Spin of a Batted BaseballAlan M. Nathana, Jonas Contakosa, Russ

Kesmana, Biju Mathewb, Wes Lukashb

aUniversity of Illinois at Urbana-ChampaignbRawlings Sporting Goods

v FM

mg

Fd

ω

Spin Affects Batted Ball Trajectories

Familiar Effects:• Backspin keeps fly ball in air longer

– greater distance

• Topspin makes line drives nosedive– and leads to grounders with tricky

bounces

• Sidespin makes ball slice or hook toward foul pole

• Backspin sometimes leads to “paradoxical popups”

2000 fps

friction

normal forcev

Mechanism for Batted Ball Spin

• Rolling: ex=0

• Sliding: ex<0

• Gripping: ex>0

Tf fx

Ti i

v -rωe = -

v -rω

•Superball: ex ~ 0.8•“usual” assumption ex=0 •Low speed: ex~0.16

Scattering Geometry

Measure v1, v2, 1, 2, Infer

• v1: 85-120 mph

1: 0, 1000-3000 rpm

Normalized Final Spin vs. Incident Angle to Normal ()

Final spins depend on , ~independent of initial spin

Incident topspin

Incident backspin

Incident topspin

Incident backspinZero incident spin

Incident topspin

Incident backspin

Final vs. Initial Tangential Speed

Zero incident spin

Incident topspin

Incident backspin

• Data consistent with ex=0.3 (gripping)• Data inconsistent with ex=0 (rolling)• For >400, “gross slip” ensues

Slope = -ex

Angular Momentum Conservation about Contact Point

CoF and Ratio of Tangential to Normal Impulse

Data consistent with very low CoF, ~0.15

Summary of Conclusions

• Final spin for given vTi nearly independent of initial spin

• Data consistent with ex=0.30, implying considerable “overspin”

• Data consistent with angular momentum conservation

• Data consistent with very low CoF– puzzling!

…and finally

v0 = 96.6 mph, = 30.5o, R = 374 ft

b = 3300 rpm s = 425 rpmThe Grip Doesn’t Matter!