This paper presents a framework for onboard trajectory planning and guidance for a large class of autonomously guided parafoils. The problem is for the parafoil to reach a given location at a specified altitude with a specified final heading. Through appropriate change of the independent variable, the trajectory planning problem is converted from a three-dimensional free-final-time problem to a two-dimensional fixed-final-time problem. Using the wellknownDubinspath synthesis andknownparafoil performanceparameters, a concept of altitudemargin is developed as aquantitativemeasure of the availablemaneuvering energy for use in trajectory planning.Ahybrid strategy using two methods to generate kinematically feasible fixed-time trajectories is presented, each targeting a different range of initial values of the altitude margin. The trajectory can be replanned onboard in every guidance cycle, making the guidance effectively closed-loop, or replanned whenever the actual deviation of the actual condition from the reference trajectory exceeds a threshold. The proposed planning and guidance algorithm applies to a large class of parafoil canopies and payloads, which encompasses wide variations in the lift-to-drag ratio, wing loading, and maximum turn rate. The guidance logic has the potential of requiring little or no tuning to accommodate variations in canopy performance. Monte Carlo simulations are conducted to evaluate the effectiveness of the algorithm with dispersions in canopy performance, loading, wind profile errors, navigation uncertainty, using lateral control only, and using both longitudinal and lateral control.

https://lib.dr.iastate.edu/cgi/viewcontent.cgi?article=1629&context=etd

In-flight trajectory planning and guidance for autonomous parafoils

The paper presents an initial move to develop a scalable high-degree-of-freedom model of the parafoilpayload system. The intention is to develop the tool capable of: i) determining basic system’s geometry parameters by observing the video data of the real descend, ii) readjusting the nominal aerodynamic and control coefficients incorporated into the well-established equations of motions, and iii) performing model identification to tune numerous relative variables to achieve the best fit with the real drop data if available. Since in the certain way such a tool would represent some kind of generalization of the modeling efforts undertaken so far, the present paper starts from a comprehensive review of publications devoted to the modeling of parafoil-payload systems. The paper then briefly addressed the current stage of the development of a scalable model. In anticipation of real drop data to validate the approach paper ends with conclusions. I. Introduction UE to their ability to cover large horizontal distances from the drop point and their controllability, gliding parachutes offer considerable scope for military application in the delivery of troops, stores and munitions, enhanced safety for aircrew, etc. One concept in the gliding-parachute category which has received attention in mid 60’s is a ram-air-inflated fabric wing (called the Jalbert load-distributing flares parafoil). It has a rectangular planform and an airfoil cross-section with an opening at the leading edge to allow ram air to enter and inflate the wing to the desired shape. The payload is suspended on lines below the wing. Some of the earliest projects involving the usage of parafoil-based systems were discussed by Nikolaides and Knapp. 1-7 Lingard 8 provided comprehensive bibliography of ram-air literature up to 1980. Some definitions that in a quarter of a century have become sort of standard, discussion on modern parafoil parameters and their design were presented by Poynter. 9 For the past 40 years a lot of models of different parafoil-payload systems were developed to address the variety of issues. Lately, the high-fidelity 8 and 9 degrees-of freedom (DoF) models were also created. This paper describes current status of an attempt to develop a scalable model of a generic parafoil-payload system based on the model that has already been developed earlier for the Pegasus payload delivery system by FXC Corp. 10 In what follows the extensive review of the aerodynamic data available for different parafoils as well as numerous attempts to model parafoil-payload systems are given first. Then a brief description of the software developed so far is presented. This tool also employs the system identification tools to better match the real drop data if available. These tools however are considered in a separate paper. 11

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On the Development of a Scalable 8-DoF Model for a Generic Parafoil-Payload Delivery System

The incompressible Navier-Stokes equations together with the one equation Spalart-Allmaras turbulence model were solved using a finite volume flow solver to examine the flowfield and forces on the central cross section of a high-performance parafoil canopy. The parafoil surfaces were assumed to be impermeable, rigid, and smooth. The flowfield consists of a vortex inside the parafoil cell opening, which effectively closes off the opening and diverts the flow around the leading edge. The flow about the parafoil experiences a rather bluff leading edge, in contrast to the smooth leading of the baseline airfoil. A separation bubble exists on the lip of the parafoil lower surface. The lift coefficient of the parafoil section increases linearly with the angle of attack up to 8.5 degrees and the parafoil lift-curve slope is about 8% smaller than the same for the baseline airfoil. The cell opening has a major effect on the drag before stall; the parafoil drag is at least twice the baseline airfoil drag. The minimum drag of the parafoil section occurs over the angle-of-attack range of 2.5-7 degrees.

Computation of Flow over a High-Performance Parafoil Canopy

Computational results for flow past a two-dimensional model of a ram-air parachute with leading edge cut are presented. Both laminar (Re=104) and turbulent (Re=106) flows are computed. A well-proven stabilized finite element method (FEM), which has been applied to various flow problems earlier, is utilized to solve the incompressible Navier-Stokes equations in the primitive variables formulation. The Baldwin-Lomax model is employed for turbulence closure. Turbulent flow computations past a Clarck-Y airfoil without a leading edge cut, for α=7.5°, result in an attached flow. The leading edge cut causes the flow to become unsteady and leads to a significant loss in lift and an increase in drag. The flow inside the parafoil cell remains almost stagnant, resulting in a high value of pressure, which is responsible for giving the parafoil its shape. The value of the lift-to-drag ratio obtained with the present computations is in good agreement with those reported in the literature. The effect of the size and location of the leading edge cut is studied. It is found that the flow on the upper surface of the parafoil is fairly insensitive to the configuration of the cut. However, the flow quality on the lower surface improves as the leading edge cut becomes smaller. The lift-to-drag ratio for various configurations of the leading edge cut varies between 3.4 and 5.8. It is observed that even though the time histories of the aerodynamic coefficients from the laminar and turbulent flow computations are quite different, their time-averaged values are quite similar.

Computation of two-dimensional flows past ram-air parachutes

The flowfield around a model MC-4 ram-air personnel parachute canopy was examined using the steady, incompressible Navier–Stokes equations together with the one-equation Spalart–Allmaras turbulence model. A finite volume flow solver was used to compute the flowfield, forces, and moments on the canopy in steady glide and at sideslip. The canopy surfaces were assumed to be impermeable and rigid. The oncoming flow barely penetrates the canopy opening, and creates a large separation bubble below the lower lip of each half-cell. The flow does not reattach, and a thick boundary layer is present on the lower surface of the canopy. The flow over the upper surface of the canopy remains attached until the separation point near the trailing edge. The lift increases linearly with the angle of attack up to about 12 deg, whereas the quarter-chord pitching moment decreases nearly linearly between 2 and 12 deg angle of attack. For sideslip angles up to 20 deg, the side force increases linearly with the sideslip angle eve...

Simulation of Flowfield Around a Ram-Air Personnel Parachute Canopy

and agree well with the semiempirical expression previously determined. Most encouraging results were obtained from an experiment performed on the elliptical airfoil of 18% thickness ratio with dual symmetrical jets. These results indicate that the leading-edge jet does not disturb the flow and actually furnishes some additional reaction force to the lift. Hence, the important application of the elliptical airfoil (or oval airfoil) with dual jets to the retreating blade of a helicopter rotor is evident. Furthermore, the results of aerodynamic response measurements of the model to cyclic changes in the blowing jet are surprisingly encouraging. The cyclic valve was tested at frequencies equivalent to twice that of the rotational speed of a conventional helicopter blade, and the response of the lift was found to be excellent with negligible delay. The response of the drag as well as the chordwise pressure distribution to the cyclic changes in the blowing jet were also found to be very good. These results clearly indicate that the periodic variation of lift on the airfoil can be fulfilled by cyclic variation of the jet momentum; hence, the circulation control problem is reduced to simply the problem of pressure control inside the model.

A review of para-foil applications

More demanding requirements f o r sounding rocket accuracy aiid flight stability, and an increasing number of flight failures have caused a recent re-examination of actual rocket flight performance. The twin t e r ro r s of Magnus Instability'and Catastrophic Yaw, which plague conventional ordnance, also stalk rockets. Investigations of the non-linear dynamic behavior of sounding rockets have been undertaken by using'a computer program for numerically integrating the six-degree-of-freedom equations of motion. The use of this computer program has made possible the comparison of experimental and analytical determinations of the flight performance of sounding rockets. A l s o , it has provided a better understanding of noli-linear effects and, most important, it has provided new methods for the analysis of flight data. Accurate angular orientation data obtained from the free flight telemetry records of two Tomahawk sounding rockets has k e n "fitted" by the Quadracyclic Theory using a special formulation of the \lethod of Differential Corrections. The exact motion of the rockets and thcir associated aerodynamic stability coefficients, CLw , C v q + GuCi and CM c! have been determined. coefficients obtained from the flight data a r e compared with wind tunnel values. the earth's atmosphere. In the othercase, the rocket was re-entering the earth's atmosphere. In both cases , the Magnus Moment is shown to play a major role in the clynamic stability of the sounding rocket. able f o r detailed analysis of (:atastropliic Yaw, special dynamic wind tunnel tests were carr ied out which demonstrate that Roll Lock-In can occur in P K' Where possible the aerodynamic stability In onc case , the Tomahawk rocket was exiting If'hjle no sounding rocket flight data was availIhc>cke'i t i c supersonic spmk . INI'KODUCTION By the end of World War 11, a considerable su r plus of rocket motors had accumulated. Thus, it was possible to initiate a program for the scientific sounding of the earth 's upper atmosphere. a s today, was to place a scientific instrument to a s high an altitude as possible. The aim was high altitude, not high accuracy. A wobbling motion of the payload was relatively unimportant. For a given rocket motor, maximum altitude was reached by minimizing the total weight of the sounding rocket. Over reducing the weight of the motor case resulted in dramatic explosions. However reduction of the weight of the stabilizing f ins , by reducing their a rea , caused no such dramatic consequences, unless, of course, the static m a r gin was decreased to zero, thereby causing the rocket to tumble. These minimum fins, however, often caused the rocket to fail to reach the desired altitude due to the drag from the resulting wobbling motion and ' also caused the rocket to be quite inaccurate. poor launchings would have been classed a s flight failures, however, the scientific investigators were not unduly concerned since their experiments did yield data on the upper atmosphere and, also, the accuracy of the trajectory was quite unimportant;except , when the rocket returned to inhabited areas , which was not infrequent. Xerodyiiamically speaking, the usual sounding rocket static margins were an order of magnitude smaller than the minimums permitted on conventional ordnance. Ordnance static margins run between 20% to XP) of missile length. Sounding rockt static margins a re often a s small a s 2% or 3%. This same situation exists even today. perform a s well a s they do. l 'he primary reason for this unnatural success, in spite of the poor a e r o d ~ ~ ~ a m i c s , is due to 111e fact that the acccleration of the souiiding rocket during burning i d quite Jyiiaiiiically stabilizing. However ~ as the c;ounding rocket leaves the cai-ths atmosphere thc nutotioiin~ motion often builds up t u a large conilig to the decreasing density of the atmosphere. inore sophisticated and large wobbling mrttio have become unacceptable. Also, soundiiig rockets ha\re become larger and more expensive. E ,astly, The primary purpose of these early launchings, In normal ordnance practice these particular In this light, it is amazing that sounding rockets In recent years scientific payloads hnoc become

The determination of aerodynamic stability coefficients from sounding rocket flight data

Investigation of the nonlinear flight dynamics of ordnance weapons

Effects of rifling and N-vanes on the Magnus characteristics of bodies of revolution

Linear and nonlinear theories which abandon the usual relations between pitch and yaw stability derivatives are developed to account for nonsymmetric aerodynamics. Motions of a 10° cone and a 60° cone are fit using two separate procedures: the numerical integration method using parametric differentiation and a newly developed approach to determine modal amplitudes, frequencies, and damping rates by the numerical inversion of Laplace transformations to begin a differential corrections procedure. It is shown that accurate fits of nonsymmetric vehicle motions are possible and that spinning bodies of revolution, at times, must be considered nonsymmetric vehicles.

John D. Nicolaides

Papers

A review of para-foil applications

The determination of aerodynamic stability coefficients from sounding rocket flight data

Investigation of the nonlinear flight dynamics of ordnance weapons

Effects of rifling and N-vanes on the Magnus characteristics of bodies of revolution

Determination of Nonsymmetric Aerodynamics of Re-entry Missiles