Development and use of one-dimensional models of a golf ball

Abstract

One-dimensional models of a golf ball are useful in modelling near-normal (90 degrees) impact. The model described here has two masses connected by a non-linear spring in parallel with a non-linear damper. The behaviour of this system in collision with an infinite rigid mass is compared with the results of tests involving real golf balls. Values of the four unknown constants are found by fitting the model results, over a range of impact speeds from zero to 50 m x s(-1), to the coefficient of restitution and duration of contact found in the tests. The simplest model (Model 1) was a good fit for duration of contact over the whole range of impact speeds, but for the coefficient of restitution only at high speed (above 20 m x s(-1)). However, when used with a similar model of a flexible faced club, the simple model predicted the coefficient of restitution of the club-ball combination, determined by direct testing, quite well and as such is a useful screening tool. More complicated Models 2 and 3 fitted the rigid target coefficients of restitution better at low speed than Model 1. However, Models 2 and 3 have other disadvantages and are no better than Model 1 for high-speed impact with flexible faced clubs.

Cricket balls: construction, non-linear visco-elastic properties, quality control and implications for the game

“…In double-sided compression, the displacement of the COM would be 0.5. Solving Equation (19) for the bottom half, that is, for L from the COM (L 5 0.5) to the contact (L 5 1), we get a displacement of the COM of 0.375. The increase in stiffness from a displacement of 0.5 to 0.375 is 1.333 [11].…”

“…As mentioned before, Equations (18) and (19) are based on an object with constant and uniform cross-section. This is, of course, not the case in a spherical object, such as a sports ball.…”

Simulation of the impact response of a sliotar core with linear and non-linear contact models

“…Thus, the damping and stiffness terms both vary nonlinearly. This approach was considered by Cochran (2002) [9] in developing simple onedimensional models of golf ball impacts. This model was not implemented for comparison in this work as although it is a simple model, it presented no clear advantage over results that would be alculated from the modified KelvineVoight model and the HunteCrossley model which were implemented.…”

“…The inadequacy of this means of regulating coefficient of restitution has been recognised in recent studies (Carré et al, 2004;Cross, 1999) [4,6]; this test does not represent the full range of conditions experienced in play which is problematic due to the non-linear dependence of coefficient of restitution on impact speed.There are many continuous contact dynamic models in literature that relate force and deformation during impact (Gilardi and Sharf, 2002) [8]. Such models have been applied successfully to represent the impact response of other types of solid and hollow sports balls (e.g., Cheng et al, 2008;Cochran, 2002;Goodwill and Haake, 2004) [5,9,10]. These models generally insert some combination of conceptual springs and dashpots at the contact point between bodies.…”

Some applications of mathematics in golf

“…Since its initial inception in this form, this Rule has been through various incarnations and has been adopted worldwide since 2003 and now even pertains to higher lofted clubs (up to 35 • ). Simple models using combinations of springs and dashpots [5] have been used to model the dynamics of impact. These provide very useful insights into the underlying physics.…”