Autorotation of square plates, with application to windborne debris

  • Martinez-Vazquez, P. (School of Civil Engineering, University of Birmingham) ;
  • Sterling, M. (School of Civil Engineering, University of Birmingham) ;
  • Baker, C.J. (School of Civil Engineering, University of Birmingham) ;
  • Quinn, A.D. (School of Civil Engineering, University of Birmingham) ;
  • Richards, P.J. (Department of Mechanical Engineering, University of Auckland)
  • Received : 2010.04.28
  • Accepted : 2010.10.04
  • Published : 2011.03.25


This paper presents the results of measurements relating to the aerodynamic forces on flat square plates which were allowed to rotate at different speeds about their horizontal axis, by modifying the velocity of the incoming flow. A 1 m square test-sheet and a 0.3 m square test-sheet were fitted with a number of pressure sensors in order to obtain information relating to the instantaneous pressure distribution acting on the test-sheet; a compact gyroscope to record the angular velocity during the rotational motion was also implemented. Previous work on autorotation has illustrated that the angular velocity varies with respect to the torque induced by the wind, the thickness and aspect ratio of the test-sheet, any frictional effects present at the bearings, and the vorticity generated through the interaction between the plate and the wind flow. The current paper sets out a method based on the solution of the equation of motion of a rotating plate which enables the determination of angular velocities on autorotating elements to be predicted. This approach is then used in conjunction with the experimental data in order to evaluate the damping introduced by the frictional effects at the bearings during steady autorotation.



  1. Baker, C.J. (2007), "The debris flight equations", J. Wind Eng. Ind. Aerod., 95(5), 329-353.
  2. Cohen, M.J. (1976), "Aerodynamics of slender rolling wings at incidence in separated flow", AIAA J., 14(7), 886-893.
  3. Bustamante, A.G. and Stone G.W. (1969), "The autorotational characteristics of various shapes for subsonic and hypersonic flows", A.I.A.A., 69-132.
  4. Daniels, P. (1970), "A study of the nonlinear rolling motion of a four-finned missile", J. Spacec. Rocket., 7, 10- 512.
  5. Dupleich, P. (1941), "Rotation in free fall of rectangular wings of elongated shape", N. A. C. A., Tech Memo No. 1201.
  6. Flachsbart, O. (1932), "Messungen an ebenen und gewolbten Platten", Ergebnisse der AVA. IV.
  7. Glaser, J.C., Northup, L.L. (1971), "Aerodynamic study of autorotating flat plates", Eng. Res. Inst., Iowa State Univ. Ames, Rep. ISU-ERI-Ames 71037.
  8. Holmes, J.D. (2004), "Trajectories of spheres in strong winds with application to windborne debris", J. Wind Eng. Ind. Aerod., 92(1), 9-22.
  9. Holmes, J.D., Baker, C.J. and Tamura Y. (2006a), "Tachikawa number: a proposal", J. Wind Eng. Ind. Aerod., 94(1), 41-47.
  10. Holmes, J.D., Letchford, C.W. and Lin, N. (2006b), "Investigation of plate-type windborne debris - Part II. Computed Trajectories", J. Wind Eng. Ind. Aerod., 94(1), 21-39.
  11. Iversen, J.D. (1979), "Autorotating flat-plate wings: the effect of the moment of inertia, geometry and Reynolds number", J.Fluid Mech., 92(2), 327-348.
  12. Kordi, B. and Kopp, A. (2009), "The debris flight equations by C.J. Baker", J. Wind Eng. Ind. Aerodyn., 97, 151-154.
  13. Lin, N., Letchford, C.W. and Holmes, J. D. (2006), "Investigation of plate-type wind borne debris. Part I, Experiments in wind tunnel and full scale", J. Wind Eng. Ind. Aerod., 94(2), 51-76.
  14. Lewis, T.L. and Dods, J.B. (1972), "Wind tunnel measurements of surface pressure fluctuations at mach numbers of 1.6, 2,0, and 2.5, using 12 different transducers", NASA Flight Research Centre, Report No NASA TN D- 7087.
  15. Lugt, H. J. (1983), "Autorotation", Annu. Rev. Fluid Mech., 15, 123-47.
  16. Martinez-Vazquez, P., Baker, C.J., Sterling, M. and Quinn, A.D. (2009a), "The flight of wind borne debris: an experimental analytical and numerical investigation: Part I (Analytical Model)", Proceedings of the 5th European and African Conference on Wind Engineering (EACWE5), Florence, Italy, July.
  17. Martinez-Vazquez, P., Bake,r C.J., Sterling, M., Quinn, A.D. and Richards P.J. (2009b), "The flight of wind borne debris: an experimental analytical and numerical investigation. Part II (Experimental work)", Proceedings of the 7th Asia-Pacific Conference on Wind Engineering (EACWE7), Taipei, Taiwan, November.
  18. Martinez-Vazquez, P., Baker, C.J., Sterling, M., Quinn, A.D. and Richards P.J. (2009c), "Aerodynamic forces on fixed and rotating plates", Wind. Struct., 13(2), 127-144.
  19. Richards, P.J., Williams, N., Laing, B., McCarty, M. and Pond, M. (2008), "Numerical calculation of the 3- Dimensional Motion of Wind-borne Debris", J. Wind Eng. Ind. Aerod., 96(10-11), 2188-2202.
  20. Schmitz, T.L., Action, J.E. and Ziegert, J.C. and Sawyer W.G. (2005), "The difficulty of measuring low friction: uncertainty analysis for friction coefficient measurements", J.Tribolt-T. ASME, 127(3), 673-678.
  21. Smith, E.H. (1971), "Autorotating wings: an experimental investigation", Univ. Michigan Aerospace Eng. Rep. 01954-2-7.
  22. Tachikawa, M. (1983), "Trajectories of flat plates in uniform flow with application to wind-generated missiles", J. Wind Eng. Ind. Aerod., 14(1-3), 443-453.
  23. Wang, K.J and Letchford, C.W. (2003), "Flight debris behaviour", Proccedings of the 11th International Conference on Wind Engineering, Lubbock, Texas, June.
  24. Wills, J.A.B., Lee, B.E. and Wyatt, T.A. (2002), "A model of wind-borne debris damage", J. Wind Eng. Ind. Aerod., 90(4-5), 555-565.

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