Page 1 AIAA, StL, October 19, 2006 Baseball Aerodynamics: What do we know and how do we know it? Alan M. Nathan University of Illinois at Urbana-Champaign Introduction Qualitative Effects of Drag and Lift Measurements of Drag and Lift Current State of our Knowledge Summary

Page 2 AIAA, StL, October 19, 2006 Forces on a Spinning Baseball in Flight F d =½ C D  Av 2 mg FdFd FLFL Courtesy, Popular Mechanics F L = ½ C L  Av 2 direction leading edge is turning

Page 3 AIAA, StL, October 19, 2006 What does C D depend on? Reynold’s Number  Re=  Dv/   Re~1x10 45 mph surface “roughness” seam orientation? spin? Question: Does a baseball experience a “drag crisis”? Achenbach, J. Fl. Mech. 65, 113 (1974)

Page 4 AIAA, StL, October 19, 2006 What does C L depend on? S  r  /v  C L ~( )S  F L = ( )  r 3  v Seam orientation? Reynold’s fixed S?

Page 5 AIAA, StL, October 19, 2006 “Straw Man” Drag and Lift more later on where these come from

Page 6 AIAA, StL, October 19, 2006 Effect of Drag and Lift on Trajectories drag effect is huge lift effect is smaller but significant

Page 7 AIAA, StL, October 19, 2006 Some Effects of Drag l Reduced distance on fly ball l Reduction of pitched ball speed by ~10%  2-seam vs. 4-seam l Asymmetric trajectory:  Total Distance  1.7 x distance at apex l Optimum home run angle ~

Page 8 AIAA, StL, October 19, 2006 Some Effects of Lift l Backspin makes ball rise  “hop” of fastball  undercut balls: increased distance, reduced optimum angle of home run l Topspin makes ball drop  “12-6” curveball  topped balls nose-dive l Breaking pitches due to spin  Cutters, sliders, etc.

Page 9 AIAA, StL, October 19, 2006 Additional Effects of Lift Balls hit to left/right curve toward foul pole

Page 10 AIAA, StL, October 19, 2006 Additional Effects of Lift: Tricky trajectories of popups --popup behind home plate with lots of backspin

Page 11 AIAA, StL, October 19, 2006 Drag and Lift: What do we know? How do we know it? How well do we know it? Two types of experiments:  Wind tunnel Measure forces directly  Video tracking of trajectory Infer forces from measured acceleration

Page 12 AIAA, StL, October 19, 2006 Data on C D Mehta,Briggs: wind tunnel Atlanta: video tracking Alaways: motion capture SHS: Hubbard parametrization RKA: Adair parametrizatoin Ref: 1.J. App. Biomechanics 17, (2001) 2.Adair, The Physics of Baseball, 3 rd Ed.

Page 13 AIAA, StL, October 19, 2006 Denver vs. NYC: Is there a sudden drag crisis? l F d =½ C D  Av 2 l Re=  Av/  l  Denver = 0.8  NYC l Re Denver =0.8Re NYC

Page 14 AIAA, StL, October 19, 2006 Data on C L Watts: wind tunnel, low speed Briggs: wind tunnel, high speed Present, Alaways: motion capture SHS: Hubbard bilinear description RKA: Adair model Ref: Am. J. Phys. 71, (2003); 73, (2005)

Page 15 AIAA, StL, October 19, 2006 Adair Model of Lift l Lift due to “differential drag” l C L =2C D S{1+0.5(v/C D )dC D /dv}  C L  S for v<50 mph Courtesy, Popular Mechanics Adair model at 100 mph

Page 16 AIAA, StL, October 19, 2006 Comparision of SHS and RKA Parametrizations of Drag and Lift Discrepency is huge at mph

Page 17 AIAA, StL, October 19, 2006 Implications for Trajectory

Page 18 AIAA, StL, October 19, 2006 New Experiment #1: Tracking Trajectory (Illinois) ATEC 2-wheel pitching machine Motion Capture System Baseball with reflecting dot

Page 19 AIAA, StL, October 19, 2006 Joe Hopkins ~15 ft Motion Capture Geometry

Page 20 AIAA, StL, October 19, 2006 Motion Capture System: 10 Eagle-4 cameras 700 frames/sec 1/2000 shutter EVaRT 4.0 software Pitching Machine: project horizontally mph rpm

Page 21 AIAA, StL, October 19, 2006 Experiment: Some Details l Motion capture:  700 fps, 1/2000 s shutter  Track over ~5 m   y  0.5 mm;  z  13 mm with some caveats  only 1 reflector  assume horizontal spin axis l Pitching machine:  Speeds: mph  Spins: rpm  Mainly topspin, some backspin  All trials “two-seam”  Initial angle ~0 o l Distances: feet l Calibrations and cross-checks  Simple ball toss gets a=g to 2%

Page 22 AIAA, StL, October 19, 2006 Typical Data

Page 23 AIAA, StL, October 19, 2006 Data Analysis l Nonlinear least-squares fit  y(t) = y CM (t) + Acos(  t+  )  z(t) = z cm (t)  Asin(  t+  ) l cm trajectory calculated numerically  RK4 l nine free parameters y cm (0), z cm (0), v y,cm (0), v z,cm (0) A, ,  C L, C D

Page 24 AIAA, StL, October 19, 2006 Typical Data and Fit

Page 25 AIAA, StL, October 19, 2006 Results of Analysis: C L

Page 26 AIAA, StL, October 19, 2006 Conclusion: No strong dependence on Re at fixed S  0.2

Page 27 AIAA, StL, October 19, 2006 Results for Lift Coefficient C L F L = 1/2  AC L v 2 S=r  /v 100 mph, 2000 rpm  S=0.17 Conclusions: --data qualitatively consistent (~20%) --RKA model inconsistent with data

Page 28 AIAA, StL, October 19, 2006 Results for Drag Coefficient C D Conclusion: Major disagreements for v= mph

Page 29 AIAA, StL, October 19, 2006 Experiment #2: Sportvision— A Potential New Tool l Track pitched baseballs with 2 cameras  High-speed not necessary  Tracking of MLB game pitches  Used by ESPN for K-Zone l From trajectory, determine  lift,drag,spin axis l Spin rate not measured Thanks to Marv White, CTO, for providing a wealth of data

Page 30 AIAA, StL, October 19, 2006 Sportvision Data batter’s view Pure backspin 180 o

Page 31 AIAA, StL, October 19, 2006 Sportvision Data batter’s view “cutter”: up and in to RHH 225 o

Page 32 AIAA, StL, October 19, 2006 Sportvision Data batter’s view “cutter”: up and away to RHH 135 o

Page 33 AIAA, StL, October 19, 2006 Sportvision Data warmup game pitches

Page 34 AIAA, StL, October 19, 2006 Sportvision Data

Page 35 AIAA, StL, October 19, 2006 How Far Did That Home Run Travel? l Ball leaves bat l Hits stands D from home plate, H above ground l How far would it have gone if no obstruction?

Page 36 AIAA, StL, October 19, ft/30 ft Range= Time can resolve 4 s 5 s 7 s See

Page 37 AIAA, StL, October 19, 2006 Synthesis of Results

Page 38 AIAA, StL, October 19, 2006 Synthesis of Results Uncertainty in drag  50 ft!

Page 39 AIAA, StL, October 19, 2006 Summary l We have much empirical knowledge of lift and drag  …and some promising new tools for future research l Things we would like to know better:  Better data on drag “drag crisis” Spin-dependent drag? Drag for v>100 mph  Dependence of drag/lift on seam orientation?  Is the spin constant?