A Theory of Three-Dimensional Parachute Dynamic Stability

White, Frank M.; Wolf, Dean

doi:10.2514/6.1966-1504

Cited by 11 publications

(9 citation statements)

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“…The values for the K ij coefficients appear to range between 0.2 and 1 in relevant studies. 2,3,5 Additionally, the ratio K 33 /K 11 = 2 has been taken in multiple recent studies and appears to provide a good match with flight data. 2, 3…”

Section: A Eaton Parachute Dynamics Modelmentioning

confidence: 52%

“…When neglecting apparent inertia (k = 0), it is found that the required C Nα for stability is small but nonzero, which is similar to the White-Wolf dynamic stability analysis. 5 It was found that the apparent inertia has a strong destabilizing effect, greatly increasing the requirements for dynamic stability. As the apparent inertia terms increase, the magnitude of the coupling moment increases.…”

Section: Apparent Inertia Dependence Resultsmentioning

confidence: 99%

“…The effect of C Nα on equilibrium is of special importance to the stability argument as a minimum C Nα is often used to describe parachute stability. 5 Unlike in the case without the apparent inertia couples where the equilibrium condition is fixed with respect to C Nα , stability analyses must now include the change in the equilibrium state. The effect of changing density was also inspected.…”

Section: Effects On Equilibrium Pointmentioning

confidence: 99%

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Parachute Dynamic Stability and the Effects of Apparent Inertia

Ginn

Clark

Braun

2014

AIAA Atmospheric Flight Mechanics Conference

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The dynamic stability and equilibrium conditions of a parachute are studied using a six degree of freedom dynamic model that includes apparent inertia effects. Existing parachute dynamic models are discussed and the selection of a relevant model is shown. The chosen dynamic model that incorporates apparent inertia is summarized and used for analysis. The moments on the parachute system caused by the apparent inertia term are shown to affect both the equilibrium point and the stability of the system. The adjustment to equilibrium is observed and discussed. A small disturbance stability analysis is performed to give a stability criterion in terms of the slope of the tangential aerodynamic force. The dynamic modes, pitching and coning, are discussed. Computational integration of the equations of motion is used to validate the small disturbance analysis as well as to show the effects of large disturbances.

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Section: A Eaton Parachute Dynamics Modelmentioning

confidence: 52%

Section: Apparent Inertia Dependence Resultsmentioning

confidence: 99%

Section: Effects On Equilibrium Pointmentioning

confidence: 99%

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Parachute Dynamic Stability and the Effects of Apparent Inertia

Ginn

Clark

Braun

2014

AIAA Atmospheric Flight Mechanics Conference

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“…[5][6][7]. Note that the longitudinal short period undamped natural frequency is also marked in Fig.…”

Section: Analysis Of the Resultsmentioning

confidence: 94%

Validation of a Simulation Model for a Planetary Entry Capsule

Guglieri

Quagliotti

2003

Journal of Aircraft

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Subsonic static and oscillatory aerodynamic coef cients were measured at Politecnico di Torino for a planetary entry capsule model. The experimental data set was included in a mathematical model of payload-decelerator system, and the results of simulations were compared with ight-test data. The frequency-domain attitude response of the capsule was reproduced during the main parachutes' deployment, and discrepancies for the drogue opening phase were observed. The impact on simulations of atmospheric turbulence and asymmetries in the parachute suspension system was also considered. The results suggest that several factors may affect the delity of simulations such as correct modeling of suspension system geometry and exibility, parachute aerodynamics, accuracy of payload inertial data, and accurate matching of real ight external perturbations. The effect of some design parameters on capsule attitude dynamics was evaluated. The arti cial increase of capsule damping coef cients produced observable effects on attitude time histories for large perturbations of the aerodynamic derivatives only. The dynamic stability of the system is reduced for large increase of riser length and parachute added mass. Nomenclaturereference length (capsule diameter) F = elastic force I ay = added moment of inertia of the parachute I x ; I y ; I z ; I x z = mass moments of inertia K = elastic constant L = rolling moment L b = additional rolling moment due to bridles l = length M = pitching moment m = mass m ax ; m ay = axial and transverse added masses of the parachute N = yawing moment N b = additional yawing moment due to bridles p; q; r = angular rates (capsule) q 1 = dynamic pressure, ½V 2 =2 Re = Reynolds number, based on capsule diameter d S = reference area, ¼ d 2 =4 S P = parachute reference area s; y; h = Earth-xed axes [T BV ] = rotation matrix from s; y; h to x B ; y B ; z B ; f .Á; µ; Ã ) [T P V ] = rotation matrix from s; y; h to x P ; y P ; z P ; f .Á P ; µ P ; Ã P ) degli Abruzzi 24; quagliotti@polito.it.Senior Member AIAA.auxiliary body-xed longitudinal axes (origin at capsule theoretical apex) x B ; y B ; z B = body-xed axes (origin at capsule c.g.) x P ; y P ; z P = body-xed axes (origin at parachute c.g.) Y = lateral force Z = normal force ®;¯= angle of attack and sideslip (capsule) 1l = length increment ² = strain, 1l=l ¾ = total angle of attack (capsule) N ¾ = measurement accuracy of wind-tunnel data ¿; Â = angular displacement of the riser with respect to s; y; h (see Fig. 1) Á; µ ; Ã = Euler angles Á a = aerodynamic roll angle (capsule) Subscripts b = bridle CG = center of gravity (capsule) CP = center of gravity (parachute) g = gust P = parachute PA = parachute attach point P2 = point of con uence of riser and suspension lines r = riser s = suspension line 0 = reference condition 1, 2, 3 = vector components

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“…White and Wolf 8 showed that the longitudinaland the lateral motion of a parachute in glide plane are suf ciently uncoupled. Therefore, the longitudinal and lateral motion of a symmetric parachute can be studied separately, similar to the study of the aircraft linearized dynamics.…”

Section: Computation Of Forces and Moments Aerodynamic Forces And Mommentioning

confidence: 99%

Six-Degree-of-Freedom Model of a Controlled Circular Parachute

Dobrokhodov

Yakimenko

Junge

2003

Journal of Aircraft

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The paper continues a series of publications devoted to modern advances in aerodynamic decelerator system technology started recently (Journal of Aircraft, Vol. 38, No. 5, 2001) and addresses the development of a sixdegree-of-freedom model of a guided circular parachute. The paper reviews existing circular parachute models and discusses several modeling issues unresolved within the frame of existing approaches or completely ignored so far. These issues include using data obtained in the aerodynamic experiments and computational-uid-dynamics modeling for both undistorted (uncontrolled) and distorted (controlled) canopy shapes, introducing and computing control derivatives, and providing comparison with the real ight data. The paper provides step-by-step development of the mathematical model of circular parachute that includes the basic equations of motion, analysis and computation of the aerodynamic forces and moments, and investigation with modeling of special modes observed in ight. It then introduces a new application of a two-step aerodynamic parameters identi cation algorithm that is based on comparison with two types of the air-drop data (uncontrolled set and controlled one). The paper ends with summary of the obtained results and proposes a vital direction for the further elaboration of the developed model. = component of an aerial delivery system (i 2 f1; 2; 3; 4g/ j = axes of fbg ( j 2 fx; y; zg/ k = actuator number (k 2 f1; 2; 3; 4g/ m, n = row and column of 6 £ 6 tensor vector Nomenclature

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A Theory of Three-Dimensional Parachute Dynamic Stability

Cited by 11 publications

References 0 publications

Parachute Dynamic Stability and the Effects of Apparent Inertia

Parachute Dynamic Stability and the Effects of Apparent Inertia

Validation of a Simulation Model for a Planetary Entry Capsule

Six-Degree-of-Freedom Model of a Controlled Circular Parachute

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