1. Petco Tracking the Baseball with the TrackMan Doppler Radar A Brief Introduction Busch

2. 2 The Doppler Technique Doppler Frequency Shift f D = Doppler Shift = F TX - F RX =  2F TX (V R /c) V R = dr/dt = rate of change of distance of ball from TM

3. 3 Doppler shiftRadial velocity Time  Pitched ball Batted ball Frequency/Velocity vs. Time Bat Bounce

4. Slightly More Detail Want to determine location of baseball as function of time –TM determines r, ,  r = distance from TM ,  =orientation angles wrt TM

5. Determining r(t) –Doppler shift determines dr/dt –Two-frequency phase shift determines r(0) Summary of TM Technique: r, , 

6. 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)

7. Determining r(t) –Doppler shift determines dr/dt –Two-frequency phase shift determines r(0) Determining  (t),  (t) –Phase shift between pairs of detectors Summary of TM Technique: r, , 

8. 8 Measuring angles Phase Shift Between Detectors  Angles Extra distance = Dsin(  )  phase shift

9. Three Detectors  , 

10. 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 trajectory Need to convert to field coordinates using location and orientation of TM Summary of Technique

11. 11 Measurement Principle: Spin Doppler frequency modulated by rotation frequency  Sidebands separated by n 

12. 12 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

13. 13 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