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Figure 1: A picture of an eight iron belonging to, professional golfer, Tiger Woods. This shows the repetition of impact with the sweet spot he makes with his club as it is worn down only on this particular spot.
Locating the Sweet Spot
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"Golfers: The Mysterious Sweet Spot." 123HelpMe.com. 23 Mar 2019
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The sweet spot is not as exact as the center of the clubface, and it cannot be expanded like previously thought. That leaves the question of how to find it. From club to club the location of the optimal strike point varies. The combination of important factors all relate back to one central variable. The sweet spot is affected by the distribution of weight in the clubface. It lies at the exact location where the club head can be totally balanced on a fine point, or the center of gravity (illustrated in figure 2 below). As the sport has evolved, developers of new equipment have been able to move the sweet spot because lighter and stronger modern materials have been introduced. This allows them to move the center of gravity without compromising the feel and performance of the whole club. By moving more material and therefore weight to the deeper parts of the club head the developers are able to move the sweet spot higher on the face. This new design can help turn low handicap into even better golfers. Unfortunately, the advanced technology complicates the sport for the average recreational golfer, making the sweet spot even more elusive than ever before.
Figure 2: A picture of the method to identify the sweet spot by finding the center of gravity. Club head rests on a pin point, perfectly balanced.
Effects of the Sweet Spot
Through exploring the perfect impact between the ball and the club one can successfully find the necessary parts of the sweet spot, but one question still remains: what benefits does it bring? In scientific terms, one could say that the sweet spot holds the point at which the coefficient of restitution is greatest. The coefficient of restitution (COR) is a measurement of the portion of energy that is retained between two objects in a collision. The measurement ranges from 1.000 to .000, where a perfect transfer of energy would be a 1.000 and no transfer of energy of energy would be a .000. An example of the perfect elastic collision with a COR of 1.000 would be two billiards balls striking each other. In this scenario, one ball would strike the other, causing the first billiards ball to stop and the second to move at the same rate as the other before the collision. An example of an inelastic collision with a COR of .000 would be two balls of putty colliding. In this situation, the ball of putty would strike the other and they would both sit still, showing there was no energy transferred during the collision. A great illustration of the measurements of COR with golf is shown in figure 3 below, where a golf ball hits a club with a neutral face angle at a known speed. The ball then bounces backward at a calculated speed. The calculated speed divided by the speed before the collision is the coefficient of restitution.
Figure 3: illustration of the coefficient of restitution
It is impossible for a golf ball to have a perfect elastic collision with the club (COR of 1.000). The first reason for this is that the clubface and the ball are made from totally different materials. Also, the club head and the ball have completely different masses. The coefficient of restitution in the sweet spot has a major effect on the distance of shot. With a swing speed of about 100 miles per hour, the difference in the distance of a shot between using a club with a COR of .830 as opposed to .800 is 12-15 yards. Through numerous tests by companies, it was found that the number one thing that effected COR was clubface thickness. Studies showed that COR capped out at about .960 with a clubface .1125 inches thick (graph shown in figure 4 below). With this information, people wonder why club manufacturers do not make the COR their drivers as high as humanly possible. The reason they do not is not because the technology is not there, but it is unfortunately illegal. The United States Golf Association (USGA) set a limit of .830 on the COR of drivers in the nation in 1998. This allows for a maximum of an 83 percent transfer of energy between the clubface and the golf ball. After creating a limit for the COR, the USGA started to test different clubs to see if they met the standard.
Compression on the Sweet Spot
A golfer’s game is defined by his ability to utilize the benefits of the sweet spot. The profits from this feat are incredible. No good feeling could outdo the sensation of effortlessly compressing a golf ball on the sweet spot. The key to this phenomena is to have the ball push into the ground by the face of the club. The compression is caused by a combination of forces including the normal force from the ground and the force from the club as shown below:
Resulting in an acceleration as shown below:
Not very surprisingly, it is extremely hard to produce this result when hitting a golf ball. For amateurs, a common mistake in the game is when the player does not push and compress the ball into the ground, and instead has the shaft leaning backwards. This is called a variety of things including “scooping” and “casting” and is the reason that many people suffer in the distance of their golf shots. This is detrimental to the performance of one’s shot, as it turns the combination of two forces on the ball into a single force of the club pushing up on the ball with little magnitude. The resulting acceleration is far less than desired and the result is extremely inconsistent (shown in figure 5). Physics is not being used to gain an advantage when one loses the compression of the golf ball between the club and the earth. Physics is essential in having an effortless golf shot.
Figure 5- Showing the difference between casting and compressing where the ball flights of casting are green and purple while compressing is in red.
Physics: The Sweet Spot of Golf
Like most sports, the game of golf relies on the concepts and laws of physics. There would be no challenge without these things that make the game painstakingly harsh and unforgiving. Every aspect of golf can be related to physics. There are so many of these aspects working in every part of the swing. Without physics, there would be no point to the game in its entirety. There would be no inertia to keep the ball moving. Also, the club would have no center of gravity, everywhere on the face would have the same effect. Most sports have physics as their backbone, but golf in particular is completely dependent upon it.
Physics educes a fantastic complexity to the game of golf and gives it its illusive qualities. These qualities go deeper than just the sweet spot. For instance, Physics brings the variable of spin to into the production on the golf course. This makes the game both challenging and intriguing, as it adds a factor that can be mastered to edge out the competition. Pros, like Bubba Watson (famous for being able to shape shots), are able to manipulate the spin of the ball to bend around trees, approach greens from different angles, and to stop the ball quickly or let it roll out. Personally, I work the ball right to left, this gives drives more roll distance. Every player has a natural draw (ball turns towards from the player) or fade (ball turns away from the player) to their shot, but the ability to master of both is just another example of how physics makes the game of golf better. Other ways physics contributes to the game of golf include the torque of the club during the down swing, sand shots, and putting on different greens with slopes.
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