APS/DFD, Nov Baseball Aerodynamics Alan M. Nathan, University of Illinois webusers.npl.uiuc.edu/~a-nathan/pob Introduction State of our previous knowledge What we are learning from newer technologies… --about baseball aerodynamics --about the game itself Summary

APS/DFD, Nov Forces and Torques on a Spinning Baseball in Flight The goal: determine the coefficients of drag, lift, and moment mg FdFd FMFM

APS/DFD, Nov Real vs. “Physics 101” Trajectory: Effect of Drag and Magnus Reduced distance on fly ball Reduction of pitched ball speed by ~10% Asymmetric trajectory Optimum fly ball angle~30 o

APS/DFD, Nov Some Effects of Spin Backspin makes ball rise –“hop” of fastball –increased distance of fly ball –tricky popups Topspin makes ball drop – “12-6” curveball – topspin line drives nose-dive Sidespin makes ball break toward foul pole Breaking pitches due to spin –curveballs, sliders, cutters, etc. mg FdFd FMFM

APS/DFD, Nov So what do we know about C D, C L, and C M ? …prior to 2 yrs ago

APS/DFD, Nov What do we know about C D ? Depends on …. Reynold’s Number –Re=  Dv/  –Re~1x10 45 mph surface “roughness” seam orientation? spin? Summary: Existing data show factor of ~2 discrepencies Character of the “drag crisis” not well determined C D above ~100 mph not well determined

APS/DFD, Nov What do we know about C L ? Depends on …. spin parameter S  R  /v Seam orientation? Reynold’s fixed S? best evidence in “no”, in region of mph In region of importance for baseball (S= ), data are consistent at 20% level

APS/DFD, Nov Conclusion: No strong dependence on Re at fixed S  0.2 Dependence of C L on Re at fixed S

APS/DFD, Nov What do we know about C M ? Almost nothing experimentally! For golf…. C M =  S  0.012S   mph   [M/R 2 ]/  v (8% larger for baseball) Therefore estimate   mph

APS/DFD, Nov New Technologies The PITCHf/x system The TrackMan Doppler radar system

APS/DFD, Nov The PITCHf/x Tracking System Two video cameras track baseball in 1/60-sec intervals (usually “high home” and “high first”) Software to identify and track pitch frame-by- frame in real time  full trajectory Installed in every MLB ballpark Image, courtesy of Sportvision

APS/DFD, Nov What kind of “stuff” can one learn? Pitch speed to ~0.5 mph –at release and at home plate Pitch location to ~0.5 inches –at release and at home plate “movement” to ~2.0 inches –both magnitude and direction Initial velocity direction Pitch classification –more on this later And all these data are freely available online!

APS/DFD, Nov Pitched ball loses about 10% of speed between pitcher and batter Average speed is ~95% of release speed Example: Pitch Speed--PITCHf/x vs. the gun v0v0 vfvf

APS/DFD, Nov Example: Pitching at High Altitude 10% loss of velocity total movement 12” 7.5% 8” PITCHf/x data contain a wealth of information about drag and lift! Toronto Denver

APS/DFD, Nov k pitches from Anaheim, 2007: Fluctuations consistent with  x  1 inch! C d vs. v 0 vs. v 0 in 2 mph bins Example: C D from Pitchf/x

APS/DFD, Nov Drag Coefficient: no evidence for “drag crisis” Good approximation: C d = 0.35±0.05 in range mph

APS/DFD, Nov Example: Pitch Classification: LHP Jon Lester, 8/4/07 catcher’s view pitches fall into neat clusters: I:4-seam FB II:2-seam FB III:slider (note the reduced spin) IV:CB

APS/DFD, Nov Compare with knuckleball pitcher Tim Wakefield FB CB

APS/DFD, Nov Josh Kalk, THT, 5/22/08 What makes an effective slider?—C. C. Sabathia This slider is very effective since it looks like a fastball for over half the trajectory, then seems to drop at the last minute (“late break”). side view

APS/DFD, Nov New Tools to Study Trajectories of Batted Balls Hitf/x –Uses Pitchf/x cameras to track initial trajectory v 0, ,  Hittracker ( –Measure landing point and flight time for home runs TrackMan Doppler radar –Tracks full batted ball trajectory –Determines initial spin Possibly spin decay

APS/DFD, Nov Example: The “carry” of a fly ball How much does a fly ball “carry”? Motivation: does the ball carry especially well in the new Yankee Stadium? “carry” ≡ (actual distance)/(vacuum distance) for same initial conditions

APS/DFD, Nov The “carry” of a fly ball 819 home runs from April 2009

APS/DFD, Nov Fly ball trajectory from TrackMan ( Safeco Field experiment) Conclusion: Simple prescription for drag and Magnus fits data beautifully. CDCD New TrackMan pitch data

APS/DFD, Nov Summary We are on the verge of major breakthrough on our ability to track baseballs and determine the aerodynamic effects In the near future we should be able to address some outstanding issues: –more precise values for C d in “crisis” region for v>100 mph –spin-dependent drag? –dependence of drag & Magnus on seam orientation, surface roughness, … –time constant for spin decay?