DOI QR코드

DOI QR Code

Analysis of the two dimensional sheet debris flight equations: initial and final state

  • Scarabino, A. (Departamento Aeronautica, Universidad Nacional de La Plata) ;
  • Giacopinelli, P. (Departamento Aeronautica, Universidad Nacional de La Plata)
  • Received : 2008.04.10
  • Accepted : 2009.07.01
  • Published : 2010.03.25

Abstract

This work presents some analytical and numerical results of a dynamic analysis of the dimensionless 2-D sheet flight equations. Two empirical models for aerodynamic forces and moments are used and compared. Results show that the initial condition of rest is always unstable, and for long times three distinct flight regimes are possible, depending on the initial angle of attack, the Tachikawa number, Ta (in fact, the parameter chosen was its inverse, ${\Omega}$), and a mass ratio ${\Phi}$. The final orbits in the velocity space and their maximum kinetic energy are compared with a theoretical asymptotic state of the motion equations, and some design considerations are proposed.

Keywords

References

  1. Baker, C.J. (2007), "The debris flight equations", J. Wind. Eng. Ind. Aerod., 95(5), 329-353. https://doi.org/10.1016/j.jweia.2006.08.001
  2. Carr, L.W. (1988), "Progress in analysis and prediction of dynamic stall", J. Aircraft, 25(1), 6-17. https://doi.org/10.2514/3.45534
  3. Elsgoltz, L. (1977), Teoria de la Estabilidad, Ecuaciones Diferenciales y Calculo Variacional, 2nd ed., MIR, Moscow, pp. 207-219.
  4. Flachsbart, O. (1932), "Messungen an ebenen und gewolbten Platten", Ergebnisse der Aerodynamischen Versuchanstalt zu Goettingen, IV.
  5. Fremaux, C.M., Vairo, D.M. and Whippe, R.D. (1995), "Effect of geometry and mass distribution on tumbling characteristics of flying wings", J. Aircraft, 32(2), 404-410. https://doi.org/10.2514/3.46730
  6. Gallaway, C.R. and Hankey, W.L. (1985), "Free-falling autorotating plate - A coupled fluid and flight mechanics problem", J. Aircraft, 22(11), 983-987. https://doi.org/10.2514/3.45235
  7. Grassberger, P. and Procaccia, I. (1983), "Measuring the Strangeness of Strange Attractors", Physica D., 9(1-2), 189-208. https://doi.org/10.1016/0167-2789(83)90298-1
  8. Hoerner, S.F. (1965), Fluid-dynamic drag, Hoerner Fluid Dynamics.
  9. Holmes, J.D. (2004), "Trajectories of spheres in strong winds with applications to windborne debris", J. Wind. Eng. Ind. Aerod., 92, 9-22. https://doi.org/10.1016/j.jweia.2003.09.031
  10. Holmes, J.D., Letchford, C.W. and Lin, N. (2006), "Investigations of plate-type windborne debris _ Part II: Computed trajectories", J. Wind. Eng. Ind. Aerod., 94, 21-39. https://doi.org/10.1016/j.jweia.2005.10.002
  11. Holmes, J.D., Baker, C. and Tamura, Y. (2006), "Tachikawa number: A proposal", J. Wind. Eng. Ind. Aerod., 94, 41-47. https://doi.org/10.1016/j.jweia.2005.10.004
  12. Iversen, J.D. (1979), "Autorotating flat-plate wings: the effect of the moment of inertia, geometry and Reynolds number", J. Fluid Mech., 92, 327-48. https://doi.org/10.1017/S0022112079000641
  13. Lin, N., Letchford, C. and Holmes, J.D. (2006), "Investigations on plat-type windborne debris, Part I, Experiments in full scale and wind tunnel", J. Wind. Eng. Ind. Aerod., 94(2), 51-76. https://doi.org/10.1016/j.jweia.2005.12.005
  14. Lugt, H. (1983), "Autorotation", Annu. Rev. Fluid Mech., 15, 123-47. https://doi.org/10.1146/annurev.fl.15.010183.001011
  15. Mittal, R., Seshadri, V. and Udaykumar, H.S. (2004), "Flutter, Tumble and Vortex Induced Autorotation", Theor. Comp. Fluid Dyn., Jan 2004: Published Online (DOI) 10.1007/s00162-003-0101-5
  16. Tachikawa, M. (1983), "Trajectories of flat plates in uniform flow with applications to wind-generated missiles", J. Wind. Eng. Ind. Aerod., 14, 443-453. https://doi.org/10.1016/0167-6105(83)90045-4
  17. Tachikawa, M. (1988), "A method for estimating the distribution range of trajectories of windborne missiles", J. Wind. Eng. Ind. Aerod., 28, 175-184.
  18. Wang, K. and Letchford, C. (2003), "Flying debris behaviour", 11th Int. Conf. on Wind Engineering, Lubbock, TX, USA June 2-5 2003.
  19. Wills, J.A.B., Lee, B.E. and Wyatt, T.A. (2002), "A model for wind-borne debris damage", J. Wind. Eng. Ind. Aerod., 90, 555-565. https://doi.org/10.1016/S0167-6105(01)00197-0

Cited by

  1. Roof tile frangibility and puncture of metal window shutters vol.17, pp.2, 2013, https://doi.org/10.12989/was.2013.17.2.185
  2. Three-dimensional probabilistic wind-borne debris trajectory model for building envelope impact risk assessment vol.102, 2012, https://doi.org/10.1016/j.jweia.2012.01.002
  3. Fragility curves for building envelope components subject to windborne debris impact vol.107-108, 2012, https://doi.org/10.1016/j.jweia.2012.05.005