A Performance Analysis System for the Sport of Bowling

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

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

possible to roll up to 21 shots in one game of bowling. Allowing a maximum of 512 bytes per ball (500 samples, plus some additional header information), 10752 bytes are required to store the "worst-case" game: 21 balls thrown at 10 mph. Serial EEPROM is now available in 8Kx8 (64K bits), 16Kx8 (128Kk bits), and 32Kx8 (256K bits) chips, with 64Kx8 (512K bits) soon to be available. The 16Kx8 chip is mandated using the above criteria. If a sample rate of 240 Hz is required, the 256Kb module would have to be specified, with a commensurate increase in cost. At a 120Hz data rate, the 256Kb chip will also accommodate three full games of bowling, which is significant, since a league series usually consists of three games. The above calculations are based on minimum ball speeds (maximum sample time per ball). However, a greater number of shots can be captured for a given size memory if the data is stored in variable length records. Such a record would consist of header information (the ball count, the activation count, the run time, the length of the record, a pointer to the previous record, a pointer to the next record, etc.) and the actual sample data. The records would be stored as a doubly-linked list, and uploaded as a group, probably at the end of each game, which would free up the memory for the next game. 2.9.4 Data Compression Although serial EEPROM memory has increased in capacity while also becoming cheaper, it is cost-effective to use the smallest memory space that will hold a game's worth of data (21 balls maximum). The data collected so far might possess characteristics that could be exploited by a data compression routine. Bearing in mind that the collected waveforms are from a single bowler and a single bowling establishment, it would be incorrect to assume that this data is representative of the entire bowling population. However, it should be possible to draw some initial useful conclusions that are worth further study. It was originally assumed that the waveform the SMARTDOT module records would have a roughly sinusoidal shape. Looking at just the lower half of the waveform, that assumption is basically valid. However, the waveform exhibits striking directionality when the module is facing the ceiling, as can be seen in Figure 2-10. By setting 0° to be that point where the module is facing directly toward the ceiling, it is apparent that the sample-to-sample values change rather rapidly (20 or more counts at a time) in the range from 270° to 90°. This phenomenon results from the fluorescent ceiling lights acting as point sources, rather than as a uniformly distributed light source, and from the module being located below the surface of the ball. However, the sample-to-sample values in the 180° of rotation between 90° and 270° change relatively slowly (only a few counts at a time). This portion includes the valleys of the waveform, which are produced when the module faces the lane surface, in the shadow of the ball. The "interesting" portion of the waveform falls within the range 10- 50 (0x0A to 0x32), where the waveform exhibits a finer granularity. This information can be used to advantage in contemplating appropriate data compression techniques. A system needs to be established that can store two samples in one byte - 4 bits per sample. If samples could be stored as a value relative to each other, or relative to some known fixed value, this goal might be accomplished. It would be beneficial to maintain a fine granularity around the inflection points of the valleys in the waveform, and loosen that granularity as the sample values move further away from those inflection points. 36
One possibility is to use a transformation table to record the data. Each sample would be compressed into four "value" bits, plus a fifth "range" bit. Two adjacent compressed values would be stored together in a byte, while the "range" bits would be stored consecutively in groups of eight comprising a "range" byte. The impact bits would also need to be stored in separate bytes. In this fashion, six bytes would be required to store eight samples: four dual sample bytes, one range byte, and one impact byte. Thus, a compression of 25% has been achieved, allowing an 8-Kbyte external EEPROM to hold a "worst-case" game's worth of sample data. The data for one waveform would be stored as shown in Figures 2-12a and 2-12b. (one header per waveform) 1 2 3 4 5-8 Ball Count Previous Record (address / 8) Next Record (address / 8) Pre-Samples Impact Byte (8 impact bits) Pre-Sample Bytes (no translation) 1 2 3 4 5 6 7 8 Figure 2-12a: Waveform Header (repeated up to 60 times for 480 samples) 1 2 3-6 Impact Byte (8 Impact bits) Range Byte (8 Range bits) Sample Bytes (translated values) 1 2 3 4 5 6 7 8 Figure 2-12b: Waveform Compressed Sample Record An example translation table is shown in Figure 2-13. Notice that this table yields a nonlinear translation, resulting in a hash function that converts 8-bit values into 5-bit values (4 data bits plus the "range" bit). For example, using the translation table of Figure 2-13, if eight consecutive samples contained the values 10, 12, 16, 38, 57, 75, 118, and 85 and impacts were registered at the third (16) and fourth (38) samples, the compressed data would appear as shown in Figure 2-12c. 1 2 3-6 Impact Byte 30h (0011 0000) Range Byte 1Fh (0001 1111) Sample Bytes (translated values) 2 2 4 5 B C E D Figure 2-12c: Compressed Samples Example 37
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: The 'F300x can write to any portion
Page 45 and 46: 2.10 SUMMARY This portion of the re
Page 47 and 48: The ball's angular velocity increas
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:
Page 97:
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A Performance Analysis System for the Sport of Bowling

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