Spin of a Batted Baseball Alan M. Nathan a, Jonas Contakos a, Russ Kesman a, Biju Mathew b, Wes Lukash b a University of Illinois at Urbana-Champaign b Rawlings Sporting Goods

FMFM mg FdFd 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 force v Mechanism for Batted Ball Spin Rolling: e x =0 Sliding: e x <0 Gripping: e x >0 Superball: e x ~ 0.8 “usual” assumption e x =0 Low speed: e x ~0.16

Scattering Geometry Measure v 1, v 2,  1,  2,  Infer  v 1 : mph  1 : 0,  rpm

Normalized Final Spin vs. Incident Angle to Normal (  ) Final spins depend on , ~independent of initial spin Incident topspin Incident backspin Incident topspin Incident backspin Zero incident spin Incident topspin Incident backspin

Final vs. Initial Tangential Speed Zero incident spin Incident topspin Incident backspin Data consistent with e x =0.3 (gripping) Data inconsistent with e x =0 (rolling) For  >40 0, “gross slip” ensues Slope = -e x

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 v Ti nearly independent of initial spin Data consistent with e x =0.30, implying considerable “overspin” Data consistent with angular momentum conservation Data consistent with very low CoF –puzzling!

…and finally v 0 = 96.6 mph,  = 30.5 o, R = 374 ft  b = 3300 rpm  s = 425 rpm The Grip Doesn’t Matter!