An Analysis of Graphical Representations of Bowling Allison Nelson Summer Ventures 2007 Appalachian State University
Abstract This research project will analyze video clips of bowling. The purpose of this project is to determine how a different release of a bowling ball impacts the trajectory of the ball. By analyzing different paths the ball takes, the way to throw the perfect strike in bowling can be determined. A frame-by-frame breakdown of several video clips will show the exact path the ball must take.
Introduction It is believed that bowling dates back almost 5200 years, as primitive bowling artifacts were found in an Egyptian boy s tomb around 3200 BC. Nine pins were originally used to play. It spread to different countries over time. It was known as bocce ball in Italy, and lawn bowling in England. Modern bowling began around the end of the nineteenth century. Bowling took a huge leap forward with the invention of the automatic pinsetter. It was invented in 1936 by Gottfried Schmidt. The sport of bowling has grown exponentially since it began showing on television in the 1950 s. It is today played by over 100 million people coming from more than 90 different countries. [1] The sport of bowling can be something very hard to perfect. It takes precise technique and skill to release the ball in such a way that it knocks all of the pins down. An experiment several years ago tested what was the best way to strike. They set up ramps and rolled balls down them. Rolling a ball straight down the lane was okay, but it often resulted in splits. They wanted to find out the perfect angle the ball must hit the pins at. It was discovered that the optimum angle for achieving a strike could only be hit by throwing a hook ball [2]. After considering these problems, several video clips of bowling were gathered and broken down into individual frames to determine the exact path of the ball. The perfect strike can be achieved by a precise combination of speed and angle of the ball release, while only a slight deviation will send the ball astray of its mark and fail at knocking down all the pins.
Methods To determine the speed and path of the bowling ball, video clips were first obtained from [2]. Using Windows Movie Maker [3], the videos were separated into frames. The frames were then imported into ImageJ, an open-source image manipulation program [4-5]. Everything in the image was deleted except a single pixel in the very center of the bowling ball. This was to pinpoint the location of the center of the ball so it could be plotted in a spreadsheet and graphed. The images were inverted (see Figure 1). The images were inverted so that the single pixel would stand out more. Figure 1 BEFORE AFTER
The images were then imported into MATLAB, a matrix manipulation program [6]. A brief program was written to pinpoint the exact location of the single white pixel on the image. The program was run for each image, and the location of the white pixel was noted. After the pixel locations were written down, a spreadsheet with these values was created and then plotted on a scatter plot. (See Figures 2 and 3.)
Results The Path of A Strike Ball in Bowling 270 260 250 y = -0.0212x 2 + 7.102x - 332.58 R 2 = 0.993 240 230 220 210 200 190 100 110 120 130 140 150 160 170 180 190 200 Figure 2 This graph displayed the path of a ball resulting in a strike. It followed a nice smooth curve, and the trendline fitted the data almost perfectly. The equation of the ball s path was shown in the upper corner of the graph. The R-squared value of the equation was.993, which indicated that the line that was drawn to fit the graph was actually really close to fitting the data points exactly. The closer an R-squared value was to one, the better it fit the data points on the graph.
Figure 3 This graph analyzes the path of a ball that was thrown rather badly. Its slight deviation from the strike ball s path resulted in a nasty 8-10 split. The equation of the ball s path before it hit the pins can be found above the red circle in the graph. The pink line on the graph shows the ball s path after impact with the pins, so it was not analyzed. (See red text above.) The R-squared value was.9274, which was still a nice fit. It was not as close to the points as the line for the strike ball, but the points on the pink line interfered with the best-fit lines. Conclusions The graphs of the balls paths suggested that the balls were initially released similarly, but the strike ball actually had more hook to it, resulting in a better ball.
This was not to say that a ball that hooks more will always do better. There were plenty of ways to achieve a strike with a straight ball, but this limits most people to a 180 average. Straight ball strikes are very hard to repeat [2]. For the purposes of this project, only hooking balls were analyzed. A problem one may have come across when bowling was that the slightest move from the strike path would result in a rather nasty split or spare. The results suggested that when the ball was thrown in a uniform curve, (such as in Figure 2), the ball was more likely to strike all of the pins. Future implications could include finding the exact speed and angle of the balls. Also different videos could be analyzed in the same way, such as videos of bowling balls picking up spares.
References [1] Michael Reker, http://www.tenpinbowling.org [2] Kenn Melvin, http://ourworld.compuserve.com/homepages/kennmelvin [3] Microsoft, Windows Movie Maker. [4] Wayne Rasband, National Institutes of Health, ImageJ. [5] Girish V, Vijayalakshmi A, http://www.bioline.org.br/request?cn04009 [6] MathWorks, MATLAB.