#### 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