Bounce of hollow balls on flat surfaces

The bounce of a hollow spherical ball from a hard flat surface results in large deformations of the thin-walled shell; these deformations increase the internal stresses in the shell near a knuckle of bending and also increase the internal gas pressure inside the shell. This paper calculates the deformation and consequent contact forces that repel the ball from the surface, and compares the results with both a finite element analysis and experimental data. A table tennis ball is considered as an example of a thin-walled elastic shell. Since for an elastic ball there are no energy losses due to inelastic material behaviour, the analysis assumes that all energy losses are due to either friction in the contact area or impulsive forces arising from the instantaneous rate-of-change of momentum in the knuckle. In practice, the table tennis ball shows energy losses that increase with increasing impact speed; these losses substantially exceed the losses taken into account by the elastic shell analysis.