Investigation into the golf ball and turf interaction

: a study on friction and impact problems

Abstract

In the game of golf the flight of the ball, as well as its interaction with the club, appear to be well understood. Standard models for these parts of the game have been available in the literature for decades, with a wealth of experimental data available on these problems, many of which were obtained in highly controlled conditions.
This thesis studies the remaining aspect of the game of golf, namely the interaction of the golf ball with the turf. Currently available experimental verification is often casual, with only a few controlled data collection campaigns available in the literature. Contemporary attempts at modelling the problem are limited, with majority of models based on some adaptation of the simple linear models for a bounce of a rigid sphere against a rigid body. This study aims at tackling both issues, by studying the bounce of the golf ball experimentally and with the aid of theoretical models.
Results of a large scale experimental campaign, investigating the bounce of a golf ball against two surfaces, are presented. The methods for the data collection and data extraction are discussed, together with the analysis of the obtained data and careful error consideration. The obtained data appears to form two clusters, which is attributed to the effects of friction – namely, the ball can either slip through the impact or enter rolling at some point when in contact with the turf.
In light of the experimental data, common models for golf ball bounce are examined. The theory of the bounce of a rigid sphere against a rigid surface under Coulomb friction is revisited and extended. Further consideration is given to a bounce model that allows compliant behaviour in only the normal direction. It is concluded that, in the absence of additional tangential forces, these models do not allow for the slip reversal observed in the experimental samples. An examination of an adaptation of the rigid bounce model, which mimics the elastoplastic behaviour of the ground, showed little agreement with available data.
We thus propose and study a generic model for elasto-plastic behaviour of the turf, allowing for the elastic and plastic properties to be modelled by nonlinear functions constrained by parsimonious physical assumptions. A careful consideration is given to the behaviour due to the friction, resolving the rolling motion using Filippov’s formalism, where rolling is considered as the lower-dimensional surface between the positive and negative slip. The analysis shows that under the effects of Coulomb friction and in the presence of tangential forces, the ball must lift off slipping almost surely, which agrees with the experimental observations.
The effects of tangential compliance and friction are concluded to be the two factors, omitted (simultaneously) in the previous modelling attempts, necessary to explain the common behaviours observed in the game of golf. Preliminary attempts are made using optimisation theory to fit parameters of physically backed piecewise-smooth models.

Date of Award	3 Oct 2023
Original language	English
Awarding Institution	University of Bristol
Supervisor	Alan R Champneys (Supervisor) & Robert Szalai (Supervisor)