Parachute Aerodynamics - Revision history

MikeLPetersen: typo

2026-02-05T21:11:52Z

typo

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	== 4.3 NEWTON'S THREE OF MOTION ==		== 4.3 NEWTON'S THREE LAWS OF MOTION ==
	Engineering mechanics are governed by the following three laws of Isaac Newton:		Engineering mechanics are governed by the following three laws of Isaac Newton:

Parachute at 18:04, 27 June 2024

2024-06-27T18:04:42Z

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	<math>W_L</math> = weight of load, lb		<math>W_L</math> = weight of load, lb

	In most cases, the drag of the load can be neglected in relation to the large drag of the parachute, With drag, <math>D=(C_DS)_p \cdot \rho /2 \cdot v^2</math>. and <math>D_T=W_T</math> and solving for v, the important equation for rate of descent, v, is obtained,		In most cases, the drag of the load can be neglected in relation to the large drag of the parachute, With drag, <math>D=(C_DS)_p \cdot \rho /2 \cdot v^2</math>. and <math>D_T=W_T</math> and solving for v, the important equation for rate of descent, v, is obtained.


	Rate of descent,		Rate of descent,
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	4.2 J, M. Macha and R J. Buffington. "Wall-Interference Corrections for Parachutes in a Closed Wind Tunnel." AIM Paper, April 1989. (AIM 89-0900-cp.)		4.2 J, M. Macha and R J. Buffington. "Wall-Interference Corrections for Parachutes in a Closed Wind Tunnel." AIM Paper, April 1989. (AIM 89-0900-cp.)
			For readers interested in a more detailed study of aerodynamics, the following books are recommended.

	For readers interested in a more detailed study of aerodynamics, the following books are recommended.		For readers interested in a more detailed study of aerodynamics, the following books are recommended.
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	4.6 J. D. Anderson, Jr. Introduction to Flights, ILS Engineering and History. McGraw-Hill Book co., New York 1978.		4.6 J. D. Anderson, Jr. Introduction to Flights, ILS Engineering and History. McGraw-Hill Book co., New York 1978.

	4.7 D. J. Cockrell. The Aerodynamics of Parachutes." AGARDograph No. 6295, available from NASA Langley Research Center, M/S ~~1M)~~, Hampton, Va., 236.		4.7 D. J. Cockrell. The Aerodynamics of Parachutes." AGARDograph No. 6295, available from NASA Langley Research Center, M/S 180, Hampton, Va., 236.

Parachute at 17:44, 27 June 2024

2024-06-27T17:44:38Z

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	<math>C_{D_i}=\frac{C^2_L}{\pi \cdot AR}</math>		<math>C_{D_i}=\frac{C^2_L}{\pi \cdot AR}</math>

	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.		The equation for induced drag indicates that increasing the aspect ratio, AR, reduces the induced drag coefficient, <math>C_{D_i}</math>, and therefore reduces the drag, D. This, 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.

	=== 4.5.4 Aircraft in Horizontal Flight ===		=== 4.5.4 Aircraft in Horizontal Flight ===
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	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.		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.





	=== 4.6.1 Blowers ===		=== 4.6.1 Blowers ===
	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.		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.
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	3. Wind<sup>-</sup>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.		3. Wind<sup>-</sup>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.

	4. In wind-tunnel tests, velocity decay does not occur during parachute inflation and operation; this is defined as testing under "infinite mass condition. " First-stage drogue chutes and parachutes with a canopy loading, W/C<sub>D</sub>S. in excess of 100 lb/ft<sup>2</sup> 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.		4. In wind-tunnel tests, velocity decay does not occur during parachute inflation and operation; this is defined as testing under "infinite mass condition." First-stage drogue chutes and parachutes with a canopy loading, W/C<sub>D</sub>S. in excess of 100 lb/ft<sup>2</sup> 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.

	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).		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).

Parachute at 15:41, 27 June 2024

2024-06-27T15:41:26Z

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	=== 4.5.3 Parasite Drag and Induced Drag ===		=== 4.5.3 Parasite Drag and Induced Drag ===
	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<~~sub~~>P</~~sub~~> , and the induced drag. D<~~sub~~>i</~~sub~~>.		The drag acting on a lift-producing air vehicle, such as a gliding parachute or an aircraft, has two primary components: the parasite drag, <math>D_p</math>, and the induced drag. <math>D_i</math>.

	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 section, and control surfaces of an airplane. Large surfaces produce surface friction drag as part of the parasite drag.		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 section, and control surfaces of an airplane. Large surfaces produce surface friction drag as part of the parasite drag.
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			Total drag, <math>D_T</math>, can be defined as

			<math>D_T=D_p+D_i</math>

			or, in the coefficient form

			<math>C_{D_T}=C_{D_p}=C_{D_i}</math>

			The parasite drag, <math>D_p</math>, and the coefficient, <math>C_{D_p}</math>, can be determined in wind-tunnel tests or calculated as the sum of the individual component drags.

			The induced drag coefficient, <math>C_{D_i}</math>, of a gliding parachute canopy or a wing profile can be calculated

			<math>C_{D_i}=\frac{C_L^2 \cdot S}{\pi \cdot b^2}</math>

			where

	~~Total drag, D~~<~~sub~~>T</~~sub~~>, ~~can be defined as~~		<math>C_{D_i}</math>= coefficient of induced drag, dimensionless

	or, ~~in the coefficient form~~		<math>C_L</math> = lift coefficient, dimensionless

	~~The parasite drag~~, ~~D<sub>p</sub>, and the coefficient, C<sub>DP</sub>, can be determined in wind-tunnel tests or calculated as the sum of the individual component drags.~~		S = surface reference area, ft2

	~~The induced drag coefficient, C~~<~~sub~~>Di</~~sub~~> ~~, of a gliding parachute canopy or a wing profile can be calculated~~		<math>\pi =3.1415</math>

	~~where~~		b = span of the wing or parachute, ft

	C = ~~coefficient of induced drag, dimensionless~~		The expression <math>b^2/S</math> is defined as the aspect ratio of a wing or parachute with the notation <math>AR=b^2/S</math>. Therefore

	~~The expression b~~<~~sup~~>~~2</sup>/S is defined as the aspect ratio of a wing or parachute with the notation~~ AR ~~b<sup>2~~</~~sup~~>~~/S. Therefore~~		<math>C_{D_i}=\frac{C^2_L}{\pi \cdot AR}</math>

	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.		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.

Parachute at 15:19, 27 June 2024

2024-06-27T15:19:11Z

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	=== 4.5.2 Gliding Parachutes ===		=== 4.5.2 Gliding Parachutes ===
	Figure 4-12 shows the balance of forces on a gliding parachute. The total weight of the system, W<~~sub~~>T</~~sub~~> . must be balanced by the resultant force. R. However, a lifting force is required for glide. To satisfy the force balance		Figure 4-12 shows the balance of forces on a gliding parachute. The total weight of the system, <math>W_T</math>. must be balanced by the resultant force. R. However, a lifting force is required for glide. To satisfy the force balance

	~~R = C~~<~~sub~~>R</~~sub~~> * S * p/2 * v		<math>R=W_T</math>

	Trajectory velocity, V<~~sub~~>T</~~sub~~>, is calculated		<math>R=\sqrt{L^2+D^2}</math>

			<math>R=C_R\cdot S \cdot \rho /2 \cdot v^2_T </math>

			<math>C_R=\sqrt{C_L^2+C_D^2}</math>

			Trajectory velocity, <math>v_T</math>, is calculated

			<math>v_T=\sqrt{\frac{2W}{S \cdot \rho}\cdot \frac{1}{\sqrt{C_L^2+C_D^2}}}</math>

			or

			<math>v_T=\sqrt{\frac{2W}{S \cdot \rho}\cdot \frac{1}{C_R}}</math>

	Horizontal velocity is calculated		Horizontal velocity is calculated

	V<~~sub>H</sub~~> = ~~V<sub>T~~</~~sub~~> ~~• cosø~~, and vertical velocity, v<~~sub>v</sub~~> = ~~V<sub>T~~</~~sub~~> ~~• sinø~~		<math>v_H=v_T \cdot cos\phi </math>, and vertical velocity, <math>v_v=v_T \cdot sin \phi</math>

	The glide ratio is obtained from		The glide ratio is obtained from

	~~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~~<~~sub~~>~~R</sub>, results in a low glide or trajectory V<sub>T</sub>, desirable for landing. A small C<sub>R</sub> results in a high glide velocity, V<sub>T~~</~~sub~~>~~, 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.~~		<math>\frac{L}{D}=\frac{v_H}{v_v}=\frac{C_L}{C_D}</math>

			Analysis of Figure 4-12 indicates that the larger the ratio of lift to drag, the better the glide ratio, L/D. A high resultant coefficient, <math>C_R</math>, results in a low glide or trajectory <math>v_T</math>, desirable for landing. A small <math>C_R</math> results in a high glide velocity, <math>v_T</math>, 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.[[File:FIGURE 4-12. Forces Acting on a Gliding Parachute..jpg\|center\|thumb\|465x465px\|FIGURE 4-12. Forces Acting on a Gliding Parachute.]]
	[[File:FIGURE 4-12. Forces Acting on a Gliding Parachute..jpg\|center\|thumb\|465x465px\|FIGURE 4-12. Forces Acting on a Gliding Parachute.]]

	=== 4.5.3 Parasite Drag and Induced Drag ===		=== 4.5.3 Parasite Drag and Induced Drag ===

Parachute at 15:07, 27 June 2024

2024-06-27T15:07:38Z

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Parachute at 22:28, 26 June 2024

2024-06-26T22:28:36Z

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Parachute at 22:04, 26 June 2024

2024-06-26T22:04:06Z

← Older revision		Revision as of 22:04, 26 June 2024
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	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.		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.

	The acceleration of gravity, ''g'', at sea ~~lavel~~ is		The acceleration of gravity, ''g'', at sea level is

	* ''g'' = 32.174 ft/s2 or 9.80665 m/s2.		''g'' = 32.174 ft/s2 or 9.80665 m/s2.

	The value g = 9.08665 m/s is standardized internationally but is accurate only for a latitude of 45 degrees.		The value g = 9.08665 m/s is standardized internationally but is accurate only for a latitude of 45 degrees.
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	=== 4.2.1 Continuity L.aw ===		=== 4.2.1 Continuity L.aw ===
	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.		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.
			[[File:FIGURE 4-1. Typical Streamline..jpg\|center\|thumb\|642x642px\|FIGURE 4-1. Typical Streamline.]]
	[~~Insert Figure~~ 4-1]

	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:		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:

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	=== 4.2.2 Bernoulli Equation ===		=== 4.2.2 Bernoulli Equation ===
	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.		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.
			[[File:FIGURE 4-2. Pressure and Velocity Distribution in a Streamline Element..jpg\|center\|thumb\|518x518px\|FIGURE 4-2. Pressure and Velocity Distribution in a Streamline Element.]]
	[~~Insert Figure~~ 4-2]FIGURE 4-2 Pressure and Velocity Distribution in a Streamline Element.

	The following equation can be written		The following equation can be written

TuanHTruong: /* 4.7 REFERENCE MATERIAL */

2024-05-07T18:30:39Z

4.7 REFERENCE MATERIAL

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	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).		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).

	= 4.7 REFERENCE MATERIAL =		== 4.7 REFERENCE MATERIAL ==

	4.1 H. H. Hurt. Aerodynamics for Naval Aviators Navy Manual NAVWEPS 00 80T 80. Chief of Naval Operations, Aviation Training Division.		4.1 H. H. Hurt. Aerodynamics for Naval Aviators Navy Manual NAVWEPS 00 80T 80. Chief of Naval Operations, Aviation Training Division.

TuanHTruong: /* 4.7 REFERENCE MATERIAL */

2024-05-07T18:29:17Z

4.7 REFERENCE MATERIAL

← Older revision		Revision as of 18:29, 7 May 2024
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	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).		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).

	== 4.7 REFERENCE MATERIAL ==		= 4.7 REFERENCE MATERIAL =
	4.1 H. H. Hurt. Aerodynamics for Naval Aviators Navy Manual NAVWEPS 00 80T 80. Chief of Naval Operations, Aviation Training Division.		4.1 H. H. Hurt. Aerodynamics for Naval Aviators Navy Manual NAVWEPS 00 80T 80. Chief of Naval Operations, Aviation Training Division.