Modeling the bounce of a gas-filled ball

TL;DR

This paper develops a simple two-parameter model to describe how the bounce efficiency of gas-filled balls varies with internal pressure and temperature, validated by experimental data on basketballs and tennis balls.

Contribution

The paper introduces a novel, simple model linking internal pressure and temperature to the coefficient of restitution for gas-filled balls, supported by experimental validation.

Findings

Model accurately predicts bounce behavior based on internal pressure.

Temperature effects on bounce are consistent with model predictions.

Good agreement between model and experimental data for basketballs and tennis balls.

Abstract

The coefficient of restitution $\epsilon$ characterizes the energy retained when a ball bounces, and can easily be measured in an ``at home'' experiment. For thin-walled gas-filled balls such as basketballs, we construct a simple two parameter model to describe how $\epsilon$ changes as a function of the ball's internal pressure. A comparison with data shows good agreement. With additional assumptions, the model also predicts how $\epsilon$ changes as a function of temperature. A comparison with tennis ball data shows surprisingly good agreement.