A Performance Analysis System for the Sport of Bowling

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$Course Syllabus - Penn State Harrisburg Math/Computer Sciences ...$

$A Simulator for the MARIE Architecture - Penn State Harrisburg Math ...$

Figure 3-1: MASTER "Raw Data" Screen Capture The non-homogenous nature of the overhead lighting can be seen in Figure 3-2, which zooms in on the first 800 msecs of Figure 3-1. Multiple local peaks are evident during each revolution, with each of these "side lobes" occurring as a row of ceiling lights comes into view of the light sensor. Looking closer, it is also evident that the side lobes grow and recede as the ball travels further down the lane. Eventually they disappear completely, as is evident in Figure 3-3, which zooms in on the last 800 msecs of the shot in Figure 3-1. The directionality of the module can be seen in the shape of Figure 3-3. The light level rapidly approaches a peak value when the light sensor is pointing almost directly at the light source, and just as rapidly retreats as the light sensor rotates away from the light. Notice that the valleys of the waveform do not display this directional characteristic. Drawing from Fourier analysis techniques, the cyclic waveform shown in Figure 3-1 must have a fundamental frequency close to that of its major peaks, which resulted from each rotation of the ball. For a cyclic waveform to exhibit such sharp peaks, there must also be a significant amount of high-frequency harmonic content. The multiple local peaks present in each revolution, as shown in Figure 3-2, will be responsible for some significant intermediate harmonic content, as well [7]. 42
Light Level 100 90 80 70 60 50 40 30 20 10 0 Release Point -50 0 100 200 300 400 500 600 700 800 Milliseconds (since Release) Figure 3-2: Raw Data Release Region (800 ms) By considering the nature of the ideal waveform (an increasing frequency "chirp"), it is possible to deduce the shape of the frequency spectrum of the raw data. Since the lane is more heavily oiled near the foul line, the coefficient of friction is lower, and the ball will slide more. This sliding prevents the ball's linear momentum from being transferred into angular momentum, thus maintaining a fairly constant velocity for the first few revolutions of the ball. Thus, a fundamental frequency is established that is close to the initial angular velocity at release. 140 120 100 Impact (Head Pin) Light Level 80 60 40 20 0 2000 2100 2200 2300 2400 2500 2600 2700 2800 Milliseconds (since Release) Figure 3-3: Raw Data Impact Region (800 ms) As the ball continues down the lane, it eventually gains angular velocity, and this change will be reflected in additional higher frequency content, albeit with a decreasing magnitude, in the frequency bands immediately adjacent to the fundamental frequency. Due to the harmonic content introduced by the sharp peaks and multiple local peaks, there should be additional frequency content at integer multiples of the fundamental frequency, appearing as an attenuated "echo" of the shape of the frequency content around the fundamental. The characteristic frequency spectrum shape just described is shown in Figure 3-4. 43
Page 1 and 2: The Pennsylvania State University T
Page 3 and 4: TABLE OF CONTENTS Section I: Introd
Page 5 and 6: LIST OF FIGURES Figure 2-1 SMARTDOT
Page 7 and 8: SECTION I: INTRODUCTION, BACKGROUND
Page 9 and 10: eceiver that stores, processes, and
Page 11 and 12: 1.3.2 Product Development Phase The
Page 13 and 14: SECTION II: COLLECTING THE DATA - T
Page 15 and 16: 2.2 Design Constraints The feasibil
Page 17 and 18: 2.3 SENSING REQUIREMENTS The module
Page 19 and 20: Pin Deck Light Foul Line Figure 2-2
Page 21 and 22: 2.4.1 Ambient Light Sensor The ambi
Page 23 and 24: 9 28 8 RST V CC V CC 5 6 hyst 7 3 +
Page 25 and 26: 2.6 HARDWARE/SOFTWARE INTERACTION D
Page 27 and 28: 2.6.3 Baud Rate The module communic
Page 29 and 30: Configuration settings and the samp
Page 31 and 32: 2.7.5 The Ball is Rolling If the wa
Page 33 and 34: covered by the wand). When the modu
Page 35 and 36: 2.8.1 Detecting Release Detecting t
Page 37 and 38: Light Level 100 90 80 70 60 50 40 3
Page 39 and 40: By filtering the data, and then cou
Page 41 and 42: The 'F300x can write to any portion
Page 43 and 44: One possibility is to use a transfo
Page 45 and 46: 2.10 SUMMARY This portion of the re
Page 47: The ball's angular velocity increas
Page 51 and 52: the fundamental frequency has been
Page 53 and 54: Since the fundamental frequency and
Page 55 and 56: Figure 3-7: MASTER "Analysis" Scree
Page 57 and 58: known, the linear momentum (and thu
Page 59 and 60: In order to find the value for v 1
Page 61 and 62: 3.5 ASSUMPTIONS AND ERROR ANALYSIS
Page 63 and 64: 3.5.3 External Forces and Friction
Page 65 and 66: 3.6.1 Implementation and Performanc
Page 67 and 68: Figure 3-11a: Effects of Phase Shif
Page 69 and 70: 3.6.3 The "Perfect" Game to Analyze
Page 71 and 72: Since the change in angular velocit
Page 73 and 74: BIBLIOGRAPHY [1] United State Paten
Page 75 and 76: APPENDIX A - SMARTDOT MODULE EMBEDD
Page 77 and 78: Appendix A: SMARTDOT Module Embedde
Page 85 and 86: APPENDIX B - SMARTDOT MODULE SOURCE
Page 87 and 88: Appendix C: SMARTDOT Module Command
Page 89 and 90: Figure C-3 Appendix C: SMARTDOT Mod
Page 91 and 92: APPENDIX E - 300 GAME MASTER SCREEN
Page 93 and 94: Appendix E: 300 Game Analysis Frame
Page 95 and 96: Appendix E: 300 Game Analysis Frame
Page 97: Appendix E: 300 Game Analysis Frame

A Performance Analysis System for the Sport of Bowling

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