Petco

Tracking the Baseball with the TrackMan Doppler Radar

A Brief Introduction

Busch

2

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

3

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 ,

10

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