Abstract

Golf provides numerous examples of common physical phenomena which can be elucidated through mathematics. This notes provides a simple introduction to mathematical modeling in golf, by briefly describing a few of the many ways mathematics can be used to understand or improve the golf drive. First we describe the double-pendulum model of a golf swing, which is a simple but useful model of the mechanical system consisting of the golfer and the golf club, used to accelerate the club head. Second we consider the basic mechanics of the energy and momentum transfer which takes place when the club head impacts the golf ball. Finally we describe the three basic forces—gravity, drag, and lift—which determine the ball's trajectory after it is struck by the club.

“Math and science are everywhere.” With those words, championship golfer Phil Mickelson began a public service television advertisement produced by ExxonMobil and premiered during the 2007 broadcast of the Masters Golf Tournament. I had the privilege to serve as the mathematical consultant for the ad and for the accompanying website, The Science of a Drive, from which the title of this article is taken. Figure 12.1 displays a still frame taken from the advertisement and another taken from the website.

The golf drive does indeed provide numerous examples of the ways mathematics elucidates common physical phenomena. Many aspects of it can be illuminated or improved through mathematical modeling and analysis of the mechanical processes entering into the game. Here I present a few simple examples collected during my consulting work.