Evaluation of Quasi-Steady Theory Applied to Windborne Flat Plates in Uniform Flow
Publication: Journal of Engineering Mechanics
Volume 135, Issue 7
Abstract
This paper analyzes models based on the quasi-steady theory for the flight of windborne plate debris. It is shown that the effects of the rotational lift, drag, and pitching moment are important and are included in the model. The model was used with success to predict the behavior of thin, square plates in a uniform stream, based on comparisons with existing experimental data. In fact, some of the scatter in the existing experimental data was explained by the numerical results. It was also shown that the buoyancy parameter was the key parameter in determining initial flight speeds and normalization of spatial coordinates with this parameter collapsed the data well.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The writers gratefully acknowledge the support provided for this work by the Natural Sciences and Engineering Research Council (Canada) and the University of Western Ontario. G.A. Kopp also gratefully acknowledges the support provided by the Canada Research Chairs Program.
References
Andersen, A., Pesavento, U., and Wang, Z. J. (2005). “Unsteady aerodynamics of fluttering and tumbling plates.” J. Fluid Mech., 541, 65–90.
ASTM. (2006). Standard E 1996-00. “Standard specification for performance of exterior windows, curtain walls, doors, and impact protective systems impacted by windborne debris in hurricanes.” Annual book of standards, ASTM International, West Conshohocken, Pa.
Baker, C. J. (2007). “The debris flight equations.” J. Wind. Eng. Ind. Aerodyn., 95, 329–353.
Belmonte, A., Eisenberg, H., and Moses, E. (1998). “From flutter to tumble: Inertial drag and Froude similarity in falling paper.” Phys. Rev. Lett., 81(2), 345–348.
Flachsbart, O. (1932). “Messungen an ebenen und gewolbten Platten.” Ergebnisse der AVA, IV, Gottingen, Germany (in German).
Hoerner, S. F. (1965). Fluid-dynamic drag, Hoerner Fluid Dynamics, Midland Park, N.J.
Holmes, J. D., Baker, C. J., and Tamura, Y. (2006a). “Tachikawa number: A proposal.” J. Wind. Eng. Ind. Aerodyn., 94, 41–47.
Holmes, J. D., Letchford, C. W., and Lin, N. (2006b). “Investigations of plate-type windborne debris—Part II: Computed trajectories.” J. Wind. Eng. Ind. Aerodyn., 94, 21–39.
Iversen, J. D. (1979). “Autorotating flat plate wings: The effect of the moment of inertia, geometry and Reynolds number.” J. Fluid Mech., 92, 327–348.
Kordi, B., and Kopp, G. A. (2008a). “Discussion: ‘The debris flight equations’ by C. J. Baker.” J. Wind Eng. Ind. Aerodyn.
Kordi, B., and Kopp, G. A. (2008b). “Effects of initial conditions on the flight of plate-like debris.” Proc., Int. Colloquium on Bluff Bodies Aerodynamics and Applications VI, Milano, Italy.
Lin, N., Letchford, C., and Holmes, J. D. (2006). “Investigation of plate-type windborne debris. Part I: Experiments in wind tunnel and full scale.” J. Wind. Eng. Ind. Aerodyn., 94, 51–76.
Lugt, H. J. (1980). “Autorotation of an elliptic cylinder about an axis perpendicular to the flow.” J. Fluid Mech., 99, 817–840.
Lugt, H. J. (1983). “Autorotation.” Annu. Rev. Fluid Mech., 15, 123–147.
Mahadevan, L., Ryu, W. S., and Samuel, A. D. T. (1999). “Tumbling cards.” Phys. Fluids, 11(1), 1–3.
Maxwell, J. C. (1854). “On a particular case of the descent of a heavy body in a resisting medium.” Cambridge and Dublin Math. J., 9, 145–148.
Minor, J. E. (1994). “Windborne debris and the building envelope.” J. Wind. Eng. Ind. Aerodyn., 53, 207–227.
Pesavento, U. (2006). “Unsteady aerodynamics of falling plates.” Ph.D. thesis, Physics Department, Cornell Univ., Ithaca, N.Y.
Pesavento, U., and Wang, Z. J. (2004). “Falling paper: Navier-Stokes solutions, model of fluid forces, and center of mass elevation.” Phys. Rev. Lett., 93, 144501.
Richards, P. J., Williams, N., Laing, B., McCarty, M., and Pond, M. (2008). “Numerical calculation of the three-dimensional motion of wind-borne debris.” J. Wind. Eng. Ind. Aerodyn., 96, 2188–2202.
Skews, B. W. (1990). “Autorotation of rectangular plates.” J. Fluid Mech., 217, 33–40.
Smith, E. H. (1971). “Autorotating wings: An experimental investigation.” J. Fluid Mech., 50, 513–534.
Sparks, P. R., Schiff, S. D., and Reinhold, T. A. (1994). “Wind damage to envelopes of houses and consequent insurance losses.” J. Wind. Eng. Ind. Aerodyn., 53, 145–155.
Surry, D., Kopp, G. A., and Bartlett, F. M. (2005). “Wind load testing of low buildings to failure at model and full scale.” Nat. Hazards Rev., 6, 121–128.
Tachikawa, M. (1983). “Trajectories of flat plates in uniform flow with application to wind-generated missiles.” J. Wind. Eng. Ind. Aerodyn., 14, 443–453.
Visscher, B. T., and Kopp, G. A. (2007). “Trajectories of roof sheathing panels under high winds.” J. Wind. Eng. Ind. Aerodyn., 95, 697–713.
Wills, J. A. B., Lee, B. E., and Wyatt, T. A. (2002). “A model of wind-borne debris damage.” J. Wind. Eng. Ind. Aerodyn., 90, 555–565.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 135 • Issue 7 • July 2009
Pages: 657 - 668
Copyright
© 2009 ASCE.
History
Received: Sep 29, 2008
Accepted: Nov 4, 2008
Published online: Mar 3, 2009
Published in print: Jul 2009
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.