MOTION'''&lt;br /&gt;
&lt;br /&gt;
Engineering mechanics are governed by the following three laws of Isaac Newton:&lt;br /&gt;
&lt;br /&gt;
1.  A body remains at rest or in an unaccelerated state of motion unless acted upon.&lt;br /&gt;
&lt;br /&gt;
2.  A force acting upon a body will produce an acceleration in the direction of the force.&lt;br /&gt;
&lt;br /&gt;
3.  An action in one direction will produce an equal reaction in the opposite direction.&lt;br /&gt;
&lt;br /&gt;
The first law is self-explanatory. The second law may be expressed by the equation&lt;br /&gt;
&lt;br /&gt;
F = m * a&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
F = force in pounds acting on the mass, 1b&lt;br /&gt;
&lt;br /&gt;
m = mass of body that the force is acting upon, slugs&lt;br /&gt;
&lt;br /&gt;
a = acceleration in ft/s2 resulting from the force, F&lt;br /&gt;
&lt;br /&gt;
The mass, m, of a body is obtained by&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
W = weight of the body, lb&lt;br /&gt;
&lt;br /&gt;
g = acceleration of gravity, ft/s2&lt;br /&gt;
&lt;br /&gt;
The mass, therefore, has the dimension of&lt;br /&gt;
&lt;br /&gt;
This unit of mass is the slug.&lt;br /&gt;
&lt;br /&gt;
the equation of Newton's second law can now be written&lt;br /&gt;
&lt;br /&gt;
                                        	&lt;br /&gt;
&lt;br /&gt;
The factor a/g is frequently called the load factor, G, and tells how much larger a force is than a force equivalent to the weight of the body. It is customary in parachute work to state that the maximum parachute force allowed is G • W or (a]g) • W. It is appropriate to write&lt;br /&gt;
&lt;br /&gt;
Maximum allowable parachute force,&lt;br /&gt;
&lt;br /&gt;
Figure 4-3 illustrates Newton's third law, explaining the principle of the rocket that can produce thrust in a perfect vacuum.&lt;br /&gt;
&lt;br /&gt;
A mass, m. ejected from a rocket at the velocity, v, per unit time, t, will produce a force, F, which in turn will create a reaction force, R. of equal magnitude but acting in the opposite direction.&lt;br /&gt;
&lt;br /&gt;
=== 4.4 FORCES ACTING ON A BODY MOVING THROUGH AIR ===&lt;br /&gt;
4.4.1 Symmetrical Body&lt;br /&gt;
&lt;br /&gt;
A body moving through air experiences forces caused by air pressure acting on the body. fie same forces if the body moves through air, such as a descending parachute, or if the body is fixed and the air moves against the body, such as a parachute or an airfoil in a wind tunnel (Figure 44).&lt;br /&gt;
&lt;br /&gt;
         	 &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
A stable parachute in a wind tunnel experiences only the force called &amp;quot;drag&amp;quot; in the direction of the airflow. drag force, D, is calculated to&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
D = drag, 1b&lt;br /&gt;
&lt;br /&gt;
Q = dynamic pressure, lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
S = total surface area of the parachute canopy, ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt; = coefficient of drag.  dimensionless&lt;br /&gt;
&lt;br /&gt;
the dynamic pressure, q, can be calculated from section 4.2.2. The surface area of the canopy, S, is selected as a reference area. The drag coefficient  C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, is a form factor that indicates the drag characteristic of a specific shape. Most aerodynamic bodies are designed for low drag or a low drag coefficient. Parachutes, generally, are designed for high drag; therefore, a high drag coefficient is desirable. this difference in drag is demonstrated by the two bodies shown in Figure 4-5.&lt;br /&gt;
&lt;br /&gt;
            	&lt;br /&gt;
&lt;br /&gt;
Both bodies have the same cross section perpendicular to the airflow. The cylindrical. streamlined body has a smooth airflow over its total body length, resulting in a drag coefficient. C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, of 0.05 to 0.1, depending on slenderness ratio, surface roughness, and shape. The drag coefficient of all streamlined bodies is much affected by Reynolds number and Mach number. fie open hemisphere, which is similar to a parachute canopy, has a drag coefficient, C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, of 1.3 to 1.4 for the same body cross section. The difference in drag is explained by the smooth airflow around the streamlined body and a separated. turbulent flow around the open hemisphere. The drag of bodies with separated flow, like parachute canopies, is little affected by Reynolds number.&lt;br /&gt;
&lt;br /&gt;
4.4.2 Airflow Around an Asymmetrical Body (Airfoil)&lt;br /&gt;
&lt;br /&gt;
Figure 4-6 shows an airfoil fixed at an angle of attack, a. against the airflow in a wind tunnel. This airfoil creates a drag force, D, in the direction of the flow; a lift force L perpendicular to the direction of the flow; and a moment, M. around the attachment point of the airfoil. fie sign convention of moments and forces shown are positive. Lift and drag can be combined for the resultant force, R.&lt;br /&gt;
&lt;br /&gt;
FIGURE. 44, Wind-Tunnel Forces Acting on an Airfoil.&lt;br /&gt;
&lt;br /&gt;
The lift, L is calculated&lt;br /&gt;
&lt;br /&gt;
L = q * S * C&amp;lt;sub&amp;gt;L&amp;lt;/sub&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
L = measured lift, 1b&lt;br /&gt;
&lt;br /&gt;
q = dynamic pressure, lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
s = reference area, ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
CL = lift coefficient, dimensionless&lt;br /&gt;
&lt;br /&gt;
The moment is&lt;br /&gt;
&lt;br /&gt;
       M = q * S * c&amp;lt;sub&amp;gt;m&amp;lt;/sub&amp;gt; * c&lt;br /&gt;
&lt;br /&gt;
Where&lt;br /&gt;
&lt;br /&gt;
The reference area, S is defined by agreement, For streamlined bodies, the maximum body cross section is used. Airfoils use the planform of the wing, and parachutes use the canopy surface area. The selection of the wing planform and the parachute surface area as references was made for practical reasons. &amp;lt;sup&amp;gt;e&amp;lt;/sup&amp;gt;me wing planform for a specific wing is fixedt whereas the cross section of the wing in the direction of the flow changes with the angle of attack. Similarly, the surface area of the parachute canopy is fixed; however, the frontal projected area of the inflated parachute canopy changes with airspeed, porosity, line length, and tm of parachute.&lt;br /&gt;
&lt;br /&gt;
Forces and moments acting on an airfoil or a parachute canopy may be presented in several ways. The two most frequently used methods, as shown in Figure 4-7, are with forces oriented to the of flight and with forces oriented to the axis of the airfoil.&lt;br /&gt;
&lt;br /&gt;
me tangential force, and the normal force, N, are calculated&lt;br /&gt;
&lt;br /&gt;
T = C&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; * S * q&lt;br /&gt;
&lt;br /&gt;
        	&lt;br /&gt;
&lt;br /&gt;
and&lt;br /&gt;
&lt;br /&gt;
      	N = C&amp;lt;sub&amp;gt;N&amp;lt;/sub&amp;gt; * S * q&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
C&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; = tangential force coefficient, dimensionless&lt;br /&gt;
&lt;br /&gt;
C&amp;lt;sub&amp;gt;N&amp;lt;/sub&amp;gt; = normal force coefficient, dimensionless&lt;br /&gt;
&lt;br /&gt;
The resultant force, R, and the moment, M, in both presentations have the same direction and the same magnitude. The airflow fixed system is preferred for aerodynamic performance calculations, and the airfoil fixed system for wing stress calculations. me aerodynamic coefficients C&amp;lt;sub&amp;gt;L&amp;lt;/sub&amp;gt;, C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, C&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, C&amp;lt;sub&amp;gt;N&amp;lt;/sub&amp;gt;, and C&amp;lt;sub&amp;gt;m&amp;lt;/sub&amp;gt; can easily be determined in wind•tunnel measurements.&lt;br /&gt;
&lt;br /&gt;
Figure 4-8 shows the relationship of both force systems on a parachute. By definition, a negative moment is stabilizing, as illustrated in Figure 4-8. It is interesting to note that in Europe the stabilizing moment is defined as positive. Wind-tunnel installations frequently measure normal and tangential force instead of lift and drag. If α, T, and N are known, the drag D, can be calculated&lt;br /&gt;
&lt;br /&gt;
D = T*cosα + N * sinα&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
For a parachute with an angle of attack, a, equal to zero, the drag force and the tangential force are synonymous.&lt;br /&gt;
&lt;br /&gt;
Figure 4-9 shows the coefficients C&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, and C&amp;lt;sub&amp;gt;m&amp;lt;/sub&amp;gt; versus angle of attack for stable and unstable parachutes.&lt;br /&gt;
&lt;br /&gt;
The coefficient presentation shows two interesting facts. ne slope of the moment coefficient curve, dC&amp;lt;sub&amp;gt;m&amp;lt;/sub&amp;gt;/dα, for the unstable parachute is positive between -25 degrees and + 25 degrees; this is, by definition, destabilizing. This parachute will oscillate approximately ± 25&lt;br /&gt;
&lt;br /&gt;
FIGURE 4-9. Coefficients C&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, and C&amp;lt;sub&amp;gt;M&amp;lt;/sub&amp;gt; Versus Angle of Attack, α, for a Stable and Unstable Parachute.&lt;br /&gt;
&lt;br /&gt;
degrees. The slope of the moment, dC&amp;lt;sub&amp;gt;m&amp;lt;/sub&amp;gt;/dα, for the stable parachute is negative over the total angle of attack; this is, by definition, stabilizing. The steeper the negative dC&amp;lt;sub&amp;gt;m&amp;lt;/sub&amp;gt;/dα slope, the greater is the stabilizing tendency of the parachute, and the better is its damping capability against unstabilizing forces such as sudden gusts of wind.&lt;br /&gt;
&lt;br /&gt;
Figure 4-10, from Reference 4.1, demonstrates the effect of airflow around a cylinder and an airfoil. The circulation around a rotating cylinder creates lift caused by the increase in velocity on one side of the cylinder and a decrease on the opposite side. This is called the Magnus effect.&lt;br /&gt;
&lt;br /&gt;
= 4.5 EQUILIBRIUM OF FORCES IN STUDY DESCENT OR FLIGHT =&lt;br /&gt;
4.5.1 Parachute in Steady Descent&lt;br /&gt;
&lt;br /&gt;
A stable parachute in unaccelerated descent has an equilibrium between the total drag of the parachute and the load, Dr, and the weight of the load and the parachute assembly, WT (Figure 4-11). For steady descent&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
D&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; = total drag, 1b&lt;br /&gt;
&lt;br /&gt;
D&amp;lt;sub&amp;gt;P&amp;lt;/sub&amp;gt; = drag of parachute, 1b&lt;br /&gt;
&lt;br /&gt;
W&amp;lt;sub&amp;gt;C&amp;lt;/sub&amp;gt; = weight of load. 1b&lt;br /&gt;
&lt;br /&gt;
In most cases, the drag of the load can be neglected in relation to the large drag of the parachute, With drag, D — (C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;S)&amp;lt;sub&amp;gt;p&amp;lt;/sub&amp;gt; • p/2• v&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; and D&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; = W&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;. and solving for v, the important equation for rate of descent, v&amp;lt;sub&amp;gt;e&amp;lt;/sub&amp;gt;, is obtained,&lt;br /&gt;
&lt;br /&gt;
Rate of descent,&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
FIGURE 4-11. Forces Acting on a Parachute in Steady Descent.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
or in parachute terminology for rate of descent at sea level&lt;br /&gt;
&lt;br /&gt;
and rate of descent at any altitude&lt;br /&gt;
&lt;br /&gt;
== For 1/, see column 4 in Table 3-3, ==&lt;br /&gt;
In the equation for rate of descent. V&amp;lt;sub&amp;gt;e&amp;lt;/sub&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
W&amp;lt;sub&amp;gt;T =&amp;lt;/sub&amp;gt; weight of load and parachute assembly, 1b&lt;br /&gt;
&lt;br /&gt;
S&amp;lt;sub&amp;gt;o&amp;lt;/sub&amp;gt; = canopy surface area, ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;&lt;br /&gt;
&lt;br /&gt;
C&amp;lt;sub&amp;gt;Do&amp;lt;/sub&amp;gt; = parachute drag coefficient related to S&amp;lt;sub&amp;gt;o&amp;lt;/sub&amp;gt;&lt;br /&gt;
&lt;br /&gt;
p = air density at a specific altitude in slugs/ft&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;, as shown in Table 3-3&lt;br /&gt;
&lt;br /&gt;
During descent from altitude, the parachute system is constantly decelerated because of the increasing air density. This can be ignored for slowly descending main parachutes. However, for drogue chute systems that descend at 200 ft/s or faster, the constant deceleration may result in velocities 3 to 5% higher than the steady rate of descent.&lt;br /&gt;
&lt;br /&gt;
4.5.2 Gliding Parachutes&lt;br /&gt;
&lt;br /&gt;
Figure 4-12 shows the balance of forces on a gliding parachute. The total weight of the system, W&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; . must be balanced by the resultant force. R. However, a lifting force is required for glide. To satisfy the force balance&lt;br /&gt;
&lt;br /&gt;
R = C&amp;lt;sub&amp;gt;R&amp;lt;/sub&amp;gt; * S * p/2 * v&lt;br /&gt;
&lt;br /&gt;
Trajectory velocity, V&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, is calculated&lt;br /&gt;
&lt;br /&gt;
Horizontal velocity is calculated&lt;br /&gt;
&lt;br /&gt;
V&amp;lt;sub&amp;gt;H&amp;lt;/sub&amp;gt; = V&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; • cosø, and vertical velocity, v&amp;lt;sub&amp;gt;v&amp;lt;/sub&amp;gt; = V&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt; • sinø&lt;br /&gt;
&lt;br /&gt;
The glide ratio is obtained from&lt;br /&gt;
&lt;br /&gt;
Analysis of Figure 4-12 indicates that the larger the ratio of lift to drag, the better the glide ratio, I./D A high resultant coefficient, C&amp;lt;sub&amp;gt;R&amp;lt;/sub&amp;gt;, results in a low glide or trajectory V&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, desirable for landing. A small C&amp;lt;sub&amp;gt;R&amp;lt;/sub&amp;gt; results in a high glide velocity, V&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, which is desirable for flying toward a target, compensating for head winds, or covering a distance quickly. Generally, gliding parachutes follow the same aerodynamic rules as low-aspect-ratio wings.&lt;br /&gt;
&lt;br /&gt;
           	   	&lt;br /&gt;
&lt;br /&gt;
FIGUR E 4-12, Forces Acting on a Gliding Parachute&lt;br /&gt;
&lt;br /&gt;
4.5-3 Parasite Drag and Induced Drag&lt;br /&gt;
&lt;br /&gt;
The drag acting on a lift-producing air vehicle, such as a gliding parachute or an aircraft, has two primary components: the parasite drag, D&amp;lt;sub&amp;gt;P&amp;lt;/sub&amp;gt; , and the induced drag. D&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Parasite drag is produced by the form drag from individual components such as the suspension lines, canopy, and the jumper of a gliding parachute, and the fuselage, tail sectiora, and control surfaces of an airplane. Large surfaces produce surface friction drag as part of the parasite drag.&lt;br /&gt;
&lt;br /&gt;
Induced drag is caused by the lifting action of the parachute canopy or the aircraft wing. Section 4.7 includes books with detailed discussions of induced drag.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Total drag, D&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;, can be defined as&lt;br /&gt;
&lt;br /&gt;
or, in the coefficient form&lt;br /&gt;
&lt;br /&gt;
The parasite drag, D&amp;lt;sub&amp;gt;p&amp;lt;/sub&amp;gt;, and the coefficient, C&amp;lt;sub&amp;gt;DP&amp;lt;/sub&amp;gt;, can be determined in wind-tunnel tests or calculated as the sum of the individual component drags.&lt;br /&gt;
&lt;br /&gt;
The induced drag coefficient, C&amp;lt;sub&amp;gt;Di&amp;lt;/sub&amp;gt; , of a gliding parachute canopy or a wing profile can be calculated&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
C = coefficient of induced drag, dimensionless&lt;br /&gt;
&lt;br /&gt;
The expression b&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;/S is defined as the aspect ratio of a wing or parachute with the notation AR b&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;/S. Therefore&lt;br /&gt;
&lt;br /&gt;
== '''                       ''' 	 ==&lt;br /&gt;
The equation for induced drag indicates that increasing the aspect ratio, AR, reduces the induced drag coefficient,  , and therefore reduces the drag, D. ms, in turn, increases the glide ratio, L/D. Increasing the glide ratio by increasing the aspect ratio is optimized on high-performance sailplanes with aspect ratios higher than 20. Increasing the glide ratio of gliding parachutes by increasing the aspect ratio has limitations, which are discussed in section 5.9.&lt;br /&gt;
&lt;br /&gt;
4.5.4 Aircraft in Horizontal Flight&lt;br /&gt;
&lt;br /&gt;
Figure 4-13 shows forces and moments on an aircraft in steady, horizontal flight. In steady, horizontal flight, an equilibrium exists between all forces and moments acting on the aircraft. Lift on the wing and tail, L&amp;lt;sub&amp;gt;W&amp;lt;/sub&amp;gt; and L&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;. and the weight of the aircraft, W&amp;lt;sub&amp;gt;A&amp;lt;/sub&amp;gt;, balance in the vertical plane. Thrust, T and drag. D, balance each other in the horizontal plane, and the positive or negative moment, M, is balanced by the positive or negative lift of the tail multiplied by the moment arm, L&amp;lt;sub&amp;gt;T&amp;lt;/sub&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
FIGURE 4-13. Forces and Moments Acting on an Aircraft in Steady night,&lt;br /&gt;
&lt;br /&gt;
Any imbalance in these forces results in descent or climb in the vertical plane or faster or slower speed in the horizontal plane. A change in the lift of the elevator initiates climb or descent. Thrust, T, is the prime contributor for climb or descent and faster or slower speed, However, a balance of forces must always be maintained for horizontal flight or steady rate oi climb or descent.&lt;br /&gt;
&lt;br /&gt;
== 4.6 WIND-TUNNEL TESTING OF PARACHUTES ==&lt;br /&gt;
Wind tunnels are an effective tool for testing air vehicles and air-vehicle components and have been used successfully for testing parachutes and parachute systems. Experience has shown that certain rules apply for the wind-tunnel testing of parachutes. Small parachutes manufactured from textiles cannot be made sufficiently similar to large parachutes in geometric design and flexibility, Lightweight material. required to obtain design similarity, is difficult to manufacture or is unobtainable.&lt;br /&gt;
&lt;br /&gt;
One cardinal rule has been established through many years of parachute wind-tunnel testing: A modification that changes the performance of a model parachute in wind-tunnel testing produces the same type and percentage of performance change in a large parachute. This rule is true for drag. stability, and opening-force characteristics.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
4.6.1 Blowers&lt;br /&gt;
&lt;br /&gt;
The simple air blower (Figure 4-14) is a proven tool for preliminary parachute testing of a chiefly qualitative nature. Unless special test conditions prevail, parachutes tested should be a minimum of 1.5 to 2 feet in diameter to obtain meaningful results.&lt;br /&gt;
&lt;br /&gt;
                                                                    &lt;br /&gt;
&lt;br /&gt;
 FIGURE 4-14. Typical Air Blower.&lt;br /&gt;
&lt;br /&gt;
An air blower is a preliminary test too! because it permits quick parachute• configuration changes and excellent visual observation.&lt;br /&gt;
&lt;br /&gt;
4.6.2 Open-Throat, No-Return Wind Tunnels&lt;br /&gt;
&lt;br /&gt;
The open-throat, no-return wind tunnel shown in Figure 4-15 permits exact measurements if parachutes of sufficient size are used. Parachutes 3 feet or more in diameter are well suited for obtaining good, quantitative test results.&lt;br /&gt;
&lt;br /&gt;
              FIGURE 4-15. Open-Throat, No-Return Wind Tunnel&lt;br /&gt;
&lt;br /&gt;
In air blowers and open-throat wind tunnels, the velocity at the skirt of the parachute (Section a-a of Figures 4-14 and 4-15) is lower than the velocity at the nozzle exit of the wind tunnel (Section b&amp;lt;sup&amp;gt;-&amp;lt;/sup&amp;gt;b of Figures 4-14 and 4-15), Care must be taken to measure the parachute test&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
velocity at Section a-a and not at Section b-b, the customary attachment point for airfoils and models.&lt;br /&gt;
&lt;br /&gt;
Wind tunnels frequently cannot test at the descent velocity of most main parachutes of 20 to 30 feet per second. Obtaining proper test results at this low is hampered by a poor velocity distribution in the wind-tunnel-test section, and by the weight of the test parachute. The latter has a tendency to pull the parachute downward, thereby providing a negative angle of attack, lusting unstable parachutes at higher presents the problem that the drag coefficient C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;, of unstable parachutes is sensitive. The drag coefficient of unstable parachutes is described in section 5.2.&lt;br /&gt;
&lt;br /&gt;
An open-throat wind tunnel permits quick changes in parachute configuration, such as changing the suspension and reefing line lengths. Large open-throat wind tunnels that are not sealed against outside elements suffer atmospheric problems such as fog formation in the test section.&lt;br /&gt;
&lt;br /&gt;
4.6.3 Closed-Throat, Full-Return Wind Tunnel&lt;br /&gt;
&lt;br /&gt;
Figure 4-16 is a drawing of a full-return, closed-throat wind tunnel. fic full-return, closed-throat wind tunnel is generally considered best suited for obtaining good. qualitative, aerodynamic data, since it has a uniform distribution in the test section. A disadvantage is the difficulty in gaining access to the test section for changing the parachute configuration.&lt;br /&gt;
&lt;br /&gt;
FIGURE 4-16. Closed-Throat, Full-Reuurn Wind Tunnel.&lt;br /&gt;
&lt;br /&gt;
4.6.4 General Comments for Wind-Tunnel Testing of Parachutes&lt;br /&gt;
&lt;br /&gt;
1. Parachute models for wind-tunnel testing should be as large and as similar as possible in geometry and flexibility to full-scale parachutes. Parachutes of less than 1.5 feet in diameter usually lack geometric similarity and material flexibility, which results in inflation characteristics and dissimilar inflated shapes.&lt;br /&gt;
&lt;br /&gt;
2.  The finished dimensions of model parachutes must be measured as accurately as possible to determine the nominal diameter, Do, and the surface area, So. Model parachutes will shrink from 5 to 10% during manufacture because of sewing take-up, which results in a notable difference in the dimensions between the drawing and the completed parachute.&lt;br /&gt;
&lt;br /&gt;
3.  Wind&amp;lt;sup&amp;gt;-&amp;lt;/sup&amp;gt;tunnel tests of parachutes are excellent for comparing different models and modifications: also, they are the most effective means for measuring coefficients of lift, drag. and normal and tangential forces, as well as for determining the load coefficient, for infinite load.&lt;br /&gt;
&lt;br /&gt;
4.  In wind-tunnel tests, velocity decay does not occur during parachute inflation and operation; this is defined as testing under &amp;quot;infinite mass condition. &amp;quot; First-stage drogue chutes and parachutes with a canopy loading, W/C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;S. in excess of 100 lb/ft&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; approach this condition. Low-canopy-loading main parachutes with rates of descent of 20 to 30 ft/s have a large velocity decay during opening, which requires careful interpretation of the opening-force data obtained in wind-tunnel tests.&lt;br /&gt;
&lt;br /&gt;
5.  In the past, to avoid wind-tunnel blockage and questionable test data. the diameter of a test parachute could not exceed about 5 to 6% of the wind-tunnel test section area. Recent Sandia investigations of single and clustered ribbon parachutes with wind-tunnel blockage ratios of up to 30% have resulted in correction methods that make it possible to test much larger parachutes (Reference 4.2).&lt;br /&gt;
&lt;br /&gt;
= 4.7 REFERENCE MATERIAL =&lt;br /&gt;
4.1 H. H. Hurt. Aerodynamics for Naval Aviators Navy Manual NAVWEPS 00 80T 80. Chief of Naval Operations, Aviation Training Division.&lt;br /&gt;
&lt;br /&gt;
4.2 J, M. Macha and R J. Buffington. &amp;quot;Wall-Interference Corrections for Parachutes in a Closed Wind Tunnel.&amp;quot; AIM Paper, April 1989. (AIM 89-0900-cp.)&lt;br /&gt;
&lt;br /&gt;
For readers interested in a more detailed study of aerodynamics, the following books are recommended.&lt;br /&gt;
&lt;br /&gt;
4.3 J, H, Dwinnel, Principle of Aerodynamics. McGraw-Hill     	Co., New York, 1949.&lt;br /&gt;
&lt;br /&gt;
4.4 J. Morane. Introduction to Theoretical and Computational Aerodynamics. John Wiley &amp;amp; Sons.&lt;br /&gt;
&lt;br /&gt;
4.5 R.S. Shevell. Fundamentals of Flight. Prentice-Hall. 1983.&lt;br /&gt;
&lt;br /&gt;
4.6 J. D. Anderson, Jr. Introduction to Flights, ILS Engineering and History. McGraw-Hill Book co., New York 1978.&lt;br /&gt;
&lt;br /&gt;
4.7 D. J. Cockrell. The Aerodynamics of Parachutes.&amp;quot; AGARDograph No. 6295, available from NASA Langley Research Center, M/S 1M), Hampton, Va., 236.&lt;/div&gt;</summary>
		<author><name>TuanHTruong</name></author>
	</entry>
	<entry>
		<id>https://mediawiki.aerodecelerator.org/index.php?title=Recovery_System_Design&amp;diff=24</id>
		<title>Recovery System Design</title>
		<link rel="alternate" type="text/html" href="https://mediawiki.aerodecelerator.org/index.php?title=Recovery_System_Design&amp;diff=24"/>
		<updated>2024-05-03T20:43:39Z</updated>

		<summary type="html">&lt;p&gt;TuanHTruong: Straight copy past of chapter 7 into editor. Will need line-by-line corrections. Many pages were images that were not pasted it, and therefore, will need line by line recreation.&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;DESIGN OF A PARACHUTE RECOVERY AND LANDING SYSTEM&lt;br /&gt;
&lt;br /&gt;
This chapter deals with the design of a parachute recovery and landing attenuation system for a military reconnaissance drone. The prime emphasis in the design of this system is on undamaged recovery of the drone from the total flight performance envelope during the development and test phase, on undamaged recovery after a completed mission during military operations, and on multiple use of the recovery system. An engineering team conducts performance and system analyses and chooses what recovery concept to use, what types of parachutes to select for high-speed deceleration and for final recovery, and what impact-attenuation system is best for the particular application. This chapter covers the selection process for concepts and components. Different engineers may make different selections based on experiences with particular types of parachutes or deployment concepts; experience is always a viable reason for selecting a particular approach. However, using the selection criteria shown in Figure 2-6. the designer must put reliability of operation, undamaged recovery, reusability of the landing system, and minimum weight and volume at the top of the list of requirements. &lt;br /&gt;
&lt;br /&gt;
7.1 REQUIREMENTS  &lt;br /&gt;
&lt;br /&gt;
7.1.1 System Requirements &lt;br /&gt;
&lt;br /&gt;
An unmanned air vehicle used for military reconnaissance must be recovered after a completed mission in rough terrain, undamaged and ready for multiple reuse. The recovery system must be able to &lt;br /&gt;
1. Recover the air vehicle after the completed mission when the vehicle has landed in rough terrain at altitudes from sea level to 5000 feet.&lt;br /&gt;
2. Recover the drone during the engineering test phase from all controlled and uncontrolled flight conditions. &lt;br /&gt;
3. Serve as a range-safety device to prevent the air vehicle from leaving the boundaries of the test range. &lt;br /&gt;
&lt;br /&gt;
The air vehicle has a takeoff weight of 7200 pounds and a landing weight, after the i completed mission, of 4800 pounds. Undamaged landing shall be possible in rough terrain with rocks up to 8 inches in diameter. Replacement parts and refurbishment cost shall be kept to a minimum.  &lt;br /&gt;
&lt;br /&gt;
7.1.2 Requirements for Normal Operation &lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|Drone weight at recovery after completed mission&lt;br /&gt;
|W&amp;lt;sub&amp;gt;d&amp;lt;/sub&amp;gt; = 4800 lb&lt;br /&gt;
|-&lt;br /&gt;
|Recovery velocity&lt;br /&gt;
|v&amp;lt;sub&amp;gt;o&amp;lt;/sub&amp;gt; = 150 to 200 KEAS&lt;br /&gt;
|-&lt;br /&gt;
|Minimum recovery altitude&lt;br /&gt;
|H&amp;lt;sub&amp;gt;o&amp;lt;/sub&amp;gt; = 2000 ft above ground level (AGL)&lt;br /&gt;
|-&lt;br /&gt;
|Maximum ground level&lt;br /&gt;
|H = 5000 ft&lt;br /&gt;
|-&lt;br /&gt;
|Maximum allowable total parachute force&lt;br /&gt;
|F&amp;lt;sub&amp;gt;o&amp;lt;/sub&amp;gt; = 16,000 lb&lt;br /&gt;
|-&lt;br /&gt;
|Maximum allowable impact deceleration at landing&lt;br /&gt;
|a = 9.0 ''g''&amp;lt;nowiki/&amp;gt;'s&lt;br /&gt;
|} &lt;br /&gt;
&lt;br /&gt;
7.1.3 Requirements for Emergency Operation &lt;br /&gt;
&lt;br /&gt;
Emergency operation includes recovery during the test phase from takeoff to landing and also includes recovery for range-safety reasons. &lt;br /&gt;
&lt;br /&gt;
Drone weight at takeoff .................................. Wdma = 7200 lb &lt;br /&gt;
&lt;br /&gt;
Maximum recovery velocity at mean sea level (MSL) ................................... vo = 490 KEAS &lt;br /&gt;
&lt;br /&gt;
Maximum recovery velocity at 38,000 to 50,000 ft altitude ........................................ vo = 1.5 Mach &lt;br /&gt;
&lt;br /&gt;
Maximum dynamic pressure .............................. qmm = 812 lb/ft2 &lt;br /&gt;
&lt;br /&gt;
Maximum allowable parachute force ........................ F0 = 22,000 lb  &lt;br /&gt;
&lt;br /&gt;
7.1.4 Requirements Analysis &lt;br /&gt;
&lt;br /&gt;
Three primary requirements pace the design of the recovery system: &lt;br /&gt;
&lt;br /&gt;
1. The drone must be able to land in rocky but level terrain without damage. &lt;br /&gt;
&lt;br /&gt;
2. Refurbishment cost and time shall be kept to a minimum. &lt;br /&gt;
&lt;br /&gt;
3. Recovery must be possible from all flight conditions during the flight test phase, including cases where the out-of-control drone flies off the range.  &lt;br /&gt;
&lt;br /&gt;
7.2 LANDING ANALYSIS AND IMPACT-ATTENUATION SYSTEM &lt;br /&gt;
&lt;br /&gt;
7.2.1 Landing Analysis &lt;br /&gt;
&lt;br /&gt;
Three known recovery concepts prevent damage during landing in rocky terrain: &lt;br /&gt;
&lt;br /&gt;
1. Midair retrieval.&lt;br /&gt;
&lt;br /&gt;
2. Dual air bags or dual frangibles.&lt;br /&gt;
&lt;br /&gt;
3. Retrorockets combined with small, nondeflatable air bags.&lt;br /&gt;
&lt;br /&gt;
The need for retrieval helicopters or retrieval aircraft makes Method 1, midair retrieval, impractical. The other two methods are affected by the deceleration distance required to meet the 9-g limit. &lt;br /&gt;
&lt;br /&gt;
In section 6.8 of this manual, the required deceleration distance(s) is determined to be&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;s=\frac{{V_{e_1}}^2-{V_{e_2}}^2}{2g(n\eta-1)}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;{V_{e_1}}&amp;lt;/math&amp;gt; = velocity of the drone descending on the parachute (rate of descent), ft/s&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;V_{e_2}&amp;lt;/math&amp;gt; = permissible impact velocity, ft/s&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;g&amp;lt;/math&amp;gt; = acceleration of gravity, ft/s2&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\eta&amp;lt;/math&amp;gt; = effectiveness of the impact attenuation system used, dimensionless&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;n&amp;lt;/math&amp;gt; = allowable impact deceleration, ratio &amp;lt;math&amp;gt;n=\frac{a}{g}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Figure 6-68 of Chapter 6 shows the range of various impact attenuation systems as a&lt;br /&gt;
&lt;br /&gt;
function of rate of descent and allowable ground impact deceleration. The information&lt;br /&gt;
&lt;br /&gt;
indicates that air bags may be the most practical concept for this application. A cursory&lt;br /&gt;
&lt;br /&gt;
analysis indicates that a rate of descent of 25 ft/s at 5000 fee: altitude will result in a close to&lt;br /&gt;
&lt;br /&gt;
optimum weight ratio of the combined parachute air bag system (see Figure 6-83). Properly&lt;br /&gt;
&lt;br /&gt;
designed air bags will have an effectiveness of 65% as shown in the stroke-pressure diagram in&lt;br /&gt;
&lt;br /&gt;
Figure 6-78 and allow ground contact or final velocity of close to 0 ft/s.&lt;br /&gt;
&lt;br /&gt;
0&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.3&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
With these assumptions, the required effective air bag deceleration stroke is obtained&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
This deceleration distance is too short for a parachute retrorocket system because of the&lt;br /&gt;
&lt;br /&gt;
required timing accuracy and rocket burning time. Retrorocket systems are most practical for deceleration distances greater than 4 or 5 feet. Crushable and frangible impact attenuators are suitable for deceleration distances of less than 15 inches. Air bag systems work best for deceleration distances of 24 to 48 inches. The original assumption that an air bag concept maybe the most practical approach for this air vehicle is therefore confirmed.&lt;br /&gt;
&lt;br /&gt;
7.2.2 Impact Attenuator System&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The design of impact attenuator systems is discussed in section 6.8 of this manual.&lt;br /&gt;
&lt;br /&gt;
Figure 7-1 shows the reconnaissance drone and the air-bag attenuator systems that consist of two deflatable, two-compartment wing-bag bags (A); a single-compartment, deflatable nose bag (B); and a nondeflatable nose-buffer bag (C). The wing bags, the primary energy absorbers, need the already calculated 24-inch effective-deceleration stroke. For design reasons, 33 inches must be added to the bag height, 19 inches for the distance from the wing underside to the underside of the jet ,i rlucts, 10 inches for ground clearance, and 4 inches for bag bottom curvature. These additio:;. result in a total bag lihight of 57 inches. To ensure landing stability, an air bag height-to-diameter ratio of 1.25 is selected for the two wing bags, resulting in a bag diameter of 48 inches. The cross-hatched lower part of the two wing bags (see Figure 7-1) deflates at impact, but the upper part stays inflated and keeps the drone off the ground. The nose bag, B, helps to absorb the impact and deflates, and the nose of the drone&lt;br /&gt;
&lt;br /&gt;
comes to rest on the nondeflatable buffer bag, C. All air bags are inflated from 3000 psi nitrogen containers using aspirators for a 50/50 nitrogen air mixture. The air bags are prepressurized to 2 psi for full bag inflation prior to landing. Multiple blowout valves consisting of staggered blowout rubber disks around the circumference of the air bags control the bag deflation to stay within the 9-g deceleration limit.&lt;br /&gt;
&lt;br /&gt;
The weight of the impact-attenuation system-air bags, nitrogen containers, plumbing,&lt;br /&gt;
&lt;br /&gt;
and A/C containers-is estimated from section 6.7 to be 2.2% of the total drone weight, or&lt;br /&gt;
&lt;br /&gt;
105.6 pounds. The air bags should be stored in containers that can be easily removed from the drone for repacking. Air bags must be deployed after the main parachutes are fully open to prevent air-bag damage caused by high dynamic pressure. Air-bag deployment begins with simultaneous pyroejecting of the removable air-bag-container covers and opening of the&lt;br /&gt;
&lt;br /&gt;
nitrogen-container valves. The wing bags, the primary nose bag, and the nose-buffer bag&lt;br /&gt;
&lt;br /&gt;
inflate. At ground contact, the bags compress, increasing the pressure inside the bags. At a preselected pressure level, the blowout valves (rubber disks, metal disks, or rubber-type sleeves) open and limit the maximum drone deceleration to the preselected level.&lt;br /&gt;
&lt;br /&gt;
7-4&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Section 2.4 defines the criteria for parachute type selection. Requirements for low weight&lt;br /&gt;
&lt;br /&gt;
and volume rule out the low-drag slotted parachutes (ribbon, ringslot, and ringsail) as well as guide-surface and cross parachutes (see Tables 5.2 and 5.3). Parachute deployment past the vertical stabilizer rules out a single parachute in favor of a cluster of two parachutes deployed independently left and right of the vertical stabilizer. No cluster experience is available with annular or cross parachutes, and no reefing experience is available with annular parachutes. Cross parachutes cannot be reefed to the low reefing ratios required for this application. Extended-skirt and polyconical parachutes have been used successfully in clusters of large, reefed parachutes.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7-6&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
A cluster of two conical full extended skirt parachutes is most suitable for this system. In&lt;br /&gt;
&lt;br /&gt;
section 5.2, Figures 5.24 and 5-25 show that properly designed extended-skirt parachutes have&lt;br /&gt;
&lt;br /&gt;
drag coefficients equal to 0.8 to 0.9 in the 20- to 25-ft/s rate of descent range. Available data&lt;br /&gt;
&lt;br /&gt;
(Reference 5.23) indicate that a cluster of two extended-skirt parachutes is sufficiently stable&lt;br /&gt;
&lt;br /&gt;
for use with air bags. Extended-skirt parachutes have a low opening-force coefficient of 1.4,&lt;br /&gt;
&lt;br /&gt;
compared to an opening-force coefficient of 1.8 for conical and triconical parachutes.&lt;br /&gt;
&lt;br /&gt;
Extended-skirt parachutes can also be reefed to low reefing ratios, a requirement for final&lt;br /&gt;
&lt;br /&gt;
descent parachutes (see Chapter 5, Figure 5-72).&lt;br /&gt;
&lt;br /&gt;
73.3 Parachute Diameter&lt;br /&gt;
&lt;br /&gt;
The rate of descent at 5000 feet altitude was selected to 25 ft/s (see section 7.3.1). The&lt;br /&gt;
&lt;br /&gt;
equivalent rate of descent at sea level is&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The drag coefficient, CDo, for a conical full extended skirt parachute with a 23.2-ft/s rate of&lt;br /&gt;
&lt;br /&gt;
descent and a suspension-line ratio, [.e/Do, of 1.0 is obtained from Figure 5-25&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
A suspension-line ratio of 1.15 is selected. This is the longest practical length for extended skirt&lt;br /&gt;
&lt;br /&gt;
parachutes (see Figure 5-20).&lt;br /&gt;
&lt;br /&gt;
The length of the riser, Lr, depends on its installation in the drone; the riser should be long&lt;br /&gt;
&lt;br /&gt;
enough to extend beyond the fuselage and vertical stabilizer of the drone (see Figure 7-2),&lt;br /&gt;
&lt;br /&gt;
which gives the final configuration of the parachute cluster, including risers and parachutes.&lt;br /&gt;
&lt;br /&gt;
7.3.4 Parachute Deployment System&lt;br /&gt;
&lt;br /&gt;
A cluster of two main parachutes is selected and deployed left and right of the vertical&lt;br /&gt;
&lt;br /&gt;
stabilizer to avoid hang-up or damage of a single parachute by the vertical stabilizer. Each&lt;br /&gt;
&lt;br /&gt;
parachute needs its own extraction and deployment system to properly deploy past the&lt;br /&gt;
&lt;br /&gt;
stabilizer and to avoid interference with the other main parachute during deployment and&lt;br /&gt;
&lt;br /&gt;
inflation.&lt;br /&gt;
&lt;br /&gt;
TWo fast-opening extraction parachutes are used on each main parachute. Stable&lt;br /&gt;
&lt;br /&gt;
parachutes will minimize interferenc, during deployment. Experience with past recovery&lt;br /&gt;
&lt;br /&gt;
systems has shown that the most positive deployment is obtained by forced ejection of the&lt;br /&gt;
&lt;br /&gt;
extractiou or pilot chutes into good airflow past the vertical stabilizer by either mortar or&lt;br /&gt;
&lt;br /&gt;
drogue gun ejection. A mortar can eject large, heavy parachutes but creates large leaction&lt;br /&gt;
&lt;br /&gt;
forces and needs considerable space for installation. Drogue gun ejection is effective, but is&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
limited to the deployment of small, lightweight parachutes such as pilot chutes. Drogue gun ejected pilot chutes are selected for initiating main parachute deployment. To ensure proper&lt;br /&gt;
&lt;br /&gt;
clearance of the vertical stabilizer, the pilot chutes are ejeLted 45 degrees upward, backward&lt;br /&gt;
&lt;br /&gt;
and outward past the vertical stabilizer. The parachute installation in the drone fuselage&lt;br /&gt;
&lt;br /&gt;
requires cross-wind deployment and therefore forced ejection of the main parachute&lt;br /&gt;
&lt;br /&gt;
deployment bags. Four different methods have been used successfully to accomplish forced&lt;br /&gt;
&lt;br /&gt;
ejection: (1) using ejector springs enclosed in a textile cylinder. (2) gas-inflating nonporous&lt;br /&gt;
&lt;br /&gt;
ejector bags, (3) catapulting the bag out of the compartment, or (4) using a lift-web&lt;br /&gt;
&lt;br /&gt;
arrangement as discussed in section 6.1.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The deployment system selected consists of a drogue gun deployed pilot chute, an&lt;br /&gt;
&lt;br /&gt;
extraction parachute, and a main parachute deployment bag lifted from the parachute&lt;br /&gt;
&lt;br /&gt;
compartment by lift webs. When the hinged compartment doors open, two drogue gun slugs&lt;br /&gt;
&lt;br /&gt;
are fired 45 degrees upward and aft; each slug deploys a pilot chute sufficiently behind the&lt;br /&gt;
&lt;br /&gt;
drone into good airflow. These pilot chutes in turn extract two extraction chutes stowed on top of the main parachute deployment bags. The extraction chutes extract and deploy the two main 0&lt;br /&gt;
&lt;br /&gt;
parachutes left and right of the vertical stabilizers. Lift webs and unsymmetrical bag handles&lt;br /&gt;
&lt;br /&gt;
lift the main parachute bags out of the drone compartment and extract the main parachute&lt;br /&gt;
&lt;br /&gt;
past the vertical stabilizer (see Figure 7-3)&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.3.5 Extraction Parachute Assembly&lt;br /&gt;
&lt;br /&gt;
The two extraction parachutes must properly deploy the two main parachutes. The size of&lt;br /&gt;
&lt;br /&gt;
the extraction parachutes and their location in the wake of the drone is determined as follows:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
A stable, 7.4-foot-diameter ringslot parachute is selected. &lt;br /&gt;
&lt;br /&gt;
The weight of the ringslot extraction parachute can be estimated from section 6.7 to 2.5 pounds, and the weight of the extraction parachute assembly including riser and deployment bag to 1.5 . 2.5 pounds = 3.75 pounds. The weight of a single 72.7-foot-diameter main parachute, as determined from section 6.7, is 54 pounds. This weight estimate assumes an efficiently designed main canopy that has a combination of tape and radial seams to carry the radial loads and has other, similar weight-saving design features. The arrangement of the extraction parachute in relation to the drone is shown in Figure 7-5. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.3.6 Pilot Parachute Assembly &lt;br /&gt;
&lt;br /&gt;
The extraction parachute assembly weight of 3.75 pounds is too heavy to be deployed by a drogue-gun slug; therefore, a small pilot chute is selected for initial deployment by the drogue-gun slug. This pilot chute, in turn, will deploy the extraction parachute.&lt;br /&gt;
&lt;br /&gt;
Evaluation of past good and poor deployments has led to the rule that the extraction force of the pilot chute should be greater than or equal to four times the weight of the unit to be extracted; in this case, the extraction parachute assembly. So that the pilot chute has enough force, a pilot chute is selected that will produce, at the minimum deployment speed of 150 KEAS, an extraction force equal to five times the weight of the extraction parachute assembly: 5. 3.75 pounds - 18.75 pounds. The minimum dynamic pressure at 150 KEAS is&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.3.7 Main Parachute Forces&lt;br /&gt;
&lt;br /&gt;
7.3.7.1 Requirements &lt;br /&gt;
&lt;br /&gt;
Drone weight ............................................. W D = 4800 lb&lt;br /&gt;
&lt;br /&gt;
Maximum deployment speed .............................. vo = 200 KEAS &lt;br /&gt;
&lt;br /&gt;
Minimum deployment speed ........................ Vo minimum = 150 KEAS &lt;br /&gt;
&lt;br /&gt;
Maximum allowable total parachute force (two main parachutes) ................................... FT = 16,000 lb &lt;br /&gt;
&lt;br /&gt;
Deployment altitude .................................. H = 2000 to 7000 ft &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.3.7.2 Velocity-Altitude Profile &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Section 5.5 states that the maximum opening force of the main parachute occurs at maximum deployment altitude. Figure 7-8 shows a velocity-altitude-versus-time profile for a typical vehicle recovery system. &lt;br /&gt;
&lt;br /&gt;
The maximum dynamic pressure, qo, occurs at the 200-KEAS deployment velocity &lt;br /&gt;
&lt;br /&gt;
2. The Pflanz method is quite accurate for all conditions including high altitude, but neglects the effect of gravity. Parachutes opened in vertical descent will have a 1-g (one weight unit) higher force than calculated. It is necessary to calculate the canopy filling times for the various reefed stages (see section 5.4.3) and to determine the drag-area-versus-time profile for the specific parachute (see section 5.4.4). This method permits the investigation of variations in filling times and drag-area-versus-time profiles. &lt;br /&gt;
&lt;br /&gt;
3. The force-trajectory-time computer method includes the effects of altitude, gravity, and changing trajectory angle. This method requires determination of a drag-area-versus-time profile for the entire parachute opening sequence (see Figure 5-52). Computers permit multiple runs with changes in times, drag-area-versus-time profiles, starting velocities, and altitudes.&lt;br /&gt;
&lt;br /&gt;
7.3.7.4 Reefed Opening Forces&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
To  save trajectory time, the reef-d pardchute is disreefed at a dynamic pressure 10 to 20% higher than the terminal reefed dynamic pressure. Therefore,&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Results of changing the canopy inflation time, tf, and the drag-area-versus-time profile, n, are shown in Thble 7-2. Reference 5-76, the Pflanz report, provides a more detailed study of the effect of canopy fill time and drag-area-increase-versus-time profile on the magnitude of the parachute force&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Force-Trajectory-Time Computer Method &lt;br /&gt;
&lt;br /&gt;
The program established oy NWC determines as a function of time the parachute forces, the vehicle deceleration, and the space-positioning (trajectory) data in a two-axis system. The method requires a drag-area-versus-time profile for the individual parachutes and the total vehicle system (Figure 7-9). This profile was previously shown in Figure 5-52. Figure 7-9 includes the change in air-vehicle drag caused by the change in vehicle attitude during the parachute opening process&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.3.7.6 Comments on Calculated Opening Forces 1. The reefed opening force for the single parachute is higher than thie contractor-requested maximum allowable force per parachute of 8000 pounds&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
2. The average disreef force is approximately 1500 pounds lower than the reefed force. Therefore, it appears logical to lower the reefed force and increase the disreef force. Although this adjustment probably cannot be made within the 8000-pound limit, 8500 pounds appears to be an obtainable goal. &lt;br /&gt;
&lt;br /&gt;
3. To meet the contractor requirement of an 8000-pound maximum force limit per parachute, two-stage reefing is required. &lt;br /&gt;
&lt;br /&gt;
4. It appears practical to determine in drop tests if a 2.0 to 2.1% reefed drag area can be obtained. This drag area would decrease the reefed opening force and somewhat increase the disreef force. However, reaching an average maximum force of less than 8000 pounds appears doubtful. &lt;br /&gt;
&lt;br /&gt;
5. In the calculations, both parachutes are assumed to have equal opening forces. In reality, opening forces of the two parachutes can differ because of variations in filling time. lead-ann-lag chute behavior caused by blanketing, and resultant nonuniform canopy inflation. 7-22 NWC TP 6575 &lt;br /&gt;
&lt;br /&gt;
The fast-opening Apollo ringsail-type main parachutes had a load distribution among the three parachutes of 40-40-20. The individual parachutes, therefore, had to be overdesigned in a 40/33 ratio. However, the total parachute force load taken by the vehicle hard points did not exceed the calculated average load because of the high-low variation of the individual parachutes. &lt;br /&gt;
&lt;br /&gt;
The two slower-opening extended-skirt parachutes used for this application are more uniform in their load distribution. A cursory analysis of available test data indicates that a 55/45 load distribution between the two parachutes and a no-overload condition for the vehicle hard points should be an acceptable load distribution. &lt;br /&gt;
&lt;br /&gt;
A contractor-subcontractor agreement is required to determine whether the individual parachutes should be designed for the 55/45 load variation or whether this overload can be accommodated by the 1.5 safety factor and the additional safety provided by the normal overstrength of textile specification materials.&lt;br /&gt;
&lt;br /&gt;
7.3.7.7 Snatch Forces &lt;br /&gt;
&lt;br /&gt;
The snatch force is caused by the acceleration of the mass of the parachute assembly to the velocity of the forebody (drone). A canopy, partially inflated at line stretch, increases the mass of the parachute by the mass of the air included in the canopy; this can increase the snatch force (mass shock) considerably.  &lt;br /&gt;
&lt;br /&gt;
Two  principal rules should be followed to keep the snatch force within allowable limits.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
1. Keep the parachute canopy closed until line (canopy) stretch occurs by use of a deployment bag o! %kirt restrictor.&lt;br /&gt;
&lt;br /&gt;
2. Accelerate I!: mass of the parachute assembly in incremental steps. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Known means of accomplishing these goals are discussed in Chapter 6.1. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The difference between a poor deployment and a deployment that accomplishes the first rule and partially accomplishes ' second is illustrated in Figure 5-54, which shows snatch and opening forces for the C-9 p. tchute with and without the quarter deployment bag. The deployment method outlined in ! tilon 7.3.4 should hold snatch forces at a level below the parachute opening forces. &lt;br /&gt;
&lt;br /&gt;
A method for calculating ,tch forces is described in Reference 2.2, the 1963 edition of the USAF parachute handbook. : nreferred method for calculating parachute deployment. including the snatch force, is cont.iiiici in J. W Purvis's AIAA paper, &amp;quot;Improved Prediction of Parachute Line Sail During I incs-First Deployment&amp;quot; (Reference 5.86)&lt;br /&gt;
&lt;br /&gt;
7.3.8 Parachute Stress Analysis &lt;br /&gt;
&lt;br /&gt;
7.3.8.1 Parachute Design Data&lt;br /&gt;
&lt;br /&gt;
A total parachute assembly is shown in Figure 7-10.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.3.8.2 Parachute Forces &lt;br /&gt;
&lt;br /&gt;
The maximum reefed opening force, FR, is 9255 pounds. The maximum disreef opening force, F., is 7404 pounds. The maximum design force for stressing the parachute assembly, FI, is 9255 pounds.&lt;br /&gt;
&lt;br /&gt;
The forces obtained in computer runs are selected as the most accurate forces for stressing the parachute assembly and its components. Based on multiple computer runs, a diligent choice must be made for the most likable forces.&lt;br /&gt;
&lt;br /&gt;
7.3.83 Main-Parachute Safety and Design Factors &lt;br /&gt;
&lt;br /&gt;
Section 6.4 is used as a guide for selecting the safety, load, loss, and design factors in Table 7.4&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
1. Connection of suspension lines to riser legs and drone hardpoints is made easier if the number of suspension lines are a multiple of 4 or 8. &lt;br /&gt;
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2. The gore at the skirt should not be wider than 3.5 feet for packing reasons. &lt;br /&gt;
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3. The canopy should have no fewer than 12 gores to avoid gore distortion during inflation. &lt;br /&gt;
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4. Radial ribbons or radial seams should not overlap at the vent; overlapping causes bunching of material and associated sewing problems. &lt;br /&gt;
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5. The strengths of available suspension-line types may affect the gore selection. &lt;br /&gt;
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Table 7-5 shows the required suspension line strength and the resultant gore width as functions of the number of gore/suspension lines used. &lt;br /&gt;
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7-25 NWC TP 6575&lt;br /&gt;
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The width of the goie of the skirt on conical, full-extended-skirt (CFES) parachutes is about 85% of the maximum gore width, Eo. Sixty-four suspension lines are selected in accordance with MIL-C-7515, TIpe XI, with 300-pound tensile strength. This selection provides a margin of safety (MS) of&lt;br /&gt;
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The suspension line will be attached to the canopy skirt in a loop connection. &lt;br /&gt;
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7.3.8.5 Canopy Stress&lt;br /&gt;
&lt;br /&gt;
No precise method has been d.-veloped for calculating the stress in a circular, solid-material, bias-construction canopy.&lt;br /&gt;
&lt;br /&gt;
Section 6.4 describes a semi-empirical method for determining the required fabric strength of a solid material canopy in pounds per unit width using the stress in a pressure vessel as an analogy. The stress in a cylindrical vessel, expressed as force per unit length, is&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
where p is the pressure in the cylindrical vessel and r is the vessel radius. Using this analogy and considering the canopy gore as part of a pressure vessel, the required material strength of the canopy per unit width is obtained&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
The maximum stress actually occurs during reefed inflation because of the smaller inflated diameter:&lt;br /&gt;
&lt;br /&gt;
7.3.8.6 Canopy Reinforcing Tapes &lt;br /&gt;
&lt;br /&gt;
1. Skirt Tape. The skirt tape should Iv. equal or greater in strength than the individual suspension lines but not less than 1000 pounds, and 1-inch-wide tape should be used for parachutes larger than 20 feet in diameter. &lt;br /&gt;
&lt;br /&gt;
The nylon tape selected is 1-inch-wide MIL-T-5038, Type IV, with 1000-pound strength. Proper connection of the skirt tape to the radial seam (tape) and the suspension line must be ensured.&lt;br /&gt;
&lt;br /&gt;
2. Vent Tape. From the geometric design of the parachute vent (Figure 7-11). the force in the vent tape, FVT, is calculated&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
A 1-inch-wide, 4000-pound webbing (MIL-W-5625) or 7/8-inch-wide, 3100-pound webbing (MIL-W-5625) is selected. &lt;br /&gt;
&lt;br /&gt;
3. Vent Lines. The strength of the vent line- should be equal to or greater than 60% of the strength of the radials&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
7.3.8.7 Design of Radials &lt;br /&gt;
&lt;br /&gt;
The following four types of radial designs are in use: &lt;br /&gt;
&lt;br /&gt;
1. Radial seams with suspension lines running in channels over the canopy and attached at the vent and the skirt as on the canopy of the C-9 personnel parachute. &lt;br /&gt;
&lt;br /&gt;
2. Suspension lines running on top of the radials over the canopy and sewn at full length to the canopy as on many heavy-duty ribtx'n parachutes. &lt;br /&gt;
&lt;br /&gt;
3. Radial tapes sewn on top of or inside the radial seams, and suspension lines attached to the radial tapes by sewing or by skirt loops (NB-7 and T-10 canopies). &lt;br /&gt;
&lt;br /&gt;
4. Radial ribbons on ribbon parachutes designed to take the total radial load with suspension lines sewn onto d e radials or connected by a skirt loop. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The following are some comments on the design of radials: &lt;br /&gt;
&lt;br /&gt;
1. Making the strength of the radials 1:qtlal to 80% of the strength of the suspension lines has been satisfactory on thousands of ribbon parachutes. &lt;br /&gt;
&lt;br /&gt;
2. When tapes or suspension lines are sewn at full length to the radials, care must be taken that fullness in the radials ensures that the radial tapes or the suspension lines are the primary load carrying members. For an explanation of fullness, see section 6.6.4. &lt;br /&gt;
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3. Uniform material distribution is of utmost importance when sewn tapes or lines are used for radial reinforcemetnt. &lt;br /&gt;
&lt;br /&gt;
For the radial design of the main parachute, we use a tape with 80% strength of the suspension lint (0.8. 300 lb - 240 Ib) sewn on top of the radial scam. A 250-pound strength, 'A-inch-wide tape is selected in accordance with MIL-T-5038, 7ýpe III. Thpe and radial seams are marked every 24 inches for proper material distribution&lt;br /&gt;
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&lt;br /&gt;
7.3.8.8 Check for Proper Gore Fullness &lt;br /&gt;
&lt;br /&gt;
When the first parachute of a new design has been completed in the manufacturing shop, a gore fullness check in accordance with Figure 7-12 should be conducted. A slight amount of slack should be noticeable in the canopy fabric in both directions when all four corners of a gore are pulled radially outward. Slack indicates that the main loads are carried by the radials and reinforcing tapes and not by the canopy fabric. Stress folds in the canopy indicate faults in the design or manufacture of the parachute&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
’&lt;br /&gt;
&lt;br /&gt;
This is a large vent opening for a reefed parachute. Several criteria may be used to determine the size of the canopy vent as follows: &lt;br /&gt;
&lt;br /&gt;
1. Unreefed parachutes with vents up to 1% of the canopy surface area, So, have been operated successfully.&lt;br /&gt;
&lt;br /&gt;
2. Reefed parachutes require a vent diameter, DV, smaller than the reefing line circle, diameter DR, of the parachute; Dv is smaller than DR (see section 5.6, Figure 5-66). &lt;br /&gt;
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3. The radials at the vent should not overlap. A 1-inch free space between radials is desirable (see Figure 7-14)&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
Stress in the canopy gore area can be relieved by making the gore at the vent 10% wider than the calculated gore dimension, ev. Therefore, ev* - 1.1 . ev - 1.1(1.6) = 1.76 inches. The vent tape is sewn to the vent at the original ev dimension, thereby gathering the vent 10% and creating a stress-relieving arcing in the gore fabric next to the vent. See Figure 7-15 for an example of final gore dimensions.&lt;br /&gt;
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&lt;br /&gt;
7.3.10 Pocket Bands The pocket bands used on every gore make canopy inflation more uniform and eliminates long and short filling times. A narrow tape is used as the pocket band, which will :ot affect the average length of the canopy filling time. Data on the dimensioning of pocket bands are given in section 6.4. As shown in Figure 7-16, the pocket band dimensions are&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The diameter of the reefing line circle, DR, is larger than the 3.64-foot vent diameter of the canopy, Dv. This difference in diameters is an important design requirement (see section 7.3.9).&lt;br /&gt;
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7.3.11.2 Strength of the Reefing Line&lt;br /&gt;
&lt;br /&gt;
The force in the reefing line is determined according to information in section 5.6.8. Test items 22 and 23 in Figure 5-76 closely resemble the main parachute used here. A reefing-lineforce-to-reefed-parachute-force ratio of 2.5% is selected for this assembly. Therefore, the force in the reefing line is&lt;br /&gt;
&lt;br /&gt;
(0.025)FR = 0.025(9255 Ib) = 231.4 lb&lt;br /&gt;
&lt;br /&gt;
The design factor, DF, for the reefing system was determined in section 7.3.8, Table 7-4, to be 2.74.&lt;br /&gt;
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7.4 HIGH-SPEED DROGUE CHUTE ASSEMBLY &lt;br /&gt;
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7.4.1 Requirements &lt;br /&gt;
&lt;br /&gt;
The following operational requirements govern the design of the first-stage drogue chute:&lt;br /&gt;
&lt;br /&gt;
1. The drone must be recoverable from any conceivable flight condition during the engineering test phase. &lt;br /&gt;
&lt;br /&gt;
2. An out-of-control drone or a drone that loses radio contact with the controller must be prevented from flying off the range. Recovery is initiated by an independent range signal. This type of recovery requires a high-speed deceleration parachute that can be deployed and operated when the drone is moving at maximum speed, or is in a spin, or during any other abnormal flight condition. &lt;br /&gt;
&lt;br /&gt;
This type of recovery established the following requirements for the type and size of the drogue chute:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
1. The drogue chute must have reliable operation in the velocity range from 200 knots at sea level to Mach 1.5 at 50,000 feet.&lt;br /&gt;
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2. Stability must be better than :: 3 degrees. &lt;br /&gt;
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3. Minimum weight and volume is mandatory. &lt;br /&gt;
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4. The drogue chute must be able to decelerate the drone to the permissible opening speed of the main parachute assemblies.&lt;br /&gt;
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5. The drogue chute must be suitable for the operational environment. Figure 7-17 shows the altitude-velocity flight envelope of the drone.&lt;br /&gt;
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7.4.2 Drogue Chute Selection &lt;br /&gt;
&lt;br /&gt;
Tables 5-1 through 5-5 in Chapter 5 list commonly used parachute types. Table 7-6 evaluates possible drogue chute candidates. Of the parachute candidates, only the conical ribbon and the hemisflo ribbon have been used successfully for similar applications.&lt;br /&gt;
&lt;br /&gt;
A 25-degree conical ribbon parachute is selected for this application. The conical ribbon parachute meets all requirements and has a higher subsonic drag coefficient than the equally&lt;br /&gt;
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7.4.3 Required Drogue Chute Diameter &lt;br /&gt;
&lt;br /&gt;
The size of the fully open drogue chute is determined by the requirement that it must decelerate the 7200-pound drone to the allowable opening speed of the main parachute, which is governed by the requirement that the opening force of the two main parachutes must stay within the 9350-pound-per-chute limit established for the 200-knot opening speed of the 4800-pound drone. &lt;br /&gt;
&lt;br /&gt;
A preliminary calculation shows that a terminal velocity of about 175 KEAS is required to limit the opening load of the reefed main parachutes to 9350 pounds. A 13- to 14-footdiameter drogue chute is needed to meet this requirement. &lt;br /&gt;
&lt;br /&gt;
To reach 175 KEAS at main parachute line stretch, the drogue chute will be disconnected by an aneroid sensor at about 7000 feet mean sea level (MSL) while descending vertically from high altitude. The drone will free-fall for 0.8 second until main parachute line stretch occurs; the free-fall causes a 10-knot increase in velocity. In addition, the changing density, p, results in&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
NWC TP 6575 &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The gain in drag caused by the longer suspension lines and the 5% loss in drag caused by forebody wake (Figure 5-21) result in a final drag coefficient, CDo, for the drogue chute of &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
CDo = 0.55. 1.085 . 0.95 = 0.57&lt;br /&gt;
&lt;br /&gt;
and a corrected drogue chute diameter &lt;br /&gt;
&lt;br /&gt;
Do - 13.61 ft&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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7.4.4 Computer Analysis of Drogue Chute Performance &lt;br /&gt;
&lt;br /&gt;
At this point, a computer program should be established to determine the following performance conditions: &lt;br /&gt;
&lt;br /&gt;
1. Balance reefed and disreef parachute forces and filling times. Start at Mach 1.5 at 34,000 feet (see point () on Figure 7-17). Check final selection for a 10,000-foot-altitude condition. &lt;br /&gt;
&lt;br /&gt;
2. Determine required opening altitude for high-speed, low-altitude deployment. This requires trajectory runs with both the drogue and main parachutes. &lt;br /&gt;
&lt;br /&gt;
3. Determine maximum horizontal range, including prevailing wind conditions. &lt;br /&gt;
&lt;br /&gt;
4. Verify that the selected main parachute opening speed of 175 KEAS is reached for all important flight conditions and that, for an opening velocity of 175 KEAS, the main parachute forces stay within the allowable force limit of 9255 pounds. &lt;br /&gt;
&lt;br /&gt;
5. Include opening of the air bags with a 6.0-second inflation time in some of the trajectories. Inflation starts after main parachute opening. &lt;br /&gt;
&lt;br /&gt;
The prime contractor should point out any special flight conditions that may require parachute recovery. The prime contractor will probably also perform recovery computer runs to determine for which flight conditions and from what altitudes recovery can be accomplished. &lt;br /&gt;
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7.4.5 Flight Emergency Recovery Conditions &lt;br /&gt;
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Certain flight conditions other than recovery command from the flight controller or the range safety officer may result in automatic on-board recovery command. These conditions include &lt;br /&gt;
&lt;br /&gt;
1. Loss of RF link. &lt;br /&gt;
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2. Loss of engine power (glide on internal power). &lt;br /&gt;
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3. High accelerations in x, y, and z caused by out-of-control flight conditions or in-flightafflicted damage on target drones. &lt;br /&gt;
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7-38&lt;br /&gt;
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NWC TP 6575 &lt;br /&gt;
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7.4.6 Drogue Chute Opening Forces &lt;br /&gt;
&lt;br /&gt;
Parachute opening forces should be obtained from the computer program. However, a hand calculation is required for defining the force range before setting up the computer program. Furthermore, canopy filling times and force coefficient, C,. must be determined before computer runs (see section 5.4). &lt;br /&gt;
&lt;br /&gt;
Determining the drogue chute opening forces with the W/CDS method is normally sufficiently accurate for high-canopy-loading drogue chutes. If no computer backup is available, the Pflanz method (see section 5.4.6) will provide good force data.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.6.1 Drogue Chute Reefed Opening Forces When the W/CDS method is used, the reefed opening force, FR, is calculated to&lt;br /&gt;
&lt;br /&gt;
and the maximum allowable drogue chute drag area with a 2Z000 force limit is calculated to&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
where &lt;br /&gt;
&lt;br /&gt;
FR, the maximum allowable force, is 22,000 lb &lt;br /&gt;
&lt;br /&gt;
q, the maximum dynamic pressure, is 813.9 lb/ft2 &lt;br /&gt;
&lt;br /&gt;
For supersonic application, Figure 5-50 in section 5.4 shows CK = C' . X1 for the supersonic deployment of conical ribbon parachutes. Most applicable are the data for the Mercury and the Cook conical ribbon parachutes, which were deployed at velocities up to Mach 1.6. CK factors of 1.3 to 1.75 have been measured in supersonic deployment of conical ribbon parachutes. Forebody wake and poor deployment greatly affect the force coefficient. Mortar deployment often produces bag strip-off before canopy stretch, causing premature partial canopy inflation and a high X1 factor. Rocket extraction or drogue gun/pilot chute deployment, both resulting in canopy stretch before skirt inflation, generally avoid this problem. A force coefficient C, = 1.25 is selected.&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
The canopy loading of the reefed drogue chute is&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The required reefing-line length for obtaining this drag area can be determined from Figure 5-73, section 5.6.6, using the method of section 7.3.11.&lt;br /&gt;
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7.4.6.2 Drogue Chute Disreef Opening Force &lt;br /&gt;
&lt;br /&gt;
An important factor to determine is reefing time. A long time is required to reach close to terminal velocity before disreef. A practical approach, based on experience, is to select the 1.1-times-terminal-velocity point for disreef. If this time is too long, then a shorter reefing time is required, resulting in a higher disreef velocity and forces&lt;br /&gt;
&lt;br /&gt;
The terminal velocity of the reefed parachute is&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
and disreef force, Fo, is calculated&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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&lt;br /&gt;
Both forces FR and Fo are close to the allowable force limit of 22,000 pounds. Because loads vary 5 to 10%, slight overloads may occur. However, the 7200-pound drone weight is the take-off weight. Off-range recovery and conceivable emergencies will occur at lighter drone weights, resulting in lower parachute forces.&lt;br /&gt;
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&lt;br /&gt;
7.4.7 Drogue Chute Stress Analysis and Design &lt;br /&gt;
&lt;br /&gt;
Dimensioning of the various components of the parachute assembly involves three primary tasks (1) establishing design and safety factors, (2) determining the loads and stresses in the assembly components, and (3) dimensioning all assembly members. The methods used for these tasks are described in section 6.4. &lt;br /&gt;
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7.4.7.1 Drogue Chute Safety, Load, Loss, and Design Factors &lt;br /&gt;
&lt;br /&gt;
The method used is similar to the one developed in section 6.4. Table 7-7 shows safety, load, and loss factors in relation to design factor.&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
7.4.7.2 Number of Gores and Suspension-Line Strength &lt;br /&gt;
&lt;br /&gt;
The drogue chute will be designed for a maximumn force, Fo, of 22,000 pounds in the reefed and full-open stages. The suspension-line arrangement was selected in accordance with Table 7-8.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.7.2 Number of Gores and Suspension-Line Strength &lt;br /&gt;
&lt;br /&gt;
The drogue chute will be designed for a maximumn force, Fo, of 22,000 pounds in the reefed and full-open stages. The suspension-line arrangement was selected in accordance with Table 7-8.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
A canopy with 24 gores and 3000-pound-individual-strength suspension lines is selected primarily for gore width and vent diameter. The relatively large vent must be covered with wide vent lines held in place by proper connections. &lt;br /&gt;
&lt;br /&gt;
The method described in section 6.4 is used for preliminary dimensioning of the horizontal ribbons. In this method, the expression Fo/(CDS)p is an indication of the pressure in the parachute canopy; the gore width, es, is an indication of the gore radius. A smaller gore width and resultant gore radius causes lower stress in the individual horizontal ribbons for a given internal pressure. Figure 6-41 shows boundary curves for the required horizontal ribbon strength. These data, based on analysis of many tested ribbon parachutes, were first presented in Reference 5.39 and subsequently updated by the author. &lt;br /&gt;
&lt;br /&gt;
For the reefed parachute,&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The gore width of the reefed parachute is obtained from the following consideration. The reefed drag area is equivalent to the drag area of a parachute with the following nominal diameter (DRJ):&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The equivalent nominal diameter for the reefed parachute is&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Two-inch-wide ribbon with 460-pound strength, MIL-T-5608, Trype DII, is selected for the upper canopy part, and 2-inch-wide ribbon with 300-pound strength, MIL-T-5608, Type CV, is used for the lower part of the canopy. This drogue parachute will be subjected to high-frequency ribbon flutter during its high-speed descent from altitude, which may include a descent on the drogue chute from 50,000 to 7000 feet. Disintegration of horizontal and vertical ribbon and the stitching connecting the ribbons has occurred in the past during long-duration, high-speed applications of reefed and unreefed ribbon chutes. This high-frequency flutter is especially pronounced on the uninflated part of reefed ribbon parachutes. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Experience has shown that the following design features will counteract this problem: &lt;br /&gt;
&lt;br /&gt;
1. Tight spacing of vertical ribbons. &lt;br /&gt;
&lt;br /&gt;
2. wo vertical ribbons, one on each side of horizontal ribbon. &lt;br /&gt;
&lt;br /&gt;
3. Three rows of stitching with F-F thread in the vertical ribbon. All three features are used in this canopy design. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.7.3 Design of Radials, Vent and Skirt Tape, and Vent Lines &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Radials.Based on experience, radials are designed to have 80% of the strength of the suspension lines; 0.8 3000 = 2400 pounds. Three 2-inch-wide tapes of MIL-T-5608 form each radial; two 1000-pound Class Eli tapes and one 460-pound Class DII tape give each radial a combined strength of 2460 pounds. It may be possible to use only two 1000-pound strength tapes that have 80% of the actual load of 2548 pounds. &lt;br /&gt;
&lt;br /&gt;
Skirt and Vent Tape. In accordance with the discussion in section 7.6.6, the selected skirt tape is equal in strength to the suspension line but is 2 inches wide. Nylon tape (MIL-T-5608, Class E, lype V) with 3000-pound strength meets this requirement.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The required strength of the vent tape is&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Because some of this load will be taken by the vent lines, a double 4000-pound webbing is chosen in accordance with MIL-W-2756, lype IL. &lt;br /&gt;
&lt;br /&gt;
Special attention is required to obtain a design that achieves proper connection between radial tape, vent tape, and vent lines. &lt;br /&gt;
&lt;br /&gt;
Vent lines. The vent lines should have 60% of the strength of the radial tapes and be 5% shorter than the finished vent diameter. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.7.4 Drogue Chute Riser Design &lt;br /&gt;
&lt;br /&gt;
The drogue chute riser is formed of bundled suspension lines. This design eliminates the 20% connection loss, u, on the parachute side and permits a highly efficient connection on the drone side. The individual lines must be secured against each other to prevent flutter abrasion. Each line runs from a loop on the canopy radial, down the riser, around the drone connection point, and up the riser to an opposite radial-tape loop. Tests should be made to determine the strength of the radial-tape and suspension-line-loop connection and the individual loop around the drone hard point. A wrap-around keeper is used on the riser suspension line transfer point.&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
7.4.8.1 Canopy Porosity &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The porosity of a ribbon canopy is defined as the percentage ratio of openings in the canopy plus the material porosity divided by the total canopy surface area. Canopy porosity affects parachute stability, drag, and opening process. A canopy with high porosity provides for good parachute stability, and uniform, low force inflation, but also lower drag than a canopy with lower porosity. Too high a canopy porosity may result in no or only partial canopy inflation.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The operational porosity limit decreases with decreasing parachute diameter from about 35% total porosity for a stable 3-foot-diameter parachute to about 12% porosity for a 100-foot-diameter parachute (see Figure 6-23 (a) and Table 6-3). Section 6.2.4 discusses the effect of canopy porosity on the design and performance of ribbon parachutes. &lt;br /&gt;
&lt;br /&gt;
Properly designed conical ribbon parachutes with the correct porosity have an oscillation equal to or less than 2 to 3 degrees; a drag coefficient, CDo, of 0.55; and an opening-force coefficient, C., of 1.05 to 1.07 for subsonic applications with low forebody drag, such as experienced in wind-tunnel tests. &lt;br /&gt;
&lt;br /&gt;
The vertical ribbon spacing discussed in section 7.4.8.2 is of utmost importance for supersonic application. A canopy porosity of 25 to 26% in accordance with Figure 6-23, Curve III, and Thble 6-3 is recommended for this application. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.8.2 Vertical Ribbon Spacing &lt;br /&gt;
&lt;br /&gt;
Ribbon parachutes in the past were designed with individual gores, and the gores were connected with radial ribbons and several rows of stitching. This arrangement created the &amp;quot;venetian blind effect&amp;quot; shown in Figure 7-19. The venetian blind effect increases the effective canopy porosity discussed in section 6.2.4. &lt;br /&gt;
&lt;br /&gt;
More recently, ribbon canopies have been designed with continuous horizontal ribbons, a design that offers savings in weight and cost. This design is described in detail in section 7.4.10. &lt;br /&gt;
&lt;br /&gt;
Figure 7-20 shows the basic arrangement of a canopy gore and ribbon grid consisting of horizontal and vertical ribbons.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Section 6.2.4 explains the relationship of canopy loading, W/(CDS)p; effective porosity, Ne; and vertical ribbon spacing, a. Ribbon parachutes used as final descent parachutes use a vertical ribbon spacing to horizontal ribbon width a/B of 2.5 to 4.0. This spacing allows advantage to be taken of the change in effective porosity. High-canopy-loading ribbon parachutes, such as first-stage drogue chutes, use a vertical ribbon spacingof I to 2 to avoid the negative effects of the change in effective porosity. A narrow vertical ribbon spacing of 1.25 times the width of the horizontal ribbon width will be used for the drogue chute.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
All previous gore dimensions and the dimensions shown in Figure 7-21 are preliminary. The horizontal ribbon spacing, b, is controlled by the required porosity, k. Required changes in horizontal ribbon spacing may result in slight changez in gore and canopy dimensions.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.9.2 Preliminary Gore-Porosity Check &lt;br /&gt;
&lt;br /&gt;
Two methods of calculating gore porosity are in use. The older method, described in Reference 5.39, has been updated in this chapter. This method allows calculation of the porosity for preliminary design purposes when no final gore drawings are available. Reference 2.2 shows how to calculate canopy porosity if a drawing is available based on the ratio of open spaces to total canopy area. Both methods include an estimation of the ribbon (material) porosity&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The porosity of a ribbon grid with variations in the distance of the horizontal ribbons is now calculated. The total porosity is estimated, and the most likable horizontal ribbon distance is selected for the first gore-porosity check (Thble 7-9). The widths of the vertical ribbon, A, and the horizontal ribbon, B, are fixed values. The ratio of vertical ribbon spacing, to horizontal ribbon width, a/B, was previously selected to 1.25, which is equal to 2.5 inches. A horizontal ribbon distance, b, of 1.1 inches is selected as first approach based on data in Thble 7-9.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
To avoid a decrease in parachute diameter, 26 horizontal ribbons are selected, changing the gore dimensions from those shown in Figure 7-21 to those shown in Figure 7-22.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.9.S General Comments on Gore Design and Porosity Selection &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The canopy gore design-total canopy porosity, XT; spacing of vertical ribbon; size of vent; and pocket-band arrangement-are the primary design features that determine the aerodynamic performance of the parachute. The most important characteristics of parachute performance are stability, smooth opening, drag, and opening-force coefficients. Determining porosity under a no-load condition is rather unrealistic, because most of the important aerodynamic characteristics occur under high-load conditions (opening shock) or medium-load conditions (descent). However, since the beginning of parachute development, aerodynamic parachute characteristics obtained in wind-tunnel and free-flight tests have been related to fixed design dimensions such as diameter and porosity. &lt;br /&gt;
&lt;br /&gt;
Determining the effective porosity caused by the changing load during the opening process and by the venetian-blind effect of the ribbon grid design is practically impossible. Furthermore, the change in effective porosity is similar on all ribbon parachutes because of the similarities of the ribbon grid designs, load factors, and related changes in material elongation that cause deformation of the ribbon grids and the parachute canopies. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.9.6 Computer Programs for Determining Gore Design and Porosity Calculation &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Both gore design and porosity calculations can be determined by computer programs. Organizations involved in frequent design of ribbon parachutes should establish these programs. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.10 Ribbon Parachute Canopies with Continuous Horizontal Ribbons &lt;br /&gt;
&lt;br /&gt;
Ribbon parachute canopies are frequently designed and manufactured with continuous horizontal ribbons either in single or two-section canopies. The continuous ribbon Jesign decreases weight and volume, increases the strength of the horizontal ribbon-radial connection, and simplifies manufacturing. Continuous horizontal ribbons change the porosity characteristics of the canopy. &lt;br /&gt;
&lt;br /&gt;
Figure 7-19 shows how the individual horizontal ribbons orient themselves in a canopy manufactured from individual triangular gores. In the inflated canopy, the horizontal ribbons in the canopy crown area orient parallel to the canopy design. However, in the skirt area, the canopy design line is almost parallel to the airflow. This design, usually called the &amp;quot;venetian blind effect,&amp;quot; causes ti:e longer leading edge of each horizoatal ribbon to bulge out and position the ribbon with a positive angle of attack to the airflow. The result is an increase in effective porosity under high dynamic pressure conditions. The venetian blind effect is discussed in section 6.2.4, and the influence of canopy loading on the change in effective porosity is shown in Figure 6-24.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Designing canopies with continuous horizontal ribbons changes the venetian blind effect. Returning to Figure 7.19, it is obvious that continuous horizontal ribbons in the canopy skirt area do not bulge out since leading and trailing ribbon edges have the same length and do not position themselves with an angle of attack to the airflow. However, in the crown area of the canopy where each gore forms a triangle, the equal length of the leading and trailing ribbon edges now gives each ribbon a negative angle of attack thereby increasing the effective porosity in the canopy crown area. The effect is minimized by large number of gores arid by the use of a center vertical ribbon, or a miniradial, as Sandia engineers call it. &lt;br /&gt;
&lt;br /&gt;
Discussion with Sandia and industry personnel indicates that no measurable difference has been found in the aerodynamic characteristics of ribbon parachute canopies designed with individual gores or with continuous horizontal ribbons so long as the canopies contain a large number of gores and a center vertical ribbon. However, a slight delay in initial inflation seems to occur on small parachutes with a small number of gores. Closer spacing of vertical ribbons in the canopy crown area should counteract this delay. Another method of counteracting the delay is by gathering the trailing edges of horizontal ribbons with several rows of stitching and using a lower porosity in the crown area. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7.4.11 Use of Kevlar Fabrics &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Many modern ribbon parachutes use Kevlar suspension lines, risers, and canopy skirt, lateral, and vent tapes, which results in a decrease in weight and volume. Section 6.5.5 discusses all aspects of working with Kevlar in the design of parachute assemblies. This includes physical characteristics of Kevlar fibers and fabrics, available Kevlar fabrics, and experience ;il designing in Kevlar. Section 6.6.5 should be studied before designing in Kevlar.&lt;/div&gt;</summary>
		<author><name>TuanHTruong</name></author>
	</entry>
	<entry>
		<id>https://mediawiki.aerodecelerator.org/index.php?title=Recovery_System_Design&amp;diff=23</id>
		<title>Recovery System Design</title>
		<link rel="alternate" type="text/html" href="https://mediawiki.aerodecelerator.org/index.php?title=Recovery_System_Design&amp;diff=23"/>
		<updated>2024-05-03T20:38:50Z</updated>

		<summary type="html">&lt;p&gt;TuanHTruong: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;DESIGN OF A PARACHUTE RECOVERY AND LANDING SYSTEM&lt;br /&gt;
&lt;br /&gt;
This chapter deals with the design of a parachute recovery and landing attenuation system for a military reconnaissance drone. The prime emphasis in the design of this system is on undamaged recovery of the drone from the total flight performance envelope during the development and test phase, on undamaged recovery after a completed mission during military operations, and on multiple use of the recovery system. An engineering team conducts performance and system analyses and chooses what recovery concept to use, what types of parachutes to select for high-speed deceleration and for final recovery, and what impact-attenuation system is best for the particular application. This chapter covers the selection process for concepts and components. Different engineers may make different selections based on experiences with particular types of parachutes or deployment concepts; experience is always a viable reason for selecting a particular approach. However, using the selection criteria shown in Figure 2-6. the designer must put reliability of operation, undamaged recovery, reusability of the landing system, and minimum weight and volume at the top of the list of requirements. &lt;br /&gt;
&lt;br /&gt;
7.1 REQUIREMENTS  &lt;br /&gt;
&lt;br /&gt;
7.1.1 System Requirements &lt;br /&gt;
&lt;br /&gt;
An unmanned air vehicle used for military reconnaissance must be recovered after a completed mission in rough terrain, undamaged and ready for multiple reuse. The recovery system must be able to &lt;br /&gt;
1. Recover the air vehicle after the completed mission when the vehicle has landed in rough terrain at altitudes from sea level to 5000 feet.&lt;br /&gt;
2. Recover the drone during the engineering test phase from all controlled and uncontrolled flight conditions. &lt;br /&gt;
3. Serve as a range-safety device to prevent the air vehicle from leaving the boundaries of the test range. &lt;br /&gt;
&lt;br /&gt;
The air vehicle has a takeoff weight of 7200 pounds and a landing weight, after the i completed mission, of 4800 pounds. Undamaged landing shall be possible in rough terrain with rocks up to 8 inches in diameter. Replacement parts and refurbishment cost shall be kept to a minimum.  &lt;br /&gt;
&lt;br /&gt;
7.1.2 Requirements for Normal Operation &lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|Drone weight at recovery after completed mission&lt;br /&gt;
|W&amp;lt;sub&amp;gt;d&amp;lt;/sub&amp;gt; = 4800 lb&lt;br /&gt;
|-&lt;br /&gt;
|Recovery velocity&lt;br /&gt;
|v&amp;lt;sub&amp;gt;o&amp;lt;/sub&amp;gt; = 150 to 200 KEAS&lt;br /&gt;
|-&lt;br /&gt;
|Minimum recovery altitude&lt;br /&gt;
|H&amp;lt;sub&amp;gt;o&amp;lt;/sub&amp;gt; = 2000 ft above ground level (AGL)&lt;br /&gt;
|-&lt;br /&gt;
|Maximum ground level&lt;br /&gt;
|H = 5000 ft&lt;br /&gt;
|-&lt;br /&gt;
|Maximum allowable total parachute force&lt;br /&gt;
|F&amp;lt;sub&amp;gt;o&amp;lt;/sub&amp;gt; = 16,000 lb&lt;br /&gt;
|-&lt;br /&gt;
|Maximum allowable impact deceleration at landing&lt;br /&gt;
|a = 9.0 ''g''&amp;lt;nowiki/&amp;gt;'s&lt;br /&gt;
|} &lt;br /&gt;
&lt;br /&gt;
7.1.3 Requirements for Emergency Operation &lt;br /&gt;
&lt;br /&gt;
Emergency operation includes recovery during the test phase from takeoff to landing and also includes recovery for range-safety reasons. &lt;br /&gt;
&lt;br /&gt;
Drone weight at takeoff .................................. Wdma = 7200 lb &lt;br /&gt;
&lt;br /&gt;
Maximum recovery velocity at mean sea level (MSL) ................................... vo = 490 KEAS &lt;br /&gt;
&lt;br /&gt;
Maximum recovery velocity at 38,000 to 50,000 ft altitude ........................................ vo = 1.5 Mach &lt;br /&gt;
&lt;br /&gt;
Maximum dynamic pressure .............................. qmm = 812 lb/ft2 &lt;br /&gt;
&lt;br /&gt;
Maximum allowable parachute force ........................ F0 = 22,000 lb  &lt;br /&gt;
&lt;br /&gt;
7.1.4 Requirements Analysis &lt;br /&gt;
&lt;br /&gt;
Three primary requirements pace the design of the recovery system: &lt;br /&gt;
&lt;br /&gt;
1. The drone must be able to land in rocky but level terrain without damage. &lt;br /&gt;
&lt;br /&gt;
2. Refurbishment cost and time shall be kept to a minimum. &lt;br /&gt;
&lt;br /&gt;
3. Recovery must be possible from all flight conditions during the flight test phase, including cases where the out-of-control drone flies off the range.  &lt;br /&gt;
&lt;br /&gt;
7.2 LANDING ANALYSIS AND IMPACT-ATTENUATION SYSTEM &lt;br /&gt;
&lt;br /&gt;
7.2.1 Landing Analysis &lt;br /&gt;
&lt;br /&gt;
Three known recovery concepts prevent damage during landing in rocky terrain: &lt;br /&gt;
&lt;br /&gt;
1. Midair retrieval.&lt;br /&gt;
&lt;br /&gt;
2. Dual air bags or dual frangibles.&lt;br /&gt;
&lt;br /&gt;
3. Retrorockets combined with small, nondeflatable air bags.&lt;br /&gt;
&lt;br /&gt;
The need for retrieval helicopters or retrieval aircraft makes Method 1, midair retrieval, impractical. The other two methods are affected by the deceleration distance required to meet the 9-g limit. &lt;br /&gt;
&lt;br /&gt;
In section 6.8 of this manual, the required deceleration distance(s) is determined to be&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;s=\frac{{V_{e_1}}^2-{V_{e_2}}^2}{2g(n\eta-1)}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;{V_{e_1}}&amp;lt;/math&amp;gt; = velocity of the drone descending on the parachute (rate of descent), ft/s&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;V_{e_2}&amp;lt;/math&amp;gt; = permissible impact velocity, ft/s&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;g&amp;lt;/math&amp;gt; = acceleration of gravity, ft/s2&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\eta&amp;lt;/math&amp;gt; = effectiveness of the impact attenuation system used, dimensionless&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;n&amp;lt;/math&amp;gt; = allowable impact deceleration, ratio &amp;lt;math&amp;gt;n=\frac{a}{g}&amp;lt;/math&amp;gt;&lt;/div&gt;</summary>
		<author><name>TuanHTruong</name></author>
	</entry>
	<entry>
		<id>https://mediawiki.aerodecelerator.org/index.php?title=Recovery_System_Design&amp;diff=22</id>
		<title>Recovery System Design</title>
		<link rel="alternate" type="text/html" href="https://mediawiki.aerodecelerator.org/index.php?title=Recovery_System_Design&amp;diff=22"/>
		<updated>2024-05-03T20:38:13Z</updated>

		<summary type="html">&lt;p&gt;TuanHTruong: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;DESIGN OF A PARACHUTE RECOVERY AND LANDING SYSTEM&lt;br /&gt;
&lt;br /&gt;
This chapter deals with the design of a parachute recovery and landing attenuation system for a military reconnaissance drone. The prime emphasis in the design of this system is on undamaged recovery of the drone from the total flight performance envelope during the development and test phase, on undamaged recovery after a completed mission during military operations, and on multiple use of the recovery system. An engineering team conducts performance and system analyses and chooses what recovery concept to use, what types of parachutes to select for high-speed deceleration and for final recovery, and what impact-attenuation system is best for the particular application. This chapter covers the selection process for concepts and components. Different engineers may make different selections based on experiences with particular types of parachutes or deployment concepts; experience is always a viable reason for selecting a particular approach. However, using the selection criteria shown in Figure 2-6. the designer must put reliability of operation, undamaged recovery, reusability of the landing system, and minimum weight and volume at the top of the list of requirements. &lt;br /&gt;
&lt;br /&gt;
7.1 REQUIREMENTS  &lt;br /&gt;
&lt;br /&gt;
7.1.1 System Requirements &lt;br /&gt;
&lt;br /&gt;
An unmanned air vehicle used for military reconnaissance must be recovered after a completed mission in rough terrain, undamaged and ready for multiple reuse. The recovery system must be able to &lt;br /&gt;
1. Recover the air vehicle after the completed mission when the vehicle has landed in rough terrain at altitudes from sea level to 5000 feet.&lt;br /&gt;
2. Recover the drone during the engineering test phase from all controlled and uncontrolled flight conditions. &lt;br /&gt;
3. Serve as a range-safety device to prevent the air vehicle from leaving the boundaries of the test range. &lt;br /&gt;
&lt;br /&gt;
The air vehicle has a takeoff weight of 7200 pounds and a landing weight, after the i completed mission, of 4800 pounds. Undamaged landing shall be possible in rough terrain with rocks up to 8 inches in diameter. Replacement parts and refurbishment cost shall be kept to a minimum.  &lt;br /&gt;
&lt;br /&gt;
7.1.2 Requirements for Normal Operation &lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|Drone weight at recovery after completed mission&lt;br /&gt;
|W&amp;lt;sub&amp;gt;d&amp;lt;/sub&amp;gt; = 4800 lb&lt;br /&gt;
|-&lt;br /&gt;
|Recovery velocity&lt;br /&gt;
|v&amp;lt;sub&amp;gt;o&amp;lt;/sub&amp;gt; = 150 to 200 KEAS&lt;br /&gt;
|-&lt;br /&gt;
|Minimum recovery altitude&lt;br /&gt;
|Ho = 2000 ft above ground level (AGL)&lt;br /&gt;
|-&lt;br /&gt;
|Maximum ground level&lt;br /&gt;
|H = 5000 ft&lt;br /&gt;
|-&lt;br /&gt;
|Maximum allowable total parachute force&lt;br /&gt;
|F&amp;lt;sub&amp;gt;o&amp;lt;/sub&amp;gt; = 16,000 lb&lt;br /&gt;
|-&lt;br /&gt;
|Maximum allowable impact deceleration at landing&lt;br /&gt;
|a = 9.0 ''g''&amp;lt;nowiki/&amp;gt;'s&lt;br /&gt;
|} &lt;br /&gt;
&lt;br /&gt;
7.1.3 Requirements for Emergency Operation &lt;br /&gt;
&lt;br /&gt;
Emergency operation includes recovery during the test phase from takeoff to landing and also includes recovery for range-safety reasons. &lt;br /&gt;
&lt;br /&gt;
Drone weight at takeoff .................................. Wdma = 7200 lb &lt;br /&gt;
&lt;br /&gt;
Maximum recovery velocity at mean sea level (MSL) ................................... vo = 490 KEAS &lt;br /&gt;
&lt;br /&gt;
Maximum recovery velocity at 38,000 to 50,000 ft altitude ........................................ vo = 1.5 Mach &lt;br /&gt;
&lt;br /&gt;
Maximum dynamic pressure .............................. qmm = 812 lb/ft2 &lt;br /&gt;
&lt;br /&gt;
Maximum allowable parachute force ........................ F0 = 22,000 lb  &lt;br /&gt;
&lt;br /&gt;
7.1.4 Requirements Analysis &lt;br /&gt;
&lt;br /&gt;
Three primary requirements pace the design of the recovery system: &lt;br /&gt;
&lt;br /&gt;
1. The drone must be able to land in rocky but level terrain without damage. &lt;br /&gt;
&lt;br /&gt;
2. Refurbishment cost and time shall be kept to a minimum. &lt;br /&gt;
&lt;br /&gt;
3. Recovery must be possible from all flight conditions during the flight test phase, including cases where the out-of-control drone flies off the range.  &lt;br /&gt;
&lt;br /&gt;
7.2 LANDING ANALYSIS AND IMPACT-ATTENUATION SYSTEM &lt;br /&gt;
&lt;br /&gt;
7.2.1 Landing Analysis &lt;br /&gt;
&lt;br /&gt;
Three known recovery concepts prevent damage during landing in rocky terrain: &lt;br /&gt;
&lt;br /&gt;
1. Midair retrieval.&lt;br /&gt;
&lt;br /&gt;
2. Dual air bags or dual frangibles.&lt;br /&gt;
&lt;br /&gt;
3. Retrorockets combined with small, nondeflatable air bags.&lt;br /&gt;
&lt;br /&gt;
The need for retrieval helicopters or retrieval aircraft makes Method 1, midair retrieval, impractical. The other two methods are affected by the deceleration distance required to meet the 9-g limit. &lt;br /&gt;
&lt;br /&gt;
In section 6.8 of this manual, the required deceleration distance(s) is determined to be&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;s=\frac{{V_{e_1}}^2-{V_{e_2}}^2}{2g(n\eta-1)}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;{V_{e_1}}&amp;lt;/math&amp;gt; = velocity of the drone descending on the parachute (rate of descent), ft/s&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;V_{e_2}&amp;lt;/math&amp;gt; = permissible impact velocity, ft/s&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;g&amp;lt;/math&amp;gt; = acceleration of gravity, ft/s2&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\eta&amp;lt;/math&amp;gt; = effectiveness of the impact attenuation system used, dimensionless&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;n&amp;lt;/math&amp;gt; = allowable impact deceleration, ratio &amp;lt;math&amp;gt;n=\frac{a}{g}&amp;lt;/math&amp;gt;&lt;/div&gt;</summary>
		<author><name>TuanHTruong</name></author>
	</entry>
	<entry>
		<id>https://mediawiki.aerodecelerator.org/index.php?title=Recovery_System_Design&amp;diff=21</id>
		<title>Recovery System Design</title>
		<link rel="alternate" type="text/html" href="https://mediawiki.aerodecelerator.org/index.php?title=Recovery_System_Design&amp;diff=21"/>
		<updated>2024-05-03T20:37:28Z</updated>

		<summary type="html">&lt;p&gt;TuanHTruong: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;DESIGN OF A PARACHUTE RECOVERY AND LANDING SYSTEM&lt;br /&gt;
&lt;br /&gt;
This chapter deals with the design of a parachute recovery and landing attenuation system for a military reconnaissance drone. The prime emphasis in the design of this system is on undamaged recovery of the drone from the total flight performance envelope during the development and test phase, on undamaged recovery after a completed mission during military operations, and on multiple use of the recovery system. An engineering team conducts performance and system analyses and chooses what recovery concept to use, what types of parachutes to select for high-speed deceleration and for final recovery, and what impact-attenuation system is best for the particular application. This chapter covers the selection process for concepts and components. Different engineers may make different selections based on experiences with particular types of parachutes or deployment concepts; experience is always a viable reason for selecting a particular approach. However, using the selection criteria shown in Figure 2-6. the designer must put reliability of operation, undamaged recovery, reusability of the landing system, and minimum weight and volume at the top of the list of requirements. &lt;br /&gt;
&lt;br /&gt;
7.1 REQUIREMENTS  &lt;br /&gt;
&lt;br /&gt;
7.1.1 System Requirements &lt;br /&gt;
&lt;br /&gt;
An unmanned air vehicle used for military reconnaissance must be recovered after a completed mission in rough terrain, undamaged and ready for multiple reuse. The recovery system must be able to &lt;br /&gt;
1. Recover the air vehicle after the completed mission when the vehicle has landed in rough terrain at altitudes from sea level to 5000 feet.&lt;br /&gt;
2. Recover the drone during the engineering test phase from all controlled and uncontrolled flight conditions. &lt;br /&gt;
3. Serve as a range-safety device to prevent the air vehicle from leaving the boundaries of the test range. &lt;br /&gt;
&lt;br /&gt;
The air vehicle has a takeoff weight of 7200 pounds and a landing weight, after the i completed mission, of 4800 pounds. Undamaged landing shall be possible in rough terrain with rocks up to 8 inches in diameter. Replacement parts and refurbishment cost shall be kept to a minimum.  &lt;br /&gt;
&lt;br /&gt;
7.1.2 Requirements for Normal Operation &lt;br /&gt;
{|&lt;br /&gt;
|Drone weight at recovery after completed mission&lt;br /&gt;
|&lt;br /&gt;
|W&amp;lt;sub&amp;gt;d&amp;lt;/sub&amp;gt; = 4800 lb&lt;br /&gt;
|-&lt;br /&gt;
|Recovery velocity&lt;br /&gt;
|&lt;br /&gt;
|v&amp;lt;sub&amp;gt;o&amp;lt;/sub&amp;gt; = 150 to 200 KEAS&lt;br /&gt;
|-&lt;br /&gt;
|Minimum recovery altitude&lt;br /&gt;
|&lt;br /&gt;
|Ho = 2000 ft above ground level (AGL)&lt;br /&gt;
|-&lt;br /&gt;
|Maximum ground level&lt;br /&gt;
|&lt;br /&gt;
|H = 5000 ft&lt;br /&gt;
|-&lt;br /&gt;
|Maximum allowable total parachute force&lt;br /&gt;
|&lt;br /&gt;
|F&amp;lt;sub&amp;gt;o&amp;lt;/sub&amp;gt; = 16,000 lb&lt;br /&gt;
|-&lt;br /&gt;
|Maximum allowable impact deceleration at landing&lt;br /&gt;
|&lt;br /&gt;
|a = 9.0 ''g''&amp;lt;nowiki/&amp;gt;'s&lt;br /&gt;
|} &lt;br /&gt;
&lt;br /&gt;
7.1.3 Requirements for Emergency Operation &lt;br /&gt;
&lt;br /&gt;
Emergency operation includes recovery during the test phase from takeoff to landing and also includes recovery for range-safety reasons. &lt;br /&gt;
&lt;br /&gt;
Drone weight at takeoff .................................. Wdma = 7200 lb &lt;br /&gt;
&lt;br /&gt;
Maximum recovery velocity at mean sea level (MSL) ................................... vo = 490 KEAS &lt;br /&gt;
&lt;br /&gt;
Maximum recovery velocity at 38,000 to 50,000 ft altitude ........................................ vo = 1.5 Mach &lt;br /&gt;
&lt;br /&gt;
Maximum dynamic pressure .............................. qmm = 812 lb/ft2 &lt;br /&gt;
&lt;br /&gt;
Maximum allowable parachute force ........................ F0 = 22,000 lb  &lt;br /&gt;
&lt;br /&gt;
7.1.4 Requirements Analysis &lt;br /&gt;
&lt;br /&gt;
Three primary requirements pace the design of the recovery system: &lt;br /&gt;
&lt;br /&gt;
1. The drone must be able to land in rocky but level terrain without damage. &lt;br /&gt;
&lt;br /&gt;
2. Refurbishment cost and time shall be kept to a minimum. &lt;br /&gt;
&lt;br /&gt;
3. Recovery must be possible from all flight conditions during the flight test phase, including cases where the out-of-control drone flies off the range.  &lt;br /&gt;
&lt;br /&gt;
7.2 LANDING ANALYSIS AND IMPACT-ATTENUATION SYSTEM &lt;br /&gt;
&lt;br /&gt;
7.2.1 Landing Analysis &lt;br /&gt;
&lt;br /&gt;
Three known recovery concepts prevent damage during landing in rocky terrain: &lt;br /&gt;
&lt;br /&gt;
1. Midair retrieval.&lt;br /&gt;
&lt;br /&gt;
2. Dual air bags or dual frangibles.&lt;br /&gt;
&lt;br /&gt;
3. Retrorockets combined with small, nondeflatable air bags.&lt;br /&gt;
&lt;br /&gt;
The need for retrieval helicopters or retrieval aircraft makes Method 1, midair retrieval, impractical. The other two methods are affected by the deceleration distance required to meet the 9-g limit. &lt;br /&gt;
&lt;br /&gt;
In section 6.8 of this manual, the required deceleration distance(s) is determined to be&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;s=\frac{{V_{e_1}}^2-{V_{e_2}}^2}{2g(n\eta-1)}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;{V_{e_1}}&amp;lt;/math&amp;gt; = velocity of the drone descending on the parachute (rate of descent), ft/s&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;V_{e_2}&amp;lt;/math&amp;gt; = permissible impact velocity, ft/s&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;g&amp;lt;/math&amp;gt; = acceleration of gravity, ft/s2&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\eta&amp;lt;/math&amp;gt; = effectiveness of the impact attenuation system used, dimensionless&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;n&amp;lt;/math&amp;gt; = allowable impact deceleration, ratio &amp;lt;math&amp;gt;n=\frac{a}{g}&amp;lt;/math&amp;gt;&lt;/div&gt;</summary>
		<author><name>TuanHTruong</name></author>
	</entry>
	<entry>
		<id>https://mediawiki.aerodecelerator.org/index.php?title=Recovery_System_Design&amp;diff=20</id>
		<title>Recovery System Design</title>
		<link rel="alternate" type="text/html" href="https://mediawiki.aerodecelerator.org/index.php?title=Recovery_System_Design&amp;diff=20"/>
		<updated>2024-05-03T20:36:29Z</updated>

		<summary type="html">&lt;p&gt;TuanHTruong: Entered the first couple of pages and tested out entering equations and tables. This will be a very slow process as the laying out properly formatted equations and table formatting is laborious.&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;DESIGN OF A PARACHUTE RECOVERY AND LANDING SYSTEM&lt;br /&gt;
&lt;br /&gt;
This chapter deals with the design of a parachute recovery and landing attenuation system for a military reconnaissance drone. The prime emphasis in the design of this system is on undamaged recovery of the drone from the total flight performance envelope during the development and test phase, on undamaged recovery after a completed mission during military operations, and on multiple use of the recovery system. An engineering team conducts performance and system analyses and chooses what recovery concept to use, what types of parachutes to select for high-speed deceleration and for final recovery, and what impact-attenuation system is best for the particular application. This chapter covers the selection process for concepts and components. Different engineers may make different selections based on experiences with particular types of parachutes or deployment concepts; experience is always a viable reason for selecting a particular approach. However, using the selection criteria shown in Figure 2-6. the designer must put reliability of operation, undamaged recovery, reusability of the landing system, and minimum weight and volume at the top of the list of requirements. &lt;br /&gt;
&lt;br /&gt;
7.1 REQUIREMENTS  &lt;br /&gt;
&lt;br /&gt;
7.1.1 System Requirements &lt;br /&gt;
&lt;br /&gt;
An unmanned air vehicle used for military reconnaissance must be recovered after a completed mission in rough terrain, undamaged and ready for multiple reuse. The recovery system must be able to &lt;br /&gt;
1. Recover the air vehicle after the completed mission when the vehicle has landed in rough terrain at altitudes from sea level to 5000 feet.&lt;br /&gt;
2. Recover the drone during the engineering test phase from all controlled and uncontrolled flight conditions. &lt;br /&gt;
3. Serve as a range-safety device to prevent the air vehicle from leaving the boundaries of the test range. &lt;br /&gt;
&lt;br /&gt;
The air vehicle has a takeoff weight of 7200 pounds and a landing weight, after the i completed mission, of 4800 pounds. Undamaged landing shall be possible in rough terrain with rocks up to 8 inches in diameter. Replacement parts and refurbishment cost shall be kept to a minimum.  &lt;br /&gt;
&lt;br /&gt;
7.1.2 Requirements for Normal Operation &lt;br /&gt;
{|&lt;br /&gt;
|Drone weight at recovery after completed mission&lt;br /&gt;
|W&amp;lt;sub&amp;gt;d&amp;lt;/sub&amp;gt; = 4800 lb&lt;br /&gt;
|-&lt;br /&gt;
|Recovery velocity&lt;br /&gt;
|v&amp;lt;sub&amp;gt;o&amp;lt;/sub&amp;gt; = 150 to 200 KEAS&lt;br /&gt;
|-&lt;br /&gt;
|Minimum recovery altitude&lt;br /&gt;
|Ho = 2000 ft above ground level (AGL)&lt;br /&gt;
|-&lt;br /&gt;
|Maximum ground level&lt;br /&gt;
|H = 5000 ft&lt;br /&gt;
|-&lt;br /&gt;
|Maximum allowable total parachute force&lt;br /&gt;
|F&amp;lt;sub&amp;gt;o&amp;lt;/sub&amp;gt; = 16,000 lb&lt;br /&gt;
|-&lt;br /&gt;
|Maximum allowable impact deceleration at landing&lt;br /&gt;
|a = 9.0 ''g''&amp;lt;nowiki/&amp;gt;'s&lt;br /&gt;
|} &lt;br /&gt;
&lt;br /&gt;
7.1.3 Requirements for Emergency Operation &lt;br /&gt;
&lt;br /&gt;
Emergency operation includes recovery during the test phase from takeoff to landing and also includes recovery for range-safety reasons. &lt;br /&gt;
&lt;br /&gt;
Drone weight at takeoff .................................. Wdma = 7200 lb &lt;br /&gt;
&lt;br /&gt;
Maximum recovery velocity at mean sea level (MSL) ................................... vo = 490 KEAS &lt;br /&gt;
&lt;br /&gt;
Maximum recovery velocity at 38,000 to 50,000 ft altitude ........................................ vo = 1.5 Mach &lt;br /&gt;
&lt;br /&gt;
Maximum dynamic pressure .............................. qmm = 812 lb/ft2 &lt;br /&gt;
&lt;br /&gt;
Maximum allowable parachute force ........................ F0 = 22,000 lb  &lt;br /&gt;
&lt;br /&gt;
7.1.4 Requirements Analysis &lt;br /&gt;
&lt;br /&gt;
Three primary requirements pace the design of the recovery system: &lt;br /&gt;
&lt;br /&gt;
1. The drone must be able to land in rocky but level terrain without damage. &lt;br /&gt;
&lt;br /&gt;
2. Refurbishment cost and time shall be kept to a minimum. &lt;br /&gt;
&lt;br /&gt;
3. Recovery must be possible from all flight conditions during the flight test phase, including cases where the out-of-control drone flies off the range.  &lt;br /&gt;
&lt;br /&gt;
7.2 LANDING ANALYSIS AND IMPACT-ATTENUATION SYSTEM &lt;br /&gt;
&lt;br /&gt;
7.2.1 Landing Analysis &lt;br /&gt;
&lt;br /&gt;
Three known recovery concepts prevent damage during landing in rocky terrain: &lt;br /&gt;
&lt;br /&gt;
1. Midair retrieval.&lt;br /&gt;
&lt;br /&gt;
2. Dual air bags or dual frangibles.&lt;br /&gt;
&lt;br /&gt;
3. Retrorockets combined with small, nondeflatable air bags.&lt;br /&gt;
&lt;br /&gt;
The need for retrieval helicopters or retrieval aircraft makes Method 1, midair retrieval, impractical. The other two methods are affected by the deceleration distance required to meet the 9-g limit. &lt;br /&gt;
&lt;br /&gt;
In section 6.8 of this manual, the required deceleration distance(s) is determined to be&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;s=\frac{{V_{e_1}}^2-{V_{e_2}}^2}{2g(n\eta-1)}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;{V_{e_1}}&amp;lt;/math&amp;gt; = velocity of the drone descending on the parachute (rate of descent), ft/s&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;V_{e_2}&amp;lt;/math&amp;gt; = permissible impact velocity, ft/s&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;g&amp;lt;/math&amp;gt; = acceleration of gravity, ft/s2&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\eta&amp;lt;/math&amp;gt; = effectiveness of the impact attenuation system used, dimensionless&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;n&amp;lt;/math&amp;gt; = allowable impact deceleration, ratio &amp;lt;math&amp;gt;n=\frac{a}{g}&amp;lt;/math&amp;gt;&lt;/div&gt;</summary>
		<author><name>TuanHTruong</name></author>
	</entry>
</feed>