Sports Engineering

, Volume 8, Issue 3, pp 145–158

Experimental and finite element analysis of a tennis ball impact on a rigid surface


DOI: 10.1007/BF02844015

Cite this article as:
Goodwill, S.R., Kirk, R. & Haake, S.J. Sports Eng (2005) 8: 145. doi:10.1007/BF02844015


An explicit finite-element (FE) model of a pressurised tennis ball is presented. The FE model was used to model an oblique impact between a tennis ball and a rigid tennis surface, to further the understanding of this impact. Impacts were also conducted in the laboratory and the results from the FE model were in good agreement with this experimental data. The FE model was used to illustrate why a tennis ball rebounds with a higher vertical coefficient of restitution in an oblique impact compared to an equivalent impact perpendicular to the surface; this equivalent perpendicular impact has the same inbound velocity as the vertical component of the oblique impact. The FE model was also used to illustrate that the structural compliance of the felt covering on a tennis ball was a contributing factor to the ball attaining more spin in the impact than would have been calculated using a conventional analytical model. Also, the spin values calculated in the FE simulation were in good agreement with experimental data.


tennis ball finite-element method oblique impact spin 



coefficient of restitution


frictional force


moment of inertia of tennis ball about its centre of mass


air pressure inside ball


normal reaction force


radius of undeformed tennis ball (= 32 mm)

V, V′

inbound and rebound ball velocities

Vx, Vy, V′x, V′y

velocity components in horizontal and vertical directions, before and after impact


volume inside ball

ω, ω′

ball spin before and after impact

Copyright information

© isea 2005

Authors and Affiliations

  1. 1.Sports Engineering Research Group Department of Mechanical EngineeringThe University of SheffieldSheffield

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