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

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

48

An analytical model for ball-barrier impact

Part 2: A model for oblique impact

S.H. Johnson

Lehigh University, Bethlehem, Pennsylvania, USA

and B.B. Lieberman

Polytechnic University, Brooklyn, New York, 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, Ball Deformation, Impact Modelling

1 Introduction

A model of oblique impact can be constructed by adding a torsion model to a model of normal impact. The normal model gives the radial deformation and the normal force. The transverse force is either the coefficient of sliding friction times the normal force during sliding or the constraint force necessary to maintain rolling. The external moment is the instantaneous radius times the transverse force. Any of the models from Part I of this paper is suitable for computing the normal force.

The equations of motion are referenced to an inertial coordinate system located at the center of the undeflected ball when it just comes in contact with the target barrier. The state variables for the normal model are x1: the position of the center of mass of the ball in the y or normal direction, which is the negative of the progress of the center of mass toward the target from the time of first contact and is also the negative of the deformation of the

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

-315-

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