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!
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