Analysis of Knuckleball Trajectories

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Presentation transcript:

Analysis of Knuckleball Trajectories Alan M. Nathan University of Illinois at Urbana-Champaign Trampoline effect “universal”: golf, tennis, baseball/softball, etc.. Physics is the same in each. Recently retired knuckleball pitcher Tim Wakefield 1

Issues to be Addressed The “movement” of knuckleball pitches The “smoothness” of knuckleball trajectories

Knuckleball thrown with very little spin  no Magnus force But still lots of erratic “movement” Origin of movement revealed in wind tunnel experiments

Wind Tunnel Data, 4S Orientation Mike Morrissey (MS Thesis) and John Borg (Marquette) Agrees with Watts & Sawyer, AJP (1975)

Studying Knuckleball Trajectories Using the PITCHf/x Tracking System Two video cameras @60 fps approximately orthogonal axes full 3D reconstruction tracks every pitch in every MLB ballpark all data publicly available Image, courtesy of Sportvision

Studies of Knuckleball Movement Movement = deviation of trajectory from straight line, with gravity removed Easily measured with PITCHf/x View from above 5” movement

Direction of movement vs. release speed (Jon Lester) Catcher’s View “Normal” pitches have predictable movement

Direction of movement vs. release speed (Tim Wakefield) Knuckleballs do not have predictable movement

But is the trajectory “smooth”? Fit to smooth function Examine RMS deviation of data from fit 9 Free Parameters: x0, y0, z0, vx0, vy0, vz0, CD, CL, 

278 pitches from August 29, 2011 Knuckleball (77) Normal (201) Normal and knuckleball pitches follow similar distributions Knuckleballs only slightly (few tenths of inch) less smooth

Two Examples: Which one is the knuckleball? 76 mph knuckleball rms=0.374” 75 mph curveball rms=0.373”

2011Aug29-161108

Summary of Conclusions Movement of knuckleball trajectories varies considerably from pitch to pitch Magnitude and direction quasi-random Any given trajectory is as smooth as those of ordinary pitches within limits of precision of tracking data (~0.3”-0.5”) Open questions/work in progress Are erratic movement and smoothness conclusions consistent with wind tunnel data? How can perception and reality be reconciled?