Tracking the Baseball with the
TrackMan Doppler Radar
A Brief Introduction
Busch
Petco
The Doppler Technique
Doppler Frequency Shift
TRANSMITTER
FTX
V
FTX
fd
RECEIVER
VR
FRX
fD = Doppler Shift = FTX - FRX =  2FTX(VR/c)
fd = FTX-FRX = 2*VR*FTX/c
VR = dr/dt = rate of change of distance
of ball from TM
2
Frequency/Velocity vs. Time
Doppler shift
Radial velocity
Batted ball
Bat
Bounce
Pitched ball
Time 
3
Slightly More Detail
• Want to determine location of
baseball as function of time
– TM determines r,,
• r = distance from TM
• ,=orientation angles wrt TM
Summary of TM Technique: r,,
• Determining r(t)
– Doppler shift determines dr/dt
– Two-frequency phase shift
determines r(0)
t
dr '
r(t) r(0)  dt
dt
0
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)
Measuring angles
Phase Shift Between Detectors Angles
TRANSMITTER
FTX
FTX
fd1
RECEIVER 1
FRX1

FTX
fd2
RECEIVER 2
D
FRX2
Extra distance
= Dsin()
(fd1 ) - (fd2) = 2**sin()*D*FTX/c
 phase shift
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Three Detectors  ,
Summary of Technique
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 trajectory
Need to convert to field coordinates using
location and orientation of TM
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Measurement Principle: Spin
Weaker reflection
Radar
w*r
r
Vtot = Vrad - w*r
w
Strong reflection
Vrad
Vtot = Vrad
Weaker reflection
w*r
Vtot = Vrad + w*r
Conclusion:
A Doppler radar does not only see one velocity, but a
velocity spectrum.
The velocity spectrum turns out to have discrete
frequency 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 trajectory
Utility of more points under study
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TrackMan Capabilities II:
Full batted ball trajectory
• Batted ball speed, launch & spray angles
Equivalent to HITf/x
• Landing point coordinates at ground level
and hang time
Equivalent to Hittracker
• Initial spin
• and more, if you want it
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