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Spin of a Batted Baseball

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. Spin Affects Batted Ball Trajectories. F M. Familiar Effects: Backspin keeps fly ball in air longer

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Spin of a Batted Baseball

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  1. Spin of a Batted Baseball Alan M. Nathana, Jonas Contakosa, Russ Kesmana, Biju Mathewb, Wes Lukashb aUniversity of Illinois at Urbana-Champaign bRawlings Sporting Goods

  2. Spin Affects Batted Ball Trajectories FM 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” Fd mg

  3. 2000 fps

  4. normal force v friction Mechanism for Batted Ball Spin • Rolling: ex=0 • Sliding: ex<0 • Gripping: ex>0 • Superball: ex ~ 0.8 • “usual” assumption ex=0 • Low speed: ex~0.16

  5. Scattering Geometry Measure v1, v2, 1, 2,  Infer  • v1: 85-120 mph • 1: 0, 1000-3000 rpm

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

  7. Final vs. Initial Tangential Speed Incident backspin Zero incident spin Incident topspin Slope = -ex • Data consistent with ex=0.3 (gripping) • Data inconsistent with ex=0 (rolling) • For >400, “gross slip” ensues

  8. Angular Momentum Conservation about Contact Point

  9. CoF and Ratio of Tangential to Normal Impulse Data consistent with very low CoF, ~0.15

  10. 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!

  11. …and finally v0 = 96.6 mph,  = 30.5o, R = 374 ft b = 3300 rpm s = 425 rpm The Grip Doesn’t Matter!

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