Oblique Impact of Thick Walled Pressurized Spheres as Used in Tennis

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Abstract
A model is presented in which the normal impact of a thick walled pressurized sphere, such as a tennis ball, is modelled as a non-linear viscoelastic spring and damper, coupled with momentum-flux forces where the shell wall deforms with high stiffness and damping. These momentum-flux forces are only present in the impact phase and do not appear during restitution. Rotation set up during an oblique impact causes the momentum-flux forces at the front and rear of the sphere to be different such that the total vertical reaction force acts in front of the centre of mass when topspin is present. The sphere was allowed to deform and this caused both the torque and the effective moment of inertia of the sphere to decrease. The result of this is that the deformed sphere gains sufficient spin during impact for reverse slip to occur when the ball reforms towards the end of impact. Tennis balls were projected at two similarly constructed surfaces with a coefficient of friction of 0.51 and 0.62. It was found that displacements and rotations from the model compared well with experimental results recorded using a high-speed video running at 7100 frames per second. The model was able to predict these results with only the coefficient of friction as the varying parameter.

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