1. Page 1 SABR36, June 29, 2006 Baseball Aerodynamics: What do we know and how do we know it? Alan M. Nathan University of Illinois at Urbana-Champaign a-nathan@uiuc.edu www.npl.uiuc.edu/~a-nathan/pob Introduction Qualitative Effects of Drag and Lift Measurements of Drag and Lift Summary

2. Page 2 SABR36, June 29, 2006 Introduction: Forces on a Spinning Baseball in Flight mg FdFd FMFM gravity: “physics 101” drag: “wind resistance” lift: Magnus force on spinning baseball

3. Page 3 SABR36, June 29, 2006 Introduction: Forces on a Spinning Baseball in Flight mg FdFd FMFM drag is opposite to direction of motion “lift” is in direction that leading edge is turning

4. Page 4 SABR36, June 29, 2006 Effect of Drag and Lift on Trajectories drag effect is huge lift effect is smaller but significant

5. Page 5 SABR36, June 29, 2006 Some Effects of Drag l Reduced distance on fly ball l Reduction of pitched ball speed by ~10% l Asymmetric trajectory:  Total Distance  1.7 x distance at apex l Optimum home run angle ~35 0

6. Page 6 SABR36, June 29, 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.

7. Page 7 SABR36, June 29, 2006 Some Effects of Lift Balls hit to left/right curve toward foul pole

8. Page 8 SABR36, June 29, 2006 Some Effects of Lift Tricky popups with lots of backspin

9. Page 9 SABR36, June 29, 2006 Let’s Get Quantitative: Measurements of Drag and Lift l What do we know? l How do we know it? l How well do we know it? l Two types of experiments:  Wind tunnel Measure forces directly  Video tracking of trajectory “You can observe a lot by watching” Infer forces from measured acceleration

10. Page 10 SABR36, June 29, 2006 Experiment #1: Tracking Trajectory (UC/Davis; Illinois) ATEC 2-wheel pitching machine Motion Capture System Baseball with reflecting dot

11. Page 11 SABR36, June 29, 2006 Joe Hopkins ~15 ft Motion Capture Geometry

12. Page 12 SABR36, June 29, 2006 Motion Capture System: 10 cameras 700 frames/sec 1/2000 shutter very fancy software www.motionanalysis.com Pitching Machine: project horizontally 50-110 mph 1500-4500 rpm

13. Page 13 SABR36, June 29, 2006 Typical Data

14. Page 14 SABR36, June 29, 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 Conclusion: data qualitatively consistent (~20%)

15. Page 15 SABR36, June 29, 2006 Results for Drag Coefficient C D F D = 1/2  AC D v 2 Conclusion: Major disagreements for v= 70-100 mph

16. Page 16 SABR36, June 29, 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

17. Page 17 SABR36, June 29, 2006 Sportvision Data batter’s view Backspin: up and in to RHH 225 o

18. Page 18 SABR36, June 29, 2006 Sportvision Data batter’s view Backspin: up and away to RHH 135 o

19. Page 19 SABR36, June 29, 2006 Sportvision Data warmup game pitches

20. Page 20 SABR36, June 29, 2006 Synthesis of Results

21. Page 21 SABR36, June 29, 2006 Synthesis of Results Uncertainty in drag  50 ft!

22. Page 22 SABR36, June 29, 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?