1. Page 1 IMAC XXIV, January 30, 2006 Effect of Spin on Flight of Baseball Joe Hopkins a, Lance Chong b, Hank Kaczmarski b, Alan M. Nathan a a Physics Department, b Beckman Institute University of Illinois at Urbana-Champaign Introduction The experiment Results Summary

2. Page 2 IMAC XXIV, January 30, 2006 Introduction: Forces on a Moving, Spinning Baseball F d =½ C D  Av 2 F M = ½ C L  Av 2 mg FdFd FMFM

3. Page 3 IMAC XXIV, January 30, 2006 Lift: What do we know? Hubbard (SHS, AJP 71, 1151, 2003): C L = 1.5S (S = R  /v <0.1) = 0.09 + 0.6S (S>0.1) Adair (The Physics of Baseball): C L = 2C D S {1 + 0.5(v/C D )dC D /dv}

4. Page 4 IMAC XXIV, January 30, 2006 Factor of ~3 difference at 100 mph, 1800 rpm Serious implications for flight of fly ball

5. Page 5 IMAC XXIV, January 30, 2006 Experiment l Fire baseball horizontally from pitching machine l Use motion capture to determine  initial conditions (x 0,y 0,v x,v y,  )  track trajectory over ~5m to get C L, C D l Measure horizontal distance D traversed (and sometimes flight time) as ball drops through y 0 (~5 ft)  a y = 2y 0 2 /D 2

6. Page 6 IMAC XXIV, January 30, 2006 Experiment: The Equipment ATEC 2-wheel pitching machine Motion Capture System Baseball with reflecting dot

7. Page 7 IMAC XXIV, January 30, 2006 Joe

8. Page 8 IMAC XXIV, January 30, 2006 Motion Capture System: (www.motionanalysis.com) Ten Eagle-4 cameras EVaRT4.0 software

9. Page 9 IMAC XXIV, January 30, 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: 50-110 mph  Spins: 1500-4800 rpm  Mainly topspin, some backspin  All trials “two-seam”  Initial angle ~0 o l Distances: 40-100 feet l Calibrations and cross-checks  Simple ball toss gets a=g to 2%

10. Page 10 IMAC XXIV, January 30, 2006 Typical Data

11. Page 11 IMAC XXIV, January 30, 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

12. Page 12 IMAC XXIV, January 30, 2006 Typical Data and Fit

13. Page 13 IMAC XXIV, January 30, 2006 Results of Analysis: C L

14. Page 14 IMAC XXIV, January 30, 2006 Conclusion: No strong v-dependence at fixed S  0.2

15. Page 15 IMAC XXIV, January 30, 2006 C L : Comparison with Previous Data Conclusion: SHS parametrization looks good

16. Page 16 IMAC XXIV, January 30, 2006 Results of Analysis: C D Conclusion: RKA looks better than SHS Caveat: C D inherently less precise than C L

17. Page 17 IMAC XXIV, January 30, 2006 Implications for Trajectory

18. Page 18 IMAC XXIV, January 30, 2006 Summary and Outlook l Even with the limited precision of the present data, there is a clear preference for the lift coefficients of Hubbard than those of Adair l We learned enough from our initial measurements to know how to do better. l New experiments are planned to provide improved determinations of lift and drag coefficients