Golf is unique among games for the sheer perfection of its range of equipment. In the wider category of sports, we might compare the perfection of golf clubs and golf balls to the bows and arrows in modern archery, or even to the range of high-technology bicycles used for the different stages of the Tour de France. The changes in golf equipment are less obvious, mainly due the work of the governing bodies of golf in keeping the game as close as possible to its traditional form. However, the science underlying these changes, including ones from the beginning of the 20th century, are equally profound. Frank Thomas titled his book, on the evolution of the golf equipment rules, From Sticks and Stones (Frankly Golf Publications, 2011). The title was clearly meant to imply an evolution from the simple clubs and balls used at the time of the first code of golf rules, established in 1744 by the Honourable Company of Edinburgh Golfers. However, the title is much more prescient than it appears.
The skills exhibited in golf are based on our unique physical ability to maintain a highly stable upright stance while the arms and upper body perform powerful athletic tasks. This allowed our earliest ancestors to throw stones and swing sticks with great precision; and later to wield hammers, axes, and even golf clubs with precise purpose. Children as young as four have an innate ability to perform these tasks. Some with exceptional athletic ability can drive a golf ball after watching a skilled golfer perform the task. Most can throw balls quite accurately underarm; by the age of six, without instruction, they naturally apply a stiff-arm swing, thereby reducing the number of degrees of freedom for increased repeatability when asked to throw underarm at targets (Jacques et al. 1989). A precisely repeatable swing is of course of little value without the stability of the stance; in fact, none of the primates with much greater strength and agility, but without a stable upright stance, can accomplish any of these tasks. This is the essence of the golf swing and the putting swing; that is, maintain the greatest stability to keep the rotation “center” of the swing as stationary as possible. This issue will be addressed in Chapter 3.
Before embarking on the story of golf science, we will consider some comparisons of performance from the car and aerospace world to put golf performance in some perspective. We will introduce some science to do this, which is not difficult to follow. All of the book chapters have easy-to-follow explanations presented in a similar form. So if you follow these initial arguments, you will be able to follow the science of all aspects of the game from the club swing, through the impact-generated launch conditions into ball flight, to the final roll of the ball on the green. The science story of the game is truly remarkable.
The back of each chapter contains the full “Details of the Modeling,” which necessitates some heavier physics. It is kept to the minimum possible but is needed to provide
Figure 1A Average force from back wheels to go from 0 to 150 mph in 15 seconds.
the necessary support for some of the very surprising conclusions that are reached throughout the text. These sections comprise about one-third of the total text and can be skipped without any loss of understanding of the science principles of the game.
For others with a deeper science-oriented background, the physics sections will hopefully stimulate discussion, and in some cases, further investigations.
Let’s start with a fantasy trip, to explain one of the most important science aspects of golf. A 15-second period of this trip is illustrated in Figure 1A. Assume you are heading out to the golf course in your Ferrari 730 hp F12berlinetta. Starting through an intersection is an empty stretch of open road, leading to the course. You step on the gas and go from zero to 150 miles per hour in 15 seconds; and coming up over a rise and around a curve, you do a 2 g deceleration, which with much tire squealing brings you back down to 30 miles per hour in 120 yards for a smooth turninto the golf club. Don’t worry if that’s just a dream, because you are about to do something even more amazing on the first tee. To appreciate this fact, we will use the car ride to understand the principles involved:
Recall that Newton told us that
force equals mass times acceleration,
and during the car sprint, your average acceleration was 10 miles per hour per second. So we can form a second relationship. The final speed is the acceleration multiplied by the time, so we can multiply our relationship by time and get
force × time = mass × acceleration × time = mass × final speed.
Now it’s just a matter of using the language of impact:
force × time = impulse; mass × final speed = momentum.
More generally, impulse is always equal to change of momentum.
The mass of our Ferrari is 1,500 kilograms (3,300 pounds), and the final speed is 67 meters per second (150 miles per hour). The conversions to metric units are given to simplify the calculations. The problem here is mass, and strictly speaking weight is not mass. Physicists get concerned about the difference because weight is the force of gravity on an object that deflects the weighing scale. In space, an object can be weightless, but it still retains its mass. Since all golf takes place on the surface of the earth, it’s actually OK to talk about a driver head “mass” of 0.44 pounds, and a ball “mass” of 0.10 pounds. But, if we use pounds with Newton’s laws.