Dynamic Response Analysis of a High Glide Ratio Parachute System

Document Type : Original Article


Department of Aerospace Engineering ,Malek-Ashtar University of Technology, Tehran, Iran


This paper is concerned with the dynamic stability study of a gliding parachute-payload system along its gliding path. To scrutinize the respective dynamic response characteristics after releasing from high altitude, a modified multi-body model is developed. In the stability analysis procedure, the yawing motion of the payload is considered in system dynamics, which in turn creates a state-dependent matrix in the stability analysis and makes the linearization algorithm more cumbersome. To solve the problem, a unified Jacobian-based symbolic differentiation algorithm is implemented and the dynamics is linearized about various operating points along gliding segment of a typical planned trajectory. Based on results, the system has short period and phugoid modes in longitudinal channel just like an aircraft. In addition to dutch roll mode, the system has a low frequency coupled roll-spiral mode in lateral-directional channel which is a result of effective canopy anhedral angle. It is shown, the coupled mode can be decomposed into two distinct roll and spiral modes for small anhedral angles. Based on results, as the parachute descends, both the period and damping ratio for the short period mode were increased by 18 and 30%, respectively. For the phugoid mode the period of oscillations is decreased by 20% and the damping ratio, almost remains constant. For the lateral-directional channel,. As the parachute descends, the dutch roll mode is destabilized whereas the other modes are stabilized. Furthermore, from a practical point of view, lengthening the suspension lines stabilizes the coupled roll-spiral mode whereas destabilizes the other modes.


Main Subjects

1.       Abbasnejad B., Shabani R., Rezazadeh G., Stability Analysis in Parametrically Excited Electrostatic Torsional Micro-actuators, International Journal of Engineering, Transactions C: Aspects, Vol. 27, No. 3, (2014) 487-498. DOI: 10.5829/idosi.ije.2014.27.03c.17.
2.     Pirzadeh M., Toloei A. R., Vali A. R., ‘Effects of Flight Dynamics on Performance of One Axis Gimbal System, Considering Disturbance Torques’, International Journal of Engineering, Transactions B: Applications, Vol. 28, No. 8, (2015) 1108-1116. DOI : 10.5829/idosi.ije.2015.28.08b.01.
3.     Berdnikov V., Lokhin V.,’Synthesis of Guaranteed Stability Regions of a Nonstationary Nonlinear System with a Fuzzy Controller’, Civil Engineering Journal, Vol. 5, No. 1, (2019), DOI: 10.28991/cej-2019-03091229.
4.     Mihajlović G., Živković M.,’ Sieving Extremely Wet Earth Mass by Means of Oscillatory Transporting Platform’, Emerging Science Journal, Vol. 4, No. 3 (2020) 172-182. DOI: 10.28991/esj-2020-01221
5.     Rahimi F., Aghayari R., Samali B.,’Application of Tuned Mass Dampers for Structural Vibration Control: A State-of-the-art Review’, Civil Engineering Journal, Vol. 6, No. 8, (2020), 1622-1651. DOI: 10.28991/cej-2020-03091571
6.     Hailiang M., Zizeng Q.,’9-DOF Simulation of Controllable Parachute System for Gliding and Stability’, Journal of National University of Defense Technology, Vol. 16, No. 2, (1994), 49–54.
7.     Iosilevskii G (1995) Center of Gravity and Minimal Lift Coefficient Limits of a Gliding Parachute. Journal of Aircraft, Vol. 32, No. 6, 1297-1302. DOI: 10.2514/3.46878
8.     Brown, G. J., ‘Parachute Steady Turn Response to Control Input’, Aerospace Design Conference, Irvine, CA, USA, (1993). DOI: 10.2514/6.1993-1241
9.     Crimi P (1990) Lateral Stability of Gliding Parachutes. Journal of Guidance, Control and Dynamics, Vol. 13, No. 6, 1060-1063. DOI: 10.2514/3.20579
10.   Lissaman, P, Brown G, “Apparent Mass Effects on Parachute Dynamics. Aerospace Design Conference”, Irvine, California, USA. (1993), DOI : 10.2514/6.1993-1236
11.   Lingard J. S., ‘Ram-air Parachute Design’.13th AIAA Aerodynamic Decelerator Systems Technology Conference; Clearwater Beach, Florida, USA, (1995).
12.   Prakash O., Daftary A., Ananthkrishnan A., ‘Bifurcation Analysis of Parachute-Payload System Flight Dynamics’,  AIAA Atmospheric Flight Mechanics Conference and Exhibit; San Francisco, California, USA, (2005). DOI: 10.2514/6.2005-5806
13.   Jann, T Advanced Features for Autonomous Parachute Guidance, Navigation and Control. 18th AIAA Aerodynamic Decelerator Systems Technology Conference and Seminar; Munich, Germany, (2005). DOI: 10.2514/6.2005-1642
14.   Barrows T  Apparent Mass of Parachutes with Spanwise Camber. Journal of Aircraft, Vol. 39, No. 3, (2002), 445-451. DOI: 10.2514/2.2949
15.   Zhang Z, Zhao Z, Fu Y., ‘Dynamics analysis and simulation of six-DOF parafoil system’, Cluster Computing, Vol. 22, No. 5, (2018), 1-12. DOI: 10.1007/s10586-018-1720-3
16.   Slegers N., Beyer E., Costello M., ‘Use of Variable Incidence Angle for Glide Slope Control of Autonomous Parachute’. Journal of Guidance, Control, and Dynamics, Vol. 31, No. 3, (2008), 585-596. DOI: 10.2514/1.32099
17.   Müller S, Wagner O, Sachs G. ’A High-Fidelity Nonlinear Multibody Simulation Model for Parachute Systems,, 17th AIAA Aerodynamic Decelerator Systems Technology Conference and Seminar; Monterey, California, (2003). DOI: 10.2514/6.2003-2120
18.   Redelinghuys C.,’A Flight Simulation Algorithm for a Parachute Suspending an Air Vehicle’, Journal of Guidance, Control, and Dynamics, Vol. 30, No. 3, (2007), 791-803. DOI: 10.2514/1.25074
19.   Slegers N  Effects of Canopy-Payload Relative Motion on Control of Autonomous Parachute. Journal of Guidance, Control, and Dynamics, Vol. 33, No. 1, (2010), 116-125. DOI: 10.2514/1.44564
20.   Mooij E, Wijnands Q, Schat, B.,’9-DOF Parachute/Payload Simulator Development and Validation’, AIAA Modeling and Simulation Technologies Conference and Exhibit; Austin, Texas, USA, (2003). DOI: 10.2514/6.2003-5459
21.   Slegers N., Castello M.,’ spects of Control for a Parachute and Payload System’, Journal of Guidance, Control and Dynamics, Vol. 26, No. 6, (2003), 898-905. DOI: 10.2514/2.6933
22.   Strickert G., Jann T., ‘Determination of the Relative Motion Between Parachute Canopy and Load Using Advanced Video-Image Processing Techniques’, 15th Aerodynamic Decelerator Systems Technology Conference; Toulouse, France, (1999), DOI: 10.2514/6.1999-1754
23.   Yang H., Song L., Chen W., ‘Research on parachute stability using a rapid estimate model’, Chinese Journal of Aeronautics, Vol. 30, No. 5, (2017), 1670-1680. DOI: 10.1016/j.cja.2017.06.003
24.   Gorman C. M., Slegers N. J., ‘Comparison and Analysis of Multi-body Parafoil Models With Varying Degrees of Freedom’, 21th AIAA Aerodynamic Decelerator Systems Technology Conference and Seminar, Dublin, Ireland, (2011). DOI: 10.2514/6.2003-5611
25.   Slotine J J., Lee W., Applied nonlinear control. New Jersey: Prentice-Hall Inc, (1991).
26.   O. A. Yakimenko, ‘Precision Aerial Delivery Systems: Modeling, Dynamics, and Control. Progress in astronautics and aeronautics’, American Institute of Aeronautics and Astronautics, Inc. Volume 248. Virginia:, (2015).