Transcript Tracking the baseball with the TrackMan Doppler radar
Tracking the Baseball with the TrackMan Doppler Radar A Brief Introduction
Busch Petco
The Doppler Technique Doppler Frequency Shift
f d
TRANSMITTER
F TX F TX
RECEIVER
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
RECEIVER 1
F RX1 f d2 F TX
RECEIVER 2
F RX2 D
Extra distance = Dsin(
(f d1 ) -
phase shift (f d2 ) = 2*
) *sin(
)*D*F TX /c
8
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 10
Radar
Measurement Principle: Spin
Weaker reflection Strong reflection Weaker reflection
w*r r w w*r Vrad Vtot = Vrad - w*r Vtot = Vrad 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
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