Determining the Correlation between Off-center Contact and Ball Speed

Table of Contents: Introduction, Method, Data, Graph, Conclusion/Evaluation, Related Links, Return to Research

Introduction:

When I was first introduced to golf I was so intrigued by the way the golf ball compressed off of the head and accelerated into the air with extremely high velocities. Club head speed is an extreme advantage when it comes to playing golf in competitions. It allows you to hit the ball much farther leaving you with shorter approach shots giving you an extreme advantage. The best driver in the world gains on average 1.07 strokes over the rest of the competition meaning that they would win on average by 1 stroke. The best players in the world swing the club upwards of 180 kmh^-1 with ball speeds ranging from 270 kmh^-1 to 300 kmh^-1. Averaging a distance of 270m off the tee. However club head speed is not the end of the story when it comes to driving. It is also essential to hit the center of the club head. As my fellow golfers know it is a lot harder than it looks. Hitting the ball not in the center of the club head can change the direction and velocity of the ball, but just how much do off center hits affect the ball speed?

Historical Background:

Over the course of the last 40 years driving distance has substantially increased from 235m on average in 1980 to 270m on average in 2018. This is the result of major technological developments within both golf balls and clubs. Throughout these years the size of the club head continued to increase, in 1980 drivers were 240 cubic centimeters and starting in 2004 they were increased to 460 cubic centimeters in 2004. This increase in club head size, as a result of this the center of the club became much easier to hit. From this the average distance off the tee increased. The club head material also changed from being made out of wood, to titanium, to mostly carbon. This change in material allowed for more forgiveness on off-center hits, contributing to the increased ball speed and total distance. In addition, the golf ball design has changed a lot over the years. Some of the very first golf balls were made with feathers on the inside. As technology of the golf ball evolved the inside changed from feathers, to rubber bands, to inner butadiene rubber mantles. This is also one of the main contributors to the increased ball speed and distance.

Research Question and Methodology:

The primary aim of this experiment is to determine how the contact area of the golf ball in proximity to the center of the club head affects the ball speed of the golf ball. This will be done by recording slow motion videos on an i-phone at 240 frames per second. Then after swinging the club measuring the distance from the center of the club head to the center most dimple of the golf ball imprint (When the club makes contact with the ball it leaves a mark on the club with dimples as the imprint). The slow motion video will then be used in vernier video analysis where both the club head speed and ball speed will be measured. Since the program only calculates horizontal and vertical velocities the magnitude of those vectors will need to be calculated for the total velocity of both the ball and the club head.

Hypothesis:

The farther away the ball is from making contact with the center of the club head the slower the ball speed will be. I believe this because when you make contact with the golf ball there is less mass in areas farther away from the center of the club head, than there is in areas closer to the center of the club head.

Experimental Variables:

The independent variable is the distance in mm the ball makes contact with the club head. There is a significant uncertainty in this due to the fact that this is measured by human eyes and a ruler. Also it was difficult to determine where the center of the golf ball made contact with the club head due to the dimples. This made it so that we had to estimate where the center of the ball actually was.

The dependent video is the velocity of the golf ball in meters per second. Given that the vernier video analysis calculates velocities to the 6th decimal place, it is safe to say that this uncertainty will not affect the results of the experiment that much.

One of the control variables is the club head speed. It is crucial that the club head speed will remain constant throughout this experiment because if there is substantial drop or rises in the velocity of the club then there will be substantial drops or rises in the velocity of the ball, negating the point of the experiment. In order to achieve this the same golfer will be used throughout all of the trials in effort to maintain a constant club head velocity. The uncertainty of the club head can be calculated via the use of the vernier video analysis and taking the max and min velocity and dividing by 2. Another control variable is the type of golf ball. The golf balls used in this experiment were mizuno range balls with 2 layers of butadiene rubber mantles. This is important because the way the ball compresses off the club head is affected by how many different mantles there are.

Method/Procedure:

1. Set up a tripod with a wide lens camera with slow motion 1 meter away from the golf ball (Face on view of golf swing, Seen in figure 1).

2. Stick two red tees in the ground 1 meter apart (Markers, Seen in figure 1).

3. Record the golf swing in slow motion (In this case 240 frames per second).

4. Using a ruler measure the distance in mm where the ball made contact with the club from the center of the club head.

5. Record the distance and continue repeating until enough trials have been reached for desired distances. (In this case 5 trials per distance with 20 distances)

6. Using Vernier Video Analysis track velocities of the golf ball, using the red tees as markers.

7. Using the horizontal and vertical velocities calculate the total velocity of the golf ball using a vector.

(Figure 1)

Reasoning For Number of Trials:

- The reasoning for the number of trials (5) is because it allows the data to create a relatively accurate average without the influence of outliers. More trials could have been conducted but simply for the reason of time it was limited to 5 trials.

- The reasoning for the number of variations (20) is because of the size of the club head. Once starting to record trials with contact farther than 20 mm from center it became harder to actually achieve those distances while making consistent contact with the club head.

Safety, Environmental, and Ethical Concerns:

- One safety concern with conducting an experiment with any high velocity projectiles is the likelihood of somebody getting hit with the golf ball. This can be prevented by simply not standing in the way of the golf ball.

- Another safety concern is somebody getting hit with the golf club. This can be prevented easily by not standing in the way or throwing the club.

Analysis/Results:

Raw and Summarized Data Table: excel--text

Distance from Center of Head (+/-0.5mm)	Golf Ball Velocity (+/-.005 m/s)					m/s	m/s
Distance from Center of Head (+/-0.5mm)	Trial 1	Trial 2	Trial 3	Trial 4	Trial 5	Average	Uncertainty
0.0	66.81	66.44	68.02	67.28	65.43	66.80	1.29
1.0	65.73	66.88	66.31	67.89	66.23	66.61	1.08
2.0	67.01	65.50	66.43	68.13	66.47	66.71	1.32
3.0	64.94	66.50	67.21	65.94	66.25	66.17	1.14
4.0	66.35	64.39	66.87	65.93	67.24	66.16	1.43
5.0	66.34	64.95	65.70	66.01	67.21	66.04	1.13
6.0	66.40	67.87	65.96	64.80	65.26	66.06	1.54
7.0	65.26	66.37	64.87	66.42	66.74	65.93	0.93
8.0	66.24	65.62	64.82	65.89	66.46	65.81	0.82
9.0	64.69	65.24	66.34	66.42	65.84	65.71	0.87
10.0	66.72	63.97	66.40	64.80	65.61	65.50	1.38
11.0	63.86	66.21	65.70	65.82	65.92	65.50	1.18
12.0	64.79	65.00	66.31	66.02	64.60	65.34	0.86
13.0	65.98	63.45	65.23	65.33	66.01	65.20	1.28
14.0	64.87	66.01	63.87	65.26	65.85	65.17	1.07
15.0	65.59	63.63	66.50	65.47	63.76	64.99	1.44
16.0	64.20	64.98	65.59	64.34	64.78	64.78	0.70
17.0	64.20	65.70	63.96	63.58	65.70	64.63	1.06
18.0	63.70	65.41	64.90	63.72	64.87	64.52	0.85
19.0	62.87	64.90	65.32	63.70	65.23	64.40	1.23
20.0	64.27	62.89	64.90	65.12	64.37	64.31	1.12

Graph:

Conclusion/Evaluation:

The objective of this experiment was to find the correlation between the point of contact and the distance from the center of the club head and how it affects the golf balls velocity. The hypothesis stated that, the farther away the ball is from making contact with the center of the club head the slower the ball speed will be. It is clear based on the calculations of mean that the data does support the hypothesis. Generally the farther the ball was from making contact with the center of the club head the slower the velocity; however there were a couple exceptions. One of those exceptions being that from 2mm to 3mm the golf ball velocity rose, another exception was 10mm to 11mm when the velocity stayed the same. However the uncertainty of the golf balls velocity was high making it more difficult to support the hypothesis. Uncertainty ranged from .7ms^-1 to 1.32ms^-1 which is relatively high considering that the golf ball velocities ranged from 64.31ms^-1 to 66.80ms^-1. However this idea that the farther the contact point is from the center of the club head the slower the velocity is supported from numerous research studies including robot testing, so the data does support the hypothesis and can be relied upon.

The trend of the data is happening due to the golf ball acting like a spring and momentum and kinetic energy of the golf club. The kinetic energy is so as the golf ball is making contact with the club it is being affected by different masses behind the head. The farther away the ball is from the center of the club head the farther the ball is from the center of mass. This means that the mass is getting smaller and smaller as it gets farther away from the center meaning the kinetic energy being transferred into the ball is less and less. The golf ball also acts like a spring, a force is applied to it and it compresses a certain distance and then rebounds at a certain velocity. F = -kx Where k is the spring constant and x is the displacement. The reason for this change as it gets farther away from the center of the club is due to less and less mass affecting the force applied to the golf ball.

One possible procedural error could be the lack of quality of the golf balls used when conducting the experiment. The golf balls used in this experiment were two layered mizuno range balls. These were used golf balls that have been hit a varying number of times from just a few times to hundreds of times. This use of the golf balls could have affected the way that they compressed off of the club head due to the damage caused to the outer layer of the golf ball. Another factor that these golf balls should be taken into consideration is the low compressibility rating meaning that it was much easier to compress it leading to possibly higher velocities on off center hits.

One possible limitation to this experiment is the use of the program Vernier Video Analysis. When recording the velocity of the golf ball it was often hard to track the position of it leading to very high uncertainties. Also another problem was the lack of frames per second in the videos. When recording the golf swing at such high speeds it made it a white blur instead of a golf ball making it almost impossible to provide accurate velocities via this program. Another possible limitation was the inability to control the club head velocity. This could only be controlled to an extent because it is impossible to swing the same speed for 100 trials unless it is a robot testing. It was controlled by the same golfer swinging the club every time and speed could vary due to many things such as tiredness and fatigue or just the body being stiff.

To further investigate the question of how does the contact area in proximity to the center of the club head affect the velocity of the golf ball, one could use a simulator such as a trackman or a gc quad. These simulators are used by most pro tour golfers and have been proven to be accurate with collecting data. However these simulators cost anywhere from $10,000- $25,000 so it was unachievable unless considered renting. In addition to this one could use a different kind of golf ball such as a three layer or four layer golf ball which would have been better suited for my particular swing speed. If you desired to remove all human error from this experiment one could test this via robot testing; some companies have developed robot testing to try and use that information to improve their product. However this technology is only available to a select few people and is the reason why it was not used when conducting this experiment. The data collected in this lab was able to fully answer the research question and does align with the already proven scientific context so we can say that the data collected does support the hypothesis.

Appendix:

Bibliography:

Tour, Pga. “Golf Stat and Records.” PGA TOUR, https://www.pgatour.com/stats/stat.02567.html.

Wilco, Daniel. “How Driving Distance Has Changed over the Past 40 Years on the PGA Tour.” Professional Golfers' Association of America, PGA of America, 3 July 2018, https://www.pga.com/archive/how-driving-distance-has-changed-over-past-40-years-pga-tour.