Forces on a Spinning Baseball in Flight

1. FL Fd=½ CDAv2 Fd FL= ½ CLAv2 mg direction leading edge is turning Courtesy, Popular Mechanics Forces on a Spinning Baseball in Flight

2. Achenbach, J. Fl. Mech. 65, 113 (1974) What does CD depend on? • Reynold’s Number • Re= Dv/ • Re~1x105 @ 45 mph • surface “roughness” • seam orientation? • spin? Question: Does a baseball experience a “drag crisis”?

3. What does CL depend on? • S  r/v • CL~(0.5-1.5)S • FL= (0.25-0.75)r3v • Seam orientation? • Reynold’s number @ fixed S?

4. “Straw Man” Drag and Liftmore later on where these come from

5. Effect of Drag and Lift on Trajectories • drag effect is huge • lift effect is smaller but significant

6. Some Effects of Drag • Reduced distance on fly ball • Reduction of pitched ball speed by ~10% • 2-seam vs. 4-seam • Asymmetric trajectory: • Total Distance  1.7 x distance at apex • Optimum home run angle ~300-350

7. Some Effects of Lift • Backspin makes ball rise • “hop” of fastball • undercut balls: increased distance, reduced optimum angle of home run • Topspin makes ball drop • “12-6” curveball • topped balls nose-dive • Breaking pitches due to spin • Cutters, sliders, etc.

8. Additional Effects of Lift Balls hit to left/right curve toward foul pole

9. Additional Effects of Lift: • Tricky trajectories of popups • --popup behind home plate with lots of backspin

10. 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

11. Data on CD Mehta,Briggs: wind tunnel Atlanta: video tracking Alaways: motion capture SHS: Hubbard parametrization RKA: Adair parametrizatoin • Ref: • J. App. Biomechanics 17, 63-76 (2001) • Adair, The Physics of Baseball, 3rd Ed.

12. Denver vs. NYC:Is there a sudden drag crisis? • Fd=½ CDAv2 • Re=Av/ • Denver = 0.8NYC • ReDenver=0.8ReNYC

13. Data on CL 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, 1152-1162 (2003); 73, 184-189 (2005)

14. Adair model at 100 mph Courtesy, Popular Mechanics Adair Model of Lift • Lift due to “differential drag” • CL=2CDS{1+0.5(v/CD)dCD/dv} • CL S for v<50 mph

15. Comparision of SHS and RKA Parametrizations of Drag and Lift Discrepency is huge at 70-100 mph

16. Implications for Trajectory

17. Motion Capture System ATEC 2-wheel pitching machine Baseball with reflecting dot New Experiment #1: Tracking Trajectory(Illinois)

18. ~15 ft Joe Hopkins Motion Capture Geometry

19. Motion Capture System: • 10 Eagle-4 cameras • 700 frames/sec • 1/2000 shutter • EVaRT 4.0 software • www.motionanalysis.com • Pitching Machine: • project horizontally • 50-110 mph • 1500-4500 rpm

20. Experiment: Some Details • 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 • Pitching machine: • Speeds: 50-110 mph • Spins: 1500-4800 rpm • Mainly topspin, some backspin • All trials “two-seam” • Initial angle ~0o • Distances: 40-100 feet • Calibrations and cross-checks • Simple ball toss gets a=g to 2%

21. Typical Data

22. Data Analysis • Nonlinear least-squares fit • y(t) = yCM(t) + Acos(t+) • z(t) = zcm(t)  Asin(t+) • cm trajectory calculated numerically • RK4 • nine free parameters • ycm(0), zcm(0), vy,cm(0), vz,cm(0) • A, ,  • CL, CD

23. Typical Data and Fit

24. Results of Analysis: CL

25. Conclusion: No strong dependence on Re at fixed S  0.2

26. Results for Lift Coefficient CL FL= 1/2ACLv2 S=r/v 100 mph, 2000 rpm S=0.17 Conclusions: --data qualitatively consistent (~20%) --RKA model inconsistent with data

27. Results for Drag Coefficient CD Conclusion: Major disagreements for v= 70-100 mph

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

29. Sportvision Data batter’s view 180o Pure backspin

30. Sportvision Data batter’s view 225o “cutter”: up and in to RHH

31. Sportvision Data batter’s view 135o “cutter”: up and away to RHH

32. Sportvision Data game pitches warmup

33. Sportvision Data

34. How Far Did That Home Run Travel? • Ball leaves bat • Hits stands D from home plate, H above ground • How far would it have gone if no obstruction?

35. 400 ft/30 ft Range=415-455 Time can resolve See www.hittrackeronline.com 4 s 5 s 7 s

36. Synthesis of Results

37. Synthesis of Results Uncertainty in drag  50 ft!

38. Summary • We have much empirical knowledge of lift and drag • …and some promising new tools for future research • 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?