A Performance Analysis System for the Sport of Bowling

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

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

SECTION III: ANALYZING THE DATA - THE MASTER APPLICATION This portion of the paper presents the data manipulations used to extract the waveform from the raw data, the assumptions for analysis of the waveform, the mathematics and physics behind those assumptions, and the possible information that can be derived from the extracted waveform. Consideration is also given to future possibilities for analysis and presentation of the data. The SMARTDOT sensor module is intended solely as a data collection device, serving as the sensing mechanism for the SMARTDOT system. The actual power of the system, however, will reside in the MASTER application. For the purposes of this portion of the project, it was necessary to develop a data-analysis program that was capable of communicating with the module, and uploading, storing, and facilitating a quick analysis and assessment of the data at the test site (a local bowling establishment) on a laptop computer. As such, the current MASTER program is a research tool - the creation of a user-friendly, GUI-based analysis and presentation package falls into the development phase of the project. 3.1 RAW DATA ANALYSIS The original premise behind the development of the SMARTDOT system was that the light waveform the module captures would be sinusoidal in nature, and that information relevant to the action of the ball could be extracted from that digitized waveform. Under ideal circumstances, with truly uniform lighting, the data that SMARTDOT collects would closely transcribe a sine wave. In actuality, the captured waveform is quite "rough" - it does exhibit "peaks" and "valleys" like a sinusoid, and it also possesses a cyclic, repetitive shape, but it only loosely resembles a simple sine wave. It is possible to visually identify and count the revolutions of the ball from the raw data, to a resolution of one-quarter to one-half revolution. The release and impact times are captured with a fair amount of accuracy, and it is easy to use them to calculate the average speed of the ball. However, the "rough" shape of the waveform makes it impossible to reliably determine the starting and ending points of a particular revolution, nor is it "easy" to determine the total number of revolutions to better than one-half rotation. After the first look at the digitized waveform data in the early portions of the research, it was obvious that the raw data would have to be digitally filtered before it could be used in an automated analysis program. 3.1.1 The "Ideal" Waveform Before developing a digital filter for the raw data, some understanding of what the desired data should look like must be gained. Recall that the ball is released with a linear velocity that is greater than the corresponding angular velocity will support - the ball is skidding (traveling faster than it is revolving). Friction between the ball and the lane works to resolve this discrepancy between the angular and linear velocities of the ball. With no other force but friction acting on the ball from the moment of release until the moment of impact with the pins, the ball experiences a monotonic increase in its angular velocity (at any instant, the ball's angular velocity is greater than at any previous instant), and a corresponding monotonic decrease in its linear velocity. 40
The ball's angular velocity increases until the discrepancy between the angular and linear velocities is resolved (a condition called roll out). If the ball rolls out before reaching the pins, it is no longer skidding, and the continuing decrease in its linear velocity due to rolling friction also directly impacts the angular velocity (it begins to monotonically decrease, as well). Under normal circumstances, the ball does not roll out before hitting the pins, and therefore, the angular velocity generally increases until the ball hits the pins. Given a uniform light distribution along the length of the lane, the light level seen by SMARTDOT will be at its highest (brightest) when the module faces directly towards the ceiling, and at its lowest (darkest) when the module faces directly towards the floor, with a smooth transition occurring between those two points. Under these circumstances, a graph of the light waveform appears as an increasing frequency "chirp". The peaks and valleys of the sinusoid are spaced further apart near the release point, and get closer together as the ball approaches the pins. Figure 3-5, which is a capture of the filtered "Waveform" screen from the MASTER program, depicts this waveform. If the ball rolls out, its angular velocity reaches a maximum at the roll out point, and then begins decreasing. It is possible to use this information to detect whether or not roll out has occurred by looking for a decrease in the angular velocity. Recall also that friction-reducing lane oil is regularly applied to the first 30-40 feet of the lane. Therefore, the ball is more prone to sliding on the upper half of the lane (nearer the foul line), with the majority of the increase in angular velocity occurring on the lower half of the lane (nearer the pins). Therefore, a graph of the angular velocity of the ball versus time (or distance from the foul line) will have a hyperbolic or exponential shape, assuming roll out has not occurred. The graph of the linear velocity will mirror that of the angular velocity, starting high and falling off at the end. Figure 3-7, which is a capture of the "Analysis" screen from the MASTER program, depicts these two graphs. If the ball had rolled out, the graph of its angular velocity in Figure 3-7 would display an inflection point at the point of roll out, decreasing after roll out, while the graph of its linear velocity would continue to decrease. Figure 3-9 depicts a waveform that resulted from the ball rolling out before hitting the pins. 3.1.2 The "Real" Waveform The "jagged" appearance of the raw data waveform, as shown in Figure 3-1, indicates that a good deal of high frequency "noise" has been captured along with the desired waveform. Since the module filters out the 120 Hz flicker of the overhead fluorescent lights while capturing the waveform, this noise must have another cause. In fact, the noise could be the result of three additional sources: the non-homogenous nature of the overhead lighting; the directionality of the light sensor that was introduced by placing the SMARTDOT module at the bottom of a finger hole, 1 3 / 8 inches below the surface of the ball; and from "aliasing" of frequencies greater than one-half the sampling frequency. These higher frequencies might result from flash bulbs, reflections, etc. Other than these transient sources, aliasing should have minimal impact, since there are no significant sources of flickering light greater than 120 Hz in a bowling center. 41
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: 2.10 SUMMARY This portion of the re
Page 49 and 50: Light Level 100 90 80 70 60 50 40 3
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
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A Performance Analysis System for the Sport of Bowling

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