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
Spin Affects Batted Ball Trajectories
Familiar Effects:
• Backspin keeps fly ball in air
longer
FM
v
ω
– 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
2000 fps
Mechanism for Batted Ball Spin
vTf -rωf
ex = vTi -rωi
v
normal force
friction
• Rolling: ex=0
• Sliding: ex<0
• Gripping: ex>0
•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 ()
Incident backspin
Zero incident spin
Incident topspin
Final spins depend on , ~independent of initial spin
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
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 rpm
The Grip Doesn’t Matter!