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Energy losses due to elastic wave propagation during an elastic impact

During the impact of an elastic sphere on an elastic, massive, substrate some of the kinetic energy is radiated into the massive substrate as elastic waves and is not available for subsequent recovery as kinetic energy. This loss of recoverable energy then determines the maximum possible value for the coefficient of restitution for any impact. In evaluating the radiated energy loss Hunter (1957) used an approximation to the displacement-time relationship in a Hertzian impact so as to obtain an analytic solution to the problem. However, in doing so he derived a force-time relationship which had a different power dependence from that of the Hertz equations. In this paper the energy loss is re-evaluated using Hunter's approximation for the displacement-time relationship but applying it in such a way as to maintain similarity with Hertz equations. This re-evaluation predicts the energy loss as being some 4.5 times greater than predicted by Hunter's analysis. It is shown that the present analysis results in a generally better fit to experimental data.