Hostname: page-component-848d4c4894-8kt4b Total loading time: 0 Render date: 2024-06-17T03:04:57.921Z Has data issue: false hasContentIssue false
  • English
  • Français

Added Fluid Mass and the Equations of Motion of a Parachute

Published online by Cambridge University Press:  07 June 2016

John A. Eaton
John A. Eaton*
Affiliation:
GEC Mechanical Engineering Laboratory, Whetstone, Leicester
Get access

Summary

While it has long been known that added fluid mass may be important in the dynamics of parachutes, due to inadequate or incorrect derivation and/or implementation of the added mass tensor its full significance in the stability of parachutes has yet to be appreciated. The concept of added mass is outlined and some general conditions for its significance are presented. Its implementation in the parachute equations of motion is reviewed, and the equations used in previous treatments are shown to be erroneous. A general method for finding the equivalent external forces and moments due to added mass is given, and the correct, anisotropic forms of the added mass tensor are derived for the six degree-of-freedom motion in an ideal fluid of rigid body shapes with planar-, twofold- and axisymmetry, These derivations may also be useful in dynamic stability studies of other low relative density bodies such as airships, balloons, submarines and torpedoes. Full nonlinear solutions of the equations of motion for the axisymmetric parachute have been obtained, and results indicate that added mass effects are more significant than previously predicted. In particular, the component of added mass along the axis of symmetry has a strong influence on stability. Better data on unsteady forces and moments on parachutes are needed.

Type
Research Article
Information
Aeronautical Quarterly , Volume 34 , Issue 3 , August 1983 , pp. 226 - 242
Copyright
Copyright © Royal Aeronautical Society. 1983

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1 Ludwig, R. and Heins, W. Theoretische Untersuchungen zur Dynamisahen Stability von Fallschirmen. Jahrbuch 1962 der WGLR, pp 224-230; also investigations on the dynamic stability of personnel guide surface parachutes. AGARD Report 444, April 1963 Google Scholar
2 White, F.M. and Wolf, D.F. A theory of three-dimensional parachute dynamic stability. Journal of Aircraft, Vol. 5, pp 86-92, January-February 1968 CrossRefGoogle Scholar
3 Gamble, J.D. A mathematical model for calculating the flight dynamics of a general parachute-payload system. NASA TN D-4859, 1968 Google Scholar
4 Wolf, D.F. and Spahr, H.R. A parachute cluster dynamic analysis, AIAA Paper 75-1398, November 1975 CrossRefGoogle Scholar
5 Wolf, D.F. and Spahr, H.R. Parachute cluster dynamic analysis, Journal of Aircraft, Vol. 14, No. 4, pp 321-322, April 1977 CrossRefGoogle Scholar
6 Doyle, G.R. and Burbrick, J.W. Dynamics of two bodies connected by an elastic tether - six degrees of freedom forebody and five degrees of freedom decelerator. NASA CR-12026, April 1974 Google Scholar
7 Ibrahim, S.K. and Engdahl, R.A. Parachute dynamics and stability analysis. NASA CR-120326, 1974 Google Scholar
8 Eaton, J.A. Validation of a Computer Model of a Parachute, Ph.D, Thesis, University of Leicester, March 1982 Google Scholar
9 Eaton, J.A. Added mass and the dynamic stability of parachutes. Journal of Airaraft, Vol. 19, No. 5, pp 414-416, May 1982 CrossRefGoogle Scholar
10 Eaton, J.A. Sensitivity analysis of the Leicester parachute model. University of Leicester Engineering Department Report 76-20, November 1976 Google Scholar
11 Green, G. Mathematical papers. p 315, 1833 Google Scholar
12 Heinrich, H.G. Experimental parameters in parachute opening theory. Shook and Vibration Bulletin, No. 19, Department of Defence, February 1953 Google Scholar
13 Birkhoff, G. Hydrodynamics - A Study in Logic, Fact and Similitude. 2nd Edn, Princeton University Press, pp 148-178, 1960 Google Scholar
14 Luneau, J.L. Sur L’Influence de l’Acceleration sur la Resistance au Mouvement dans les Fluides. Publ. Sci. Min, Air., No. 363, Paris 1950 Google Scholar
15 Iversen, H.W. and Baient, R. A correlating modulus for fluid resistance in accelerated motion. Journal App. Physios, Vol. 22, pp 324-328, 1951 CrossRefGoogle Scholar
16 Bugliarello, G. La resistenza al moto accelerato di sfere in acqua. Rioerca Scientifica, Vol. 26, pp 437-461, 1956 Google Scholar
17 Eaton, J.A. and Cockrell, D.J. The validity of the Leicester computer model for a parachute with fully-deployed canopy. AIAA Paper 79-0460, March 1979 CrossRefGoogle Scholar
18 Nayler, J.L. Glauert, H.B. and Gates, S.B. The stability of parachutes in rectilinear motion; also The stability of a parachute;, both in Aero. Research Comm., R & M No. 862, compiled by Jones, R., London, pp 50-62, June 1923 Google Scholar
19 Jones, R. Experiments on rigid parachute models. Aero. Research Comm., London R & M No. 2520, November 1943 Google Scholar
20 Kirchhoff, G. Über die Bewegung eines Rotationskörpers in einer Flüssigkeit Crelles Jour., Vol. 71, pp 237-273, 1869 Google Scholar
21 Lester, W.G.S. A note on the theory of parachute stability. Aero. Research Council, London, R & M No. 3352, 1962 Google Scholar
22 Byushgens, A.G. and Shilov, A.A. The dynamic model of a parachute and determination of its characteristics. Uchenyye Zapiski TsAGI, Vol. 3, No. 4, pp 49-58 (Translation FTD-MT-24-0551-75, Jan. 1975), 1972 Google Scholar
23 Henn, H. Die Absinkseigenschaften von Fallschirmen. ZWB - U & M No. 6202, Berlin, October 1944 Google Scholar
24 Lamb, H. Hydrodynamics. 6th Edn., Cambridge Univ. Press, 1932 Google Scholar
25 Shilov, A.A. The stability of motion of a parachute in the steady-state reduction mode. Uchenyye Zapiski TsAGI, Vol. 2, No, 4, pp 76-83 (Translation FTD-MT-24-465-75, Jan. 1975), 1971 Google Scholar
26 Shilov, A.A. An analysis of the plane slightly damped oscillations of a parachute in free steady descent. Uchenyye Zapiski TsAGI. Vol. 4, No. 1, pp 137-143 (Translation FTD-MT-24-510-75, Jan. 1975), 1973 Google Scholar
27 Wolf, D.F. Dynamic stability of non-rigid parachute and payload system. Journal of Airoraft, Vol. 8, pp 603-609, August 1971 CrossRefGoogle Scholar
28 Tory, A.C. and Ayres, R.M. Computer model of a fully deployed parachute. Journal of Aircraft, Vol. 14, pp 675-679, July 1977 CrossRefGoogle Scholar
29 Goodrick, T.F. Theoretical study of the longitudinal stability of high performance gliding airdrop systems. AIAA Paper 75-1394, November 1975 CrossRefGoogle Scholar
30 Goodrick, T.F. Simulation studies of the flight dynamics of gliding parachute systems. AIAA Paper 79-0417, March 1979 CrossRefGoogle Scholar
31 Ibrahim, S.K. Apparent Added Mass and Moment of Inertia of Cup-Shaped Bodies in Unsteady Incompressible Flow. Ph.D. Thesis, University of Minnesota, Minneapolis, May 1965 Google Scholar
32 Solt, G.A. Performance and Design Criteria for Deployable Aerodynamic Decelerators. USAF Flight Dynamics Laboratory, Ohio, ASD-TR 61-579, December 1963 Google Scholar
33 Sedov, L.I. Two-Dimensional Problems in Hydrodynamics and Aerodynamics. J. Wiley and Sons, New York, pp 14-35, 1965 Google Scholar
34 Eaton, J.A. and Cockrell, D.J. An experimental technique for data acquisition from parachutes in flight. AIAA Paper 79-0439, March 1979 CrossRefGoogle Scholar
35 Cockrell, D.J., Eaton, J.A. and Morgan, C.J. Longitudinal oscillation damping for fully-inflated parachute canopies. AIAA Paper 79-0459, March 1979 CrossRefGoogle Scholar
36 Cockrell, D.J., Huntley, I.D. and Ayres, R.M. Aerodynamic and inertial forces on model parachute canopies. AIAA Paper 75-1371, November 1975 CrossRefGoogle Scholar