### Busch Petco

The Doppler Technique Doppler Frequency Shift

f d

TRANSMITTER

F TX F TX

F RX V V R f D f d = F TX -F RX = 2*V R *F TX /c = Doppler Shift = F TX - F RX =

2F TX (V R /c)

V R = 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) r(t)  r(0)  t 0  dr dt dt '

Determining r(0) • Transmit two wavelengths  1 – Initially in phase and  2 • 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

F TX f d1 F TX

F RX1 f d2 F TX

F RX2 D

Extra distance = Dsin(

(f d1 ) -

phase shift (f d2 ) = 2*

 

) *sin(

)*D*F TX /c

8

 

### 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 10

Measurement Principle: Spin

Weaker reflection Strong reflection Weaker reflection

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

 11

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 12

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 13