A Performance Analysis System for the Sport of Bowling

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

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

3.6 IMPLEMENTATION, PERFORMANCE, AND ACCURACY The version of the MASTER application that was used to generate the screen captures for this paper incorporates most of the derivations and methods given in Sections 3.1 to 3.4. Figure 3-8 presents a data flow diagram of the various routines that generate the data for the graphs displayed on the "Spectrum", "Waveform", and "Analysis" screens. Appendix D contains the 'C' source code for those routines. MASTER Analysis Calculations Data Flow Diagram From: Upload/Archive Routines A vCalcSpectrum (page D-3) Initialize: RealData[ ] = RawData[ ] Calc Spectrum: RealSpectrum[ ] = FFT (RealData[ ]) Calc Magnitudes: FFTMag[ ] = FFTMagnitude (RealSpectrum[ ]) Calc Frequencies: FFTFreq[ ] = FFTFrequency() Find Fundamental: FundFreq = max (FFTMag[ ]), Freq > 2.0 Hz Normalize: FFTMag[ ] / FFTMag[FundFreq] Find Pass Band Limits: LOFilterIndex, HIFilterIndex vCalcVelocityData (page D-15) Calc RPM Energies: RPMEnergy[i] = k * RPMData[i] 2 Calc RPM Ave Energy: RPMAveEnergy = Σ (RPMEnergy[ ]) / (PinImpactIndex - ReleaseIndex) Estimate Linear Energy: SpeedAveEnergy = ((LaneLength * SamplingFreq) / (PinImpactIndex - ReleaseIndex)) 2 Calc Ball Ave Energy: BallAveEnergy = (1+FrictionCoef) * RPMAveEnergy * SpeedAveEnergy Calc Linear Velocities: VelocityData[i] = (BallAveEnergy - ((1 + FrictionCoef) * RPMEnergy[i])) 1/2 Get Ball Loft Distance: Get Release Velocity: BallLoft = Σ ((VelocityData[i] * 12.0) / SamplingFreq), ReleaseIndex ≤ i ≤ LaneImpactIndex ReleaseVelocity = VelocityData[ReleaseIndex] vCalcFilterData (page D-5) Remove LO Freqs: RealData[i] = 0.0, i < LOFilterIndex Remove HI Freqs: RealData[i] = 0.0, i > HIFilterIndex Keep Pass Band Freqs: RealData[i] = RealSpectrum[i], LOFilterIndex ≤ i ≤ HIFilterIndex Get Impact Velocity: ImpactVelocity = VelocityData[PinImpactIndex] Get Ball Speed: BallSpeed = (LaneLength * SamplingFreq) / (PinImpactIndex - ReleaseIndex) Get Ball Time: BallTime = (PinImpactIndex - ReleaseIndex) / SamplingFreq Filter Data: RealData[ ] = FFT -1 (RealData[ ]) Remove DC Bias: RealData[ ] - Min (RealData[ ]) vCalcDistanceData (page D-16) Calc Distance to Sample: Distance[i] = Σ ((VelocityData[j] * 12.0) / SamplingFreq), 0 ≤ j ≤ i fAnalyzeData (page D-7) Fill Distance Vectors: RPMDistance[ ], VelocityDistance[ ], RawRPMDistance[ ], ImpactDistance[ ] Find Rev Loc Indices: RevBGNLoc[ ], RevENDLoc[ ] Interpolate: RPMLoc[i] = Interpolate (RevENDLoc[i-1], RevBGNLoc[i]) Calc Angular Velocities: CalcRPMs[i] = 1 / (RPMLoc[i] - RPMLoc[i-1]) Remove Doppler: RPMData[ ] = PolyCurveFit (CalcRPMs[ ]) Get Release RPMs: ReleaseRPMs = RPMData[ReleaseIndex] Get Impact RPMs: ImpactRPMs = RPMData[PinImpactIndex] Calc Rev Distance: vCalcRevLocations (page D-17) Fill Distance Vector: RevLocDistance[ ] RevDistance[rev] = Σ ((VelocityData[i] * 12.0 ) / SamplingFreq), 0 ≤ i ≤ RPMLoc[rev] A Figure 3-8 To: Graphing Routines 58
3.6.1 Implementation and Performance There are several performance issues with the current version of the MASTER software that are currently being addressed. • The coefficient of friction calculations from Section 3.4.3 have not yet been incorporated. Instead, a command-line argument specifies the percentage of the change in angular momentum that is lost due to friction. For this paper, frictional losses were set at 10%. • A somewhat less accurate method for deriving the linear velocities than that described in Section 3.3 is currently implemented. This method derives the average linear momentum from the average linear velocity of the ball, and calculates the average angular momentum from the angular velocities for each revolution. Although this yields the proper shape for the waveform, it misrepresents the magnitude of the linear velocities. See vCalcVelocityData in Figure 3-8 for more detail. • The current linear velocity extraction algorithm does not check for roll out of the ball (that the angular velocity is decreasing). Therefore, under the constant energy assumption, when the angular velocity begins to decrease, the calculated linear velocity increases. The graph in Figure 3-9 demonstrates this phenomenon. Figure 3-9: Effects of Roll Out, "Analysis" Screen Capture 59
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 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: 3.5.3 External Forces and Friction
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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