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Combining HITf/x with Landing Point Alan Nathan, Univ. of Illinois

• Introduction• What can be learned

directly from the data?• Fancier analysis

methods• The Big Question:

– How well can HITf/x predict

• landing point?• hang time?• full trajectory?

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(379,20,5.2)

hitf/xhittracker

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Why do we care?

• HITf/x data come for “free”

• If HITf/x can determine full trajectory, then we have a handle on– Hang time– Fielder range and reaction time– Outcome-independent hitting metrics– Accurate spray charts– …..

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My approach to studying the problem

A. Get initial trajectory from HITf/x

B. Get landing point and flight time from hittrackeronline.com

– thanks to Greg Rybarczyk

C. Determine how well A determines B

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The physics issues

• If we know the initial conditions (HITf/x) and we know all the forces, then we can predict the full trajectory.

• What are the forces and how well are they known?

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What are the Forces?

• Gravity• Drag (“air resistance”)• Magnus Force (due to spin)

v

mg

Fdrag

FMagnus

• Drag and Magnus depend on air density, wind• Drag depends on “drag coefficient” Cd

• Magnus depends on spinbackspin b: upward forcesidespin s: sideways force

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What can be learned directly from the data?

• characteristics of home runs

• effect of sidespin

• effect of backspin

• effect of drag and spin on fly ball distance--does a ball “carry” better in some ball parks

than in others?

--is there a “Yankee Stadium” effect?

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SOB and Launch Angle

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How important is SOB?

each additional mph of SOBincreases range by ~4 ft

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What is optimum launch angle for home runs?

approximately 300

normalized range = range/(k*v0)

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sideways break sidespin (s)

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x (ft)

f

iRF foul line

1B

i- f measures sideways break

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Effect of Sidespin

break to right

break to left

RFCFLF

• balls breaks towards foul pole• amount of break increases with spray angle• balls hit to CF seem to slice• the slice results in asymmetry between RHH and LHH

LHH

RHH

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Hang Time:ratio to vacuum value

• backspin increase hang time

• drag decreases hang time

• ratio of hang time to vacuum value approaches 1 with larger launch angle

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0

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actual trajectory

vacuum trajectory

(379,20,5.2)

v0 = 100 mph = 29o

b = 2500 rpm

(532,20,4.2)

R = actual distance/vacuum distance = D/D0

= 379/532 = 0.71

Effect of Drag and Lift on Range

D0

D

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R = D/D0 vs. initial vertical velocity

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Normalized R by Park

0.940.960.981.001.021.041.061.08

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Larger normalized R means better “carry”

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Normalized R by Park

0.940.960.981.001.021.041.061.08

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best carry: Houston, Denverworst carry: Cleveland, Detroit, Oaklandbest-worst: 10% or about 40 ft

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Does the ball carry better in Yankee Stadium?

No evidence for better carry in the present data.

Coors

YS

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Home Run Spray Chart

RFLF

CF

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Fancier Analysis Methods

• There are things we don’t know well– the spin on the batted ball (b and s)– the drag coefficient Cd

• Therefore, we will use the actual data as a way to constrain b, s, Cd

– develop relationships between these quantities and initial velocity vector

– investigate how well these relationships reproduce the landing point data.

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0

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0 50 100 150 200 250 300 350 400Horizontal Distance (ft)

(379,20,5.2)

v0 = 100 mph = 29o

b = 2500 rpm

hitf/xhittracker

• for given hitf/x initial conditions, adjust Cd, b, s to reproduce landing point (x,y,z) at the measured flight time • unique solution is always possible

--flight time determines b

--horizontal distance and flight time determines Cd

--sideways deflection determines s

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How Far Did That Ball Travel?

• How to extrapolate from D to R

• Compare angle of fall to launch angle tan(fall)=H/(R-D)

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(379,20,5.2)

hitf/xhittracker

D

R

H

R-D

fall H

R-D

fall

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fall

fall/

R fall/ = 1.4

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Sidespin

LHH

LHH

s (rpm)

(deg)

(deg)

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Backspinb (rpm)

(deg)

(deg)

b (rpm)

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Summary• we have expressions for b() and s() • there is lots of scatter of the data about these mean values

– Is the scatter real?

• that means we still have a ways to go to meet our goal of predicting landing point and hang time from HITf/x data alone

• but we have learned some things along the way– Optimum launch angle for home run– Importance of SOB: 4 ft/mph – L-R asymmetry in s

– characterization of “carry”

• look forward to landing data from hit balls other than home runs