# Science and Golf II: Proceedings of the 1994 World Scientific Congress of Golf

By A. J. Cochran; M. R. Farrally | Go to book overview

47

An analytical model for ball-barrier impact

Part 1: Models for normal impact

B.B. Lieberman

Polytechnic University, Brooklyn, New York, USA

and S.H. Johnson

Lehigh University, Bethlehem, Pennsylvania, USA

Abstract

The golf ball-barrier collision has proven to be too complicated to be characterized successfully by conventional coefficients of restitution and spin restitution, even if the coefficients are velocity-dependent and angle-dependent. An alternative is to use the parameters of an ordinary differential equation model of the transient viscoelastic deformation of a ball during impact. A five-parameter, nonlinear model of normal impact of solid balls has been successful in representing ball-barrier collisions over a wide range of approach velocities. A new, six-parameter version successfully represents wound balls in normal impact. With the addition of a torsion model, oblique impact can be simulated.

Keywords: Normal Impact, Oblique Impact, Impact Modelling

1 Introduction

A first step to understanding the impact between a golf ball and a golf club requires that one be able to model the impact of a solid elastic sphere upon a massive plate. A minimum result for the study would be the ability to predict rebound angle, velocity, and spin-rate for a given ball and plate from knowledge of the incoming velocity, angle, and spin-rate for a set of values which could range in velocity from 0 to 180 fps and in angle from 0 to 60 degrees. It would be desirable to characterize the interaction in the simplest possible manner.

For the model to be successful it must reflect well-known facts and recent results obtained during the 1987 groove study. A list of some of these features include: (1) energy is lost during the impact; (2) the ball's coefficient of restitution (COR) decreases very slowly with increasing velocity; (3) the contact time during the impact decreases with increasing velocity; (4) the compression phase of the impact is less than one-half of the contact

Science and Golf II: Proceedings of the World Scientific Congress of Golf. Edited by A.J. Cochran and M.R. Farrally. Published in 1994 by E & FN Spon, London. ISBN 0 419 18790 1

-309-

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