Petco
Tracking the Baseball with the TrackMan Doppler Radar
A Brief Introduction
Busch
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TRANSMITTER
RECEIVER
FTX
FTX
FRX
V
VR
fd
fd = FTX-FRX = 2*VR*FTX/c
The Doppler Technique
Doppler Frequency Shift
fD = Doppler Shift = FTX - FRX = 2FTX(VR/c)
VR = dr/dt = rate of change of distance of ball from TM
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Doppler shift Radial velocity
Time
Pitched ball
Batted ball
Frequency/Velocity vs. Time
Bat
Bounce
Slightly More Detail• Want to determine location of
baseball as function of time– TM determines r,,
• r = distance from TM,=orientation angles wrt TM
• Determining r(t)– Doppler shift determines dr/dt– Two-frequency phase shift
determines r(0)
Summary of TM Technique: r,,
't
0
dtdt
drr(0)r(t)
Determining r(0)
• Transmit two wavelengths 1 and 2
– Initially in phase
• After reflection and detection, out of phase by 2r(1/ 1 - 1/ 2)
• Measuring phase shift at t=0 determines r(0)
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Measuring anglesPhase Shift Between Detectors Angles
TRANSMITTER
RECEIVER 1
FTX
FTX
FRX1fd1
(fd1 ) - (fd2) = 2**sin()*D*FTX/cRECEIVER 2FRX2
fd2
FTX
D
Extra distance = Dsin() phase shift
Three Detectors ,
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Doppler shift determines dr/dt
Two wavelength phase shift determines r(0)r(0) + dr/dt r(t)
3-detector array phase shifts determine (t), (t)
r(t), (t), (t) gives full 3D trajectoryNeed to convert to field coordinates using
location and orientation of TM
Summary of Technique
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Measurement Principle: Spin
w*r
w*r
VradRadar
Strong reflection
Weaker reflection
Weaker reflection
rw
Vtot = Vrad - w*r
Vtot = Vrad + w*r
Vtot = Vrad
Conclusion:A Doppler radar does not only see one velocity, but avelocity spectrum.
The velocity spectrum turns out to have discretefrequency components spaced with the spin frequency w.
Doppler frequency modulated by rotation frequency
Sidebands separated by n
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TrackMan Capabilities I:Full pitched ball trajectory
• Everything PITCHf/x gives plus….
• Actual release point (“extension”) perceived velocity
• Total spin (including “gyro” component)
• Many more points on the trajectoryUtility of more points under study
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TrackMan Capabilities II:Full batted ball trajectory
• Batted ball speed, launch & spray anglesEquivalent to HITf/x
• Landing point coordinates at ground level and hang timeEquivalent to Hittracker
• Initial spin
• and more, if you want it