An Experiment into the Relationship Between Temperature and the Bounce Height of Golf Balls
By: Brad Allworth
The standard golf ball has evolved over a period of 500 years. It began with a wood ball, which was then proceeded by a leather ball stuffed with feathers. The ball evolved over the years through periods of gutta-percha and rubber. The period of the leather ball lasted for almost 400 years before new inventions began to be tried (Titleist). The game, however, remained generally the same through the evolution of the golf ball. “On January 1, 1932, standardization of golf ball weight and size was established by the United States Golf Association following 1930 standards set by the British Golf Association for a slightly smaller ball. The weight was set at a maximum of 1.620 oz., and diameter not to be less than 1.680 in. Later, after a testing apparatus was developed to measure velocity, a maximum velocity of 250 feet per second was added by the USGA” (Titleist). This standard has remained for over 70 years, and has been greatly affected by the development of materials such as silicone, titanium and several kinds of urethane. The dimples on a golf ball vary in number depending on design but all serve the same basic purpose. “It's well known that the number of dimples – their size, shape and configuration on the surface of a ball – controls the ball's flight dynamics” (Kullman). These dynamics consist of lift (the force upwards on the golf ball while in flight) and drag (the horizontal force against the ball in flight). The dimples reduce the drag on the ball and cause backspin, which creates the lift on the ball, thus causing greater distance. The most recent two and three-piece designs are intended to increase energy transfer between the clubface and the ball, causing a greater exit speed. Depending on the materials used, “in general, a harder ball will travel further than a softer ball because it deforms less and will efficiently transfer more energy from club to ball. During the impact between the ball and club head, kinetic energy is transferred and stored as the ball tries to regain its original shape” (Fritts). Noting this, the temperature of the ball, and the air through which it is traveling also matters. This is because then density of the ball changes according to the temperature, and the temperature and density of the air affects the drag on the ball, thus affecting the distance.
The purpose of this experiment is to find the relationship between golf ball temperature and the height of its bounce when dropped from a controlled height.
Since there are many manufacturers of golf balls, this leads to a wide variance in quality of the golf ball as well as what materials are used and the quality of the materials. However, most of the general physics of golf ball rebound, velocity and action is well covered by both (Kullman) and (Fritts). Both inquiries accurately explain and utilize the physics of the golf ball, giving a good background of general information. Titleist points out variances in golf ball development and the origins of the golf ball that will be used in the experiment. This is essential because it allows a general prediction to be made based on the knowledge about the core and general construction of the ball. On his website, Fritts also points out that the main forces acting on the ball are lift and drag, and that the transfer of energy is greatest when the golf ball is harder. Warring’s experiment elaborates on this topic, and provides a very detailed, useful exploration of golf ball flight and how golf ball flight may be affected. This may be applicable within the experiment because the density will increase (making the ball harder) when the temperature is decreased, however, this does not guarantee the same results. Titleist gives the general specifications for a USGA approved golf ball, providing important figures that can be used to discover expected tendencies and reactions of golf balls when dropped. The most specific information about golf ball construction and rebound came from (K. Tanaka, F. Sato, H. Oodaira, Y. Teranishi and S Ujihashi 2005). The researchers explore the impact characteristics of various kinds of cores and substances used to create golf balls. A detailed look into the experiment reveals velocities and the effect of different impact angles on trajectory. The most significant thing to be taken from this experiment is the essential need to keep every variable constant except for the temperature of the golf ball. Any outside influence, such as a non-perpendicular drop angle, has the potential to compromise the results of the experiment.
I believe that when the temperature of the ball is heated or cooled using various methods, the bounce height will differ from the control bounce height and velocity. Bounce is defined as the vertical height obtained due to the transfer of energy from a vertical drop and the subsequent rebound. This change in reaction is because the temperature will change the density of the ball, thus making it harder when cold and “softer” when warm. I predict that the bounce will increase in height as temperature increases in relation to the control temperature and that the colder temperatures will cause a lower bounce than the control.
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Materials
-70 Pinnacle Gold Long Drive golf balls
-7 foot step ladder
-A pair of leather gloves (for safety)
-Tongs (To hold golf balls for safety)
-2 blocks of Dry Ice
-2 coolers
-2 Teapots
-Tape
-Video Camera
-Thermometer
Method
I first prepared the set up necessary to perform the experiment; this consisted of setting the 7 foot ladder on a level surface, using the tape to establish a scale (by placing the tape on specified heights on the ladder) on which to relate the bounce height on the video camera. After finishing the set up, I began exposing the golf balls to the different temperatures. Each group of seven golf balls remained in the environments for approximately 10 minutes in order to make sure each group established a constant temperature for the drop. Seven of the golf balls were placed in a relatively airtight cooler with two blocks of dry ice (-78.5 degrees Celsius). Similarly, seven golf balls were placed in a teapot of boiling water (100 degrees Celsius) and seven golf balls were placed in the open air (15 degrees Celsius). The other environmental temperatures used between 0 and 100 degrees Celsius (40, 50, 60 and 80 degrees Celsius) were obtained by heating the water on a stove to the specified temperature (measured using a thermometer). The environmental temperatures between 0 and –78.5 degrees Celsius were produced by mixing dry ice with isopropyl alcohol (rubbing alcohol) until the desired temperature was achieved. These procedures were designed to allow for control of the golf ball temperature.
The first balls dropped were the seven golf balls in boiling water (approx. 100 Celsius). The golf balls with the higher temperatures were done first in order to minimize the loss of heat due to air exposure and or the elapsing of time. Similarly, the seven golf balls that were in the dry ice (approx. –78.5 Celsius) were dropped immediately after the heated golf balls were done in order to avoid any significant temperature increase of the golf balls. The last group of seven balls was the control group at 15 Celsius. The drop process was relatively uncomplicated. Each ball was dropped one at a time. The ball was grabbed with the tongs and dropped from the designated height (7 feet) from the top of the ladder. Each drop was recorded using the video camera and after all drops at all temperatures had been completed, the first bounce height was recorded of each drop (only the first bounce was used for data) and then analyzed by playing back the video and relating the bounce height to the tape scale on the ladder. The camera was at a measured height of 4 feet and was approximately 8 feet from the ladder. This process was performed 7 times for each experimental group and 7 times for the control group (Every ball was used only once). This method was designed with the theory that methodological simplicity would help prevent inconsistencies within the performance of the experiment and the collection of data. I wanted to prevent complication but maintain a level of detail that allowed for a significant amount of variable manipulation without compromising the controlled portions of the experiment.
Data Collection
Data was collected by analyzing the video footage in half speed and observing the maximum bounce height in feet achieved by the golf ball by relating it to the scale placed behind the drop site. After gathering the raw dated I converted the bounce heights from feet to meters in order to better analyze and graph the data.
Results
Sampling of Raw Data
Due to the large amount of raw data that was collected, only a sampling of the raw data will be shown in order to provide an example of how raw data was collected and to establish trends for the interpretation of the overall averages of the raw data.
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Analysis of Raw Data - Data File
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This graph evaluates the arithmetic mean of each temperature condition. While not extremely accurate, it does provide a good basis on which to evaluate my hypothesis. The accuracy of this data is hindered by the fact that it is primarily based on estimated heights that were analyzed by evaluating the video footage. It would be difficult and fairly irrelevant to calculate uncertainties for the type of data collected because there was a slight angle that could not be accounted for due to the difference in drop heights and the height of the camera. The main uncertainty in this experiment is holistic human observation and judgment; which cannot be measured. There were several errors in the collection of data, particularly in the fact that it was judged primarily on human interpretation, which contains in itself a certain inherent uncertainty. Also, a possible discrepancy in the data collection process was the quality of the video playback in half speed, as it is possible that the true maximum height of a bounce could have been contained between frames, thus skewing the human interpretation of the height.
When evaluating the data collected, it appears that my hypothesis was not supported by the data I collected. Instead of the balls placed in boiling water bouncing the highest, the balls that were at an approximate temperature of 50 degrees Celsius achieved the highest bounce height. Based on the averages that were calculated, the Control balls bounced approximately .066 meters higher than the golf balls placed in the highest experimental temperature (100 degrees Celsius) and approximately .39 meters higher than the golf balls placed in the lowest experimental temperature (-78.5 degrees Celsius). The maximum average golf ball bounce height of 1.7199 m was calculated at a temperature of 50 degrees Celsius. It is likely, however, that the true maximum bounce height is somewhere in between 45 and 55 degrees Celsius based on the shape of the curve formed by the average bounce heights. The failure of my hypothesis may rest in the fact that the cores of the golf balls placed in the boiling water began to soften slightly due to the heat, which most likely impacted the integrity of the golf ball, thus lowering the drop height. However, my hypothesis held some truth in that the golf balls placed in higher temperatures that were not the extreme temperature, did bounce higher than the golf balls placed in sub-freezing environments. The balls that were placed in dry ice bounced significantly lower than the other groups of golf balls. This is most likely because the decrease in temperature caused a significant change in the density of the golf ball (made it harder) causing the decrease in bounce height.
The procedures used in this experiment did not achieve the accuracy desired due to the dependence on human interpretation (analyzing the heights by video). However, given the resources I feel that the experiment was conducted in a consistent manner and allowed for a consistent way to collect useable data. The set up was simplistic enough to allow the manipulation and control of variables to an adequate extent. However, greater temperature stability could have been achieved by using containers with more insulation than the teapot and cooler that were used, and perhaps using highly insulated containers in a better controlled environment than the outdoors would have produced more accurate results. A significant limitation of this experiment was my inability to do a larger number of drops at many more temperature points in order to obtain a more representative data set, however, given the possible fluctuation of atmospheric conditions and temperature I decided not to perform the experiment more than the 70 original drops. This limitation can also be considered an error because it is possible that conducting the experiment inside would have more adequately controlled the environment. Also, my data collection technique would have been much more accurate had I been able to utilize a digital computerized system to analyze the individual drops and more accurately calculate the bounce height. It is very possible that by conducting the experiment in a more controlled environment, and using digital equipment to calculate the bounce height that the experiment could have been improved significantly. It would also be extremely interesting to explore the effect of temperature when actually hitting a golf ball rather than just dropping it, however, there would have to be a way to control the power and speed of the swing.