The Physics Of Golf As anyone who has played a round of golf will attest to, the sport is based around many fundamental principals of physics. These basic laws are involved with every aspect of the game from how a player swings the club to how the ball moves through the air on its way toward the pin. It is the challenge that physics presents to the golfer that has allowed the game, and equipment used, to develop so drastically over the past one hundred years. The first golf balls used were called featheries. They were made with a horsehide cover packed with wet goose feathers. When the balls dried they became extremely hard. The major flaw with the featheries was that they could not be used when the conditions were wet because they would soften again. Despite the flaw of the featheries, they remained the only ball used up until the middle of the 19th century when the revolutionary gutta-percha ball was invented. The new ball, sometimes referred to as a guttie, was molded from the warmed, dried gum of the sapodilla tree. These balls were cheap to manufacture and opened up the game of golf to a more diverse socio-economic group.
This in turn made the game of golf very popular, which led to dramatic improvements in golf balls in the next decades. In 1900 a unique event occurred. Some claim that it can be called the first professional sports endorsement. The Spalding Company paid Englands Harry Vardon a considerable sum of money to come to the United States to demonstrate what he could do in winning tournaments using the latest ball design. He won the U.S.
Open using the new rubber-wound Haskell ball. This led to another major revolution in the design of the golf ball. Not only was this ball cheap to manufacture, but also it could be hit farther than any other ball previously used. The Haskell ball was such a success that it was not until 1968 that the two-piece balls of today emerged in the market. Obviously a lot of time, effort, research, and money were put forth into the development of the golf ball, as it is manufactured today. The reason for this ongoing process is to help a golfer use some laws of physics to his advantage (i.e. placing spin on the ball to create lift) while finding a work around for other physical properties that can be detrimental to a players golf game (i.e. drag which causes the ball to slow down and fly closer to the ground).
When examining the physics, which surrounds the game of golf, one must carefully consider all aspects of the game, not just the golf ball or even just the equipment being used. The stroke is by far the most important aspect to any participants round of golf. Among the scientific community, an event, such as the golf stroke, is thought of as a dynamic process using the physical principals of mechanics based on Newtons Laws of motion. The stroke is actually three separate events; the swing of the club, the impact of the club head with the ball, and the flight of the ball toward the target. It is the sum of these three parts that makes a successful stroke.
Before delving into the details of the golf stroke, it is important for one to consider the general concepts of motion that control the swing of the golf club. Two men are most influential in this area of study, Galileo Galilee and Isaac Newton. It is the principles of these two men that will be used during the discussion of the physics of golf. A brief explanation of momentum, moment of inertia, torque, centripetal force, and centrifugal force can be located in Appendix 4. These terms were derived from the experiments and research of first Galileo, and then expanded upon by Newton. Although neither of these two men are solely responsible for all of the physical principals presented in this paper, Galileo and Newton were two of the most influential men in these areas of study. When a scientist attempts to explain something, he or she always develops a model to work with.
In the case of the golf stroke, it has become evident that comparing such an action to the snapping of a whip lends itself nicely to a deeper understanding. The model appropriate to the study of a whip, such as a bullwhip, would be a large number of small rods with flexible connections. This is important to understanding how the whip works. At the start of the motion, as the hand moves the handle of the whip, the momentum of the whip increases. The hand exerts a force on the whip handle for a time, producing, according to Newtons Second Law, an increase of momentum.
This force moving the whip handle a few feet also does work on the whip, giving it kinetic energy. When the hand stops, the whip exerts a force on the hand, and this force in turn decreases the momentum of parts of the whip. Thus, momentum is not conserved because a force acts and there is no displacement because the hand remains still. During the stroke, successive parts of the whip are stopped, and the kinetic energy of these parts is fed into the successively smaller and smaller sections of the whip. The kinetic energy of a body depends on its mass and the square of its velocity according to the equation KE = m v2. Therefore, at the start of the stroke, the total mass of the whip is moving with a moderate speed. Toward the end of the stroke, a much smaller mass must be moving at a much higher speed to have the same kinetic energy.
This is shown to be true by the cracking of the whip, or the sonic shockwave the tip of the whip sends out. Although it may not seem possible, a human swinging a golf club works in a very similar manner to the whip. First, one must consider where the energy for the stroke comes from. In the whip it obviously came from the muscles in the arm. However, when swinging a golf club, much more energy is required, in fact it has been estimated that the amount of energy transferred into the golf ball during impact is about two horsepower. Because muscle generates approximately 1/8th horsepower per pound, it would take about 32lbs  of fully loaded muscle to generate enough energy to produce two horsepower. If however the muscle is not suitably loaded, then more then 32lbs of muscle would be needed.
If that seems to the reader to be a lot of muscle, their assumption is correct; that is a lot of muscle. The average person does not have that much muscle in their arms. Instead they must rely on the much larger muscles in their back and legs. The person uses their body to transfer the energy from these muscles into their arms. The explanation of how this is done can be found in Appendix 3 of this paper. It shows a graph of the five torques which work on the arms during the swing.
This is the first aspect of how the whip works; the transferring of energy. When interviewed, several professional golfers, including Sam Snead, Tommy Amour, Cary Middlecoff and Frank Beard, although unable to give the scientific reasons behind their down stroke, stated in one form or another, that the left shoulder pulls the left arm. The scientific explanation of what they stated is that as the horizontal pull of the left shoulder on the left arm produces a positive angular acceleration to help with the downswing. This shows clearly that the energy is transferred from the body into the arms and subsequently down the shaft of the golf club and into the ball. The way this energy was calculated was through the use of a computer program. It was setup so that it gave the total kinetic energy of the arms and the club and the kinetic energy of each of them separately.
This can be seen by curves A, B, and C in appendix 1 (please refer to the explanation at the bottom of the graph for an explanation of the curves). A fourth curve, D, was also graphed. This curve shows that work done by the golfer as a function of the downswing angle as he applies the torque on his arms. To skip ahead to the point, the total kinetic energy of the system when the club head makes contact with the ball comes 71% from the work TS * a(i), 13% from the decrease in the potential energy of the system, and 16% from the work down on the system in the shift of the golfer toward the target.  The total kinetic energy is very important to ones game of golf.
According to the conservation of momentum principal, with any given club and any given ball, the speed of the ball depends directly on the speed of the club head. Therefore it is necessary to use the large muscles of the body to generate the necessary club head speed (about 100mph) needed to hit the ball far enough in order to approach the possibility of playing par golf. The chart below demonstrates how ones game would be affected if they were not able to generate enough club head speed. Assuming that the golfer is able to sink each of his puts, the first example reveals that if the golfer were only able to drive the ball 160 yards, he would lose 15 strokes because of his lack of distance off the tee. As his driving distance increases, the number of strokes the golfer would loose decreases until he is able to drive the ball 230 yards (or hit the ball with a club head traveling about 100mph). Yards 160 170 180 190 200 210 220 230 Stroke Lost to par 15 12 9 7 5 3 1 0 The physics surrounding a game of golf is not just based on the swing as shown above.
While 50% of the game of golf is the stroke used to hit the ball, the other 50% of the game is how the ball travels through the air toward the pin. Because the flight of the ball cannot be controlled with the same precision by the golfer that he can control his swing with, many developments have been made toward creating an ideal golf ball. Just looking back as few as 50 years one can see the tremendous affect physics has played on the design of the golf ball. First, it was discovered that worn golf balls tended to stay in the air longer because their uneven surface caused a greater spin as the ball passed through the air at a high velocity. Later it was determined that dimples on the golf ball serve the same purpose, and not only that, improve on the affect first observed by the ware and tare on the original golf balls.
In the past 5 years, golf balls are being manufactured with three different sized dimples placed in strategic locations on the ball. This allows the ball to remain in the air as long as possible while sacrificing as little energy to overcoming drag as possible. As demonstrated by any golfer who can hit a ball in a straight line, the aerodynamic forces at work on a golf ball are what make the flight of the ball so unique. If one were to stand behind a golfer and watch the flight of the golf ball, that person would not see a parabolic arch as one might expect. Instead, the ball will appear to climb in a straight line for a few seconds and then begin to fall back to earth slowly.
According to Newtons First Law (a body continues in a straight line at a constant speed unless a force acts on it) the observed path of the ball does not seem possible. As the designer of the golf ball would be quick to point out, it is the aerodynamic force on the dimpled, spinning, ball, traveling at a high speed, that was balancing the vertical force of gravity which caused non uniform motion in the path of the balls flight. British scientist, P.G. Tait, performed the first experiments done with the aerodynamics of a golf ball in 1887. Professor Tait showed through his studies the importance of spin on the flight of the golf ball. He states that in his youth he was taught, all spin is detrimental. He practiced vigorously to hit a ball virtually spin free. After completing his research, Tait wrote, I understand it now, too late by 35 years at least. What Tait was referring to was the importance of spin on a golf ball. He and his son performed experiments where, we fastened one end of a long untwisted tape to the ball and the other to the ground, and induced a good player to drive the ball (perpendicularly to the tape) into a stiff clay face a yard or two off, we find the tape is always twisted; no doubt to different amounts by different playerssay from 40 to 120 or so turns per second. The fact is indisputable. Professor Tait clearly states that a ball driven with spin about a horizontal axis with the top of the ball coming toward the golfer has a lifting force on it that keeps the ball in the air much longer than would be possible without spin.
What the scientist was observing was the competing affects of lift and drag. While it is possible to generate equations and solutions for different swings and velocities and come up with an optimum ratio of lift to drag, it has been stated that it is better for the individual golfer to discover this for himself because not every swing is the same. Research has shown that a larger spin produces a larger drag, which makes the ball slow down more rapidly and thus decreases the distance it travels, but a larger spin produces more lift, which keeps the ball in the air for a longer time and thus allows it to fly father. An experienced golfer knows that the force of lift will superceded the force of drag, however it is left up to the individual to find their own balance between these two forces. The next logical step in the explanation of the physics surrounding a game of golf is to relate the two aspects just discussed.
The following text is an explanation of what happens between the time when the energy of the swing is transferred into the club and the flight of the ball; or more specifically how the collision between the club head and the ball transfers spin and energy into the ball. First, the collision must be considered. During the collision between the club head and the ball, several things happen. The club head is slowed down, and the ball is sent off with a high speed at some angle above the horizontal with a high rate of spin. This all happens in less than a thousandth of a second while the club head moves less than an inch. Such a short time makes it extremely difficult to observe what is happening during the collision. The force between the ball and the club head averaged over the time of the c …