Page 1 SABR36, June 29, 2006 Baseball Aerodynamics: What do we know and how do we know it? Alan M. Nathan University of Illinois at Urbana-Champaign [email protected]

Page 2SABR36, June 29, 2006

Introduction:Forces on a Spinning Baseball in Flight

v

ω

mg

Fd

FM

• gravity: “physics 101”

• drag: “wind resistance”

• lift: Magnus force on spinning baseball


Introduction:Forces on a Spinning Baseball in Flight

v

ω

mg

Fd

FM

• drag is opposite to direction of motion

• “lift” is in direction that leading edge is turning


Effect of Drag and Lift on Trajectories

• drag effect is huge

• lift effect is smaller but significant

0

20

40

60

80

100

120

0 100 200 300 400 500 600 700

distance (ft)

no drag or lift

drag, no lift drag and lift


Some Effects of Drag

Reduced distance on fly ball

Reduction of pitched ball speed by ~10%

Asymmetric trajectory:Total Distance 1.7 x distance

at apex

Optimum home run angle ~350

0

20

40

60

80

100

120

0 100 200 300 400 500 600 700

distance (ft)

no drag or lift

drag, no lift

0

50

100

150

200

250

300

350

400

10 20 30 40 50 60 70 80 90

Range (ft)

(deg)

Range vs.

2000 rpm

0 rpm


Some Effects of Lift

Backspin makes ball rise“hop” of fastball

undercut balls: increased distance, reduced optimum angle of home run

Topspin makes ball drop “12-6” curveball

topped balls nose-dive

Breaking pitches due to spinCutters, sliders, etc.

0

20

40

60

80

100

120

0 100 200 300 400 500 600 700

distance (ft)

no drag or lift

drag, no lift drag and lift



Balls hit to left/right curve toward foul pole


0

50

100

150

200

0 10 20 30 40 50 60

distance (ft)


Tricky popups with lots of backspin


Let’s Get Quantitative:Measurements of Drag and Lift

What do we know? How do we know it? How well do we know it?

Two types of experiments:Wind tunnel

• Measure forces directlyVideo tracking of trajectory

• “You can observe a lot by watching”

• Infer forces from measured acceleration


Experiment #1: Tracking Trajectory(UC/Davis; Illinois)

ATEC 2-wheel pitching machine

Motion Capture System

Baseball with reflecting dot


Joe Hopkins

~15 ft

Motion Capture Geometry


Motion Capture System:

• 10 cameras

• 700 frames/sec

• 1/2000 shutter

• very fancy software

www.motionanalysis.com

Pitching Machine:• project horizontally• 50-110 mph• 1500-4500 rpm


Typical Data

61

62

63

64

65

66

0 5 10 15

distance (ft)

94 mph3000 rpm topspin1.8g


Results for Lift Coefficient CL

FL= 1/2ACLv2

S=r/v100 mph, 2000 rpm

S=0.17

0.0

0.1

0.2

0.3

0.4

0.5

0.6

present

Alaways 2-Seam

Alaways 4-Seam

Watts & Ferrer

Briggs

0.0 0.2 0.4 0.6 0.8 1.0

CL

S

Conclusion: data qualitatively consistent (~20%)


Results for Drag Coefficient CD

FD= 1/2ACDv2

Conclusion:

Major disagreements for v= 70-100 mph

0.0

0.2

0.4

0.6

0.8

60 70 80 90 100 110

CD

v (mph)

SHSRKA

present

Alaways


Experiment #2: Sportvision—A Potential New Tool

Track pitched baseballs with 2 camerasHigh-speed not necessaryTracking of MLB game pitchesUsed by ESPN for K-Zone

From trajectory, determine lift,drag,spin axis

Spin rate not measured

Thanks to Marv White, CTO, for providing a wealth of data


Sportvision Data

-15.00

-10.00

-5.00

0.00

5.00

10.00

15.00

0 50 100 150 200 250 300

dx or dz vs.

dxdz

(deg)

batter’s view

Backspin:

up and in to RHH

225o


Sportvision Data

-15.00

-10.00

-5.00

0.00

5.00

10.00

15.00

0 50 100 150 200 250 300

dx or dz vs.

dxdz

(deg)

batter’s view

Backspin:

up and away to RHH

135o


Sportvision Data

0

0.2

0.4

0.6

0.8

1

1.2

50 60 70 80 90 100

V (mph)

Drag/Weight

Lift/Weight

warmup game pitches


Synthesis of Results

0

0.5

1

1.5

2

0 25 50 75 100 125 150Speed in mph

Drag/Weight

Lift/Weight@1800 rpm


Synthesis of Results

0

20

40

60

80

100

120

0 100 200 300 400 500

distance (ft)

Uncertainty in drag 50 ft!


Summary

We have much empirical knowledge of lift and drag…and some promising new tools for future

research Things we would like to know better:

Better data on drag • “drag crisis”• Spin-dependent drag?• Drag for v>100 mph

Dependence of drag/lift on seam orientation?Is the spin constant?

Documents

Page 1 SABR36, June 29, 2006 Baseball Aerodynamics: What do we know and how do we know it? Alan M. Nathan University of Illinois at Urbana-Champaign [email protected]