Oblique impact of inflated balls at large deflections

Abstract

A planar theory for oblique impact of thin-walled spherical balls against a rough rigid surface has been developed on the basis of an assumed deformation field—an initially spherical ball is assumed to flatten against the constraint surface while the remainder of the ball remains undeformed. For inflated thin-walled balls, which are represented by these assumptions (basketballs, soccer balls, volleyballs, etc) the normal reaction force acting on the flattened contact patch is predominately due to the internal gas pressure—the reaction due to shell bending is insignificant in comparison with this gas force. During impact of a thin-walled ball there also is a non-conservative momentum flux reaction that is caused by the flow of momentum into and out-of the flattened contact patch. If the ball is translating as well as rotating about an axis perpendicular to the plane of motion, the distribution of the normal component of velocity for material entering and exiting the flattened contact patch results in a distribution of momentum flux force intensity around the periphery of the contact patch and consequently, a momentum flux torque acting on the flattened sphere. The effect of these reaction forces and torque on oblique impact of thin-walled spherical balls is calculated as a function of the ball deflection (or normal component of impact velocity). In comparison with rigid body calculations for oblique impact of a spinning ball against a rough surface at angles<45° from normal, the effect of maximum deflections as large as half the initial radius is to slightly accentuate the effect of friction on angle of rebound and moderately decrease the angular velocity of the ball. However, for angles >45° from normal, the final angular velocity can be as small as 40% of that predicted by rigid body theory. The most significant changes in rebound angle are for cases with initial backspin—a technique commonly used in many ball sports.