Logarithmic visco-elastic impact modelling of golf balls

The stress relaxation in golf balls follows the logarithmic law, based on which a logarithmic impact model was developed. The model allows the conversion of the stiffness measured at different deflection rates into the velocity-independent elasticity parameter, as well as the calculation of impact forces. The stiffness and the viscosity parameter were derived from compression and stress relaxation tests respectively. The softer, or less stiff, a ball is, the smaller is its viscosity constant. Wound balls are generally less viscous than solid core balls. The impact forces calculated from the model were compared to forces measured in impact tests at approximately 10 m/s. The logarithmic visco-elastic model predicts peak impact forces accurately. However, the measured impact forces were partially inconsistent with a high standard deviation. As a recommendation, golf balls should be graded with two compression numbers (instead of the conventional Atti or Riehle numbers), or with the gradient of the mean stiffness, in addition to the conventional compression numbers.