: 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.

/pdf/six-degree-of-freedom-model-of-a-controlled-circular-2o015tin1i.pdf

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

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.

Dynamic Stability of a Nonrigid Parachute and Payload System

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.

Flexibility as a Model Parachute Performance Parameter

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

Aerodynamic decelerators - An engineering review

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.

Performance, Control, and Simulation of the Affordable Guided Airdrop System

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.

Dean F. Wolf

Papers

A theory of three-dimensional parachute dynamic stability

A theory of three-dimensional parachute dynamic stability