A theory of three-dimensional parachute dynamic stability
01 Jan 1968-Journal of Aircraft (American Institute of Aeronautics and Astronautics (AIAA))-Vol. 5, Iss: 1, pp 86-92
TL;DR: In this paper, the three-dimensional motion of a freely descending parachute is studied with a five-degreeoffreedom analysis (the roll motion is neglected), and equations of motion are non-dimensionalized and the resulting parameters discussed.
Abstract: The three-dimensional motion of a freely descending parachute is studied with a five-degreeoffreedom analysis (the roll motion is neglected). The equations of motion are nondimensionalized and the resulting parameters discussed. Exact expressions are given for the longitudinal and lateral small-disturbance stability of the familiar gliding motion of parachutes. The breakdown of these small-disturbance expressions is illustrated by exact large-disturbance studies. A large longitudinal disturbance of most parachutes will result in a large pitching motion, whereas a large lateral (out of the glide plane) disturbance will usually cause a large angle vertical coning motion. Exact algebraic expressions are given for the coning mode, which is a stable rotation, and a small amount of available coning data is included for comparison. Some parametric computer studies of the various motions are also shown.
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TL;DR: In this article, a six-degree-of-freedom model of a guided circular parachute is presented, which includes the basic equations of motion, analysis and computation of the aerodynamic forces and moments, and investigation with modeling of special modes observed in flight.
Abstract: : 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 six-degree- 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-fluid-dynamics modeling for both undistorted (uncontrolled) and distorted (controlled) canopy shapes, introducing and computing control derivatives, and providing comparison with the real flight 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 flight. It then introduces a new application of a two-step aerodynamic parameters identification 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.
49 citations
TL;DR: In this article, the three-dimensional motion of a non-rigid parachute and pay load system is studied, where both the parachute and payload are assumed to have five degrees of freedom (roll about the axes of symmetry is neglected).
Abstract: The three-dimensional motion of a nonrigid parachute and pay load system is studied. Both the parachute and payload are assumed to have five degrees-of-freedom (roll about the axes of symmetry is neglected). They are coupled together by a fixed-length connector, or riser. The general nonlinear equations of motion are put in a form that is convenient for digital computer solutions. All equations are written in dimensionless form and, using smalldisturbance theory, are linearized. The linear equations are then examined in a stability analysis. A proposed method of checking the linear stability criterion by forming the general solution of the linear equations is discussed. A sample stability analysis is presented to show how the methods developed might be applied to a particular problem. The problem consists of selecting a parachute to stabilize a statically unstable payload. With the methods developed, it is possible to examine in considerable detail the dynamic behavior of a nonrigid parachute and payload system.
34 citations
TL;DR: In this paper, a stiffnessweight index was proposed to define the structural characteristics of a parachute model and fabrications details for building models with a low stiffness index were developed for wind-tunnel and catapult tests with models of different stiffness indexes.
Abstract: In parachute model experiments, performed for the study of static and dynamic parachute characteristics, one must consider, besides Reynolds and Mach number influences, the effects of canopy porosity, weight, and flexibility. Porosity can be expressed as a function of Reynolds and Mach numbers. For the definition of the structural characteristics, a stiffnessweight index is proposed. Fabrication details for building models with a low stiffness index were developed. Wind-tunnel and catapult tests with models of different stiffness indexes showed significant differences in parachute drag, inflation, and squidding characteristics.
32 citations
TL;DR: In this paper, the authors defined the drag coefficient based on S CDS -drag area of fully inflated fully inflated parachute, ft2 d = constructed parachute diameter across base of conical parachute, msl, ft j£t = outflow coefficient (approximately 0.6) Ki = inflow coefficient (a value o^f 0.7 is used for a first approximation, and adjusted as determined by experimental data) Lr = circumferential length of reefing line.
Abstract: Nomenclature CD = drag coefficient based on S CDS — drag area of fully inflated parachute, ft2 (CiwS)r == drag area of reefed parachute, ft2 d = constructed parachute diameter across base of conical parachute, ft Di = inflated diameter, f d, ft hr — release altitude, msl, ft j£t = outflow coefficient (approximately 0.6) Ki = inflow coefficient (a value o^f 0.7 is used for a first approximation, and adjusted as determined by experimental data) Lr = circumferential length of reefing line, ft AP = pressure across canopy, lb/ft2 q = dynamic pressure JpF2, lb/ft2 R = radius of canopy during inflation normal to mean local canopy contour, ft Rm = maximum inflated radius of canopy, ft (approximately | of constructed radius) RQ = initial radius of canopy at start of inflation, ft (radius of suspension lugs or pack radius) s = tensile stress, lb/ft2 S = area of base of conical chute, 7rd2/4, ft2 t = thickness of ribbon, ft if = filling time, sec T — ribbon tensile load, Ib V = vehicle velocity, fps Fo = vehicle velocity at start of parachute filling, fps w = ribbon width, ft W = vehicle weight, Ib XG = geometric porosity of canopy p = air density, slugs/ft3
31 citations
14 Aug 2000
TL;DR: In this article, the development of an autonomous guidance, navigation and control system for a flat solid circular parachute is addressed, which is a part of the Affordable Guided Airdrop System (AGAS) that integrates a low-cost guidance and control systems into fielded cargo air delivery systems.
Abstract: This paper addresses the development of an autonomous guidance, navigation and control system for a flat solid circular parachute. This effort is a part of the Affordable Guided Airdrop System (AGAS) that integrates a low-cost guidance and control system into fielded cargo air delivery systems. The paper describes the AGAS concept, its architecture and components. It then reviews the literature on circular parachute modeling and introduces a simplified model of a parachute. This model is used to develop and evaluate the performance of a modified bang-bang control system to steer the AGAS along a pre-specified trajectory towards a desired landing point. The synthesis of the optimal control strategy based on Pontryagin's principle of optimality is also presented. The paper is intended to be a summary of the current state of AGAS development. The paper ends with the summary of the future plans in this area.
30 citations
References
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01 Apr 1965
TL;DR: An experimental arrangement for determining the apparent moment of inertia of parachute canopy models is described in this paper, where the rigid canopy models are attached to a simple torsion pendulum and the periods of oscillation of the models and suspension system in air and in water are measured and used to calculate the apparent moments of inertia.
Abstract: : An experimental arrangement for determining the apparent moment of inertia of parachute canopy models is described. The rigid canopy models are attached to a simple torsion pendulum and the periods of oscillation of the models and suspension system in air and in water are measured and used to calculate the apparent moment of inertia of the model canopies. The validity of the experimental arrangement was verified by measuring the apparent mass of some simple geometric bodies such as spheres and cubes and comparing the results with known theoretical values. Models of the circular flat, ribbon and ribless guide surface canopy shapes were tested for angular motion about two different axes and the results are presented in nondimensional coefficient form. Additional results showing the effect of geometric porosity on the apparent moment of inertia of a ribbon type parachute canopy model are presented in the appendix.
22 citations
01 Jun 1965
TL;DR: In this article, the dynamic stability of a parachute load system has been analytically investigated for a pointmass load and a statically stable parachute, using the apparent mass and apparent moment of inertia, as well as the aerodynamic coefficients of the parachute canopy.
Abstract: : The dynamic stability of a parachute load system has been analytically investigated for a pointmass load and a statically stable parachute. A typical system consisting of a relatively large suspended load mass and small ribless guide surface parachute has been numerically calculated. Utilizing the apparent mass and apparent moment of inertia, as well as the aerodynamic coefficients of the parachute canopy, the equations of motion for the system have been solved. The influence of several design parameters upon the dynamic stability characteristics of the system have been discussed.
8 citations