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Experimental Baseball Physics

Experimental Baseball Physics. Alan M. Nathan a-nathan@uiuc.edu webusers.npl.uiuc.edu/~a-nathan/pob Department of Physics University of Illinois. Courtesy, Trey Crisco. Courtesy, Dan Russell. 1927 Yankees: Greatest baseball team ever assembled. 1927 Solvay Conference :

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Experimental Baseball Physics

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  1. Experimental Baseball Physics Alan M. Nathan a-nathan@uiuc.edu webusers.npl.uiuc.edu/~a-nathan/pob Department of Physics University of Illinois Courtesy, Trey Crisco Courtesy, Dan Russell

  2. 1927 Yankees: Greatest baseball team ever assembled 1927 Solvay Conference: Greatest physics team ever assembled MVP’s The Baseball/Physics Connection

  3. Some Topics I Will Cover • The ball-bat collision • The flight of the baseball

  4. The Ball-Bat Collision vball vbat BBS q=0.20 BBS = q vball + (1+q) vbat z • e:“coefficient of restitution” 0.50 • (energy dissipation—mainly in ball, some in bat) • r  mballz2/I6 :bat recoil factor = 0.25 • (momentum and angular momentum conservation) • ---heavier is better but…

  5. Studies of the Collision Efficiency q • Independent of reference frame • Measure in bat rest frame: q=vf/vi • Use q to predict field performance Sports Sciences Laboratory, Washington State University

  6. Independence of End Conditions • strike bat in barrel—look at response in handle • handle moves only after ~0.6 ms delay • collision nearly over by then • nothing on knob end matters • size, shape • boundary conditions • hands! • confirmed experimentally

  7. Studies of the Collision Efficiency q • Independent of end conditions Vf (mph) Courtesy, Keith Koenig

  8. q: Field Study vs. Laboratory Crisco, Smith, AMN

  9. f1 = 179 Hz f3 = 1181 Hz f2 = 582 Hz f4 = 1830 Hz frequency time Modal Analysis of a Baseball Bat www.kettering.edu/~drussell/bats.html

  10. Vibrations, COR, and the “Sweet Spot” Strike bat here at ~ node 2 vibrations minimized COR maximized BBS maximized best “feel” + e vf Evib Note: COP is irrelevant to feel and performance

  11. Aluminum Bats and the “Trampoline” Effect: A Simple Physical Picture • Two springs mutually compress each other • KE  PE  KE • PE shared between “ball spring” and “bat spring” • …sharing depends on “kball/kbat” • PE in ball mostly dissipated(~80%!) • PE in bat mostly restored • Net effect: less overall energy dissipated • ...and therefore higher ball-bat COR • …more “bounce”—confirmed by experiment • …and higher BBS • Also seen in golf, tennis, … demo

  12. Softball Data and Model Russell, Smith, AMN Wood change kbat change kball • Conclusions: • COR of Al bat can be significantly higher • essential physics is understood

  13. Regulating Performance of Non-Wood Bats:A Science-Based Approach Used by NCAA BBS = q vball + (1+q) vbat • Specify maximum q • approx. same as for wood bats of similar wt. • implies bats swung alike will perform alike • Specify minimum MOI to limit bat speed • smaller than wood • Together, these determine a maximum BBS • gap between wood and aluminum  5% • does that mean aluminum should be banned? • an issue many are struggling with

  14. Batting cage study show how bat speed depends on I for college baseball players • ~ [1/I6]n 0<n<0.5 n  0.3 aluminum wood Crisco, Greenwald, AMN Other studies show bat speed independent of M for fixed I

  15. 102 mph max vf 97 mph BESR limit typical wood MOI limit Example: 34” Bats =q+1/2 All bats below horizontal line and to right of vertical line are allowed

  16. What About Corked Bats?or..What was Sammy thinking? no trampoline effect! • Conclusion: • No increase in BBS • increase in swing speed • decrease in collision efficiency • ~ [1/I6]n 0<n<0.5

  17. What About Juiced Baseballs? Conclusion: No evidence for juiced ball

  18. Putting spin on the ball: Low speeds no spin topspin backspin Cross & AMN • Conclusions: • slide-then-roll model approximately works • curveball is hit with more backspin than fastball

  19. High-Speed Version:Work in Progress

  20. FM  Fd Fd=½ CDAv2 mg FM= ½ CLAv2 CL = CMR/v Courtesy, Popular Mechanics direction leading edge is turning Flight of the Baseball • Gravity • Drag (“air resistance”) • Lift (or “Magnus”)

  21. Motion Analysis System ATEC 2-wheel pitching machine Baseball with reflecting dot Measuring Magnus Force Using High-Speed Motion Analysis

  22. ~15 ft Joe Hopkins Motion Analysis Geometry

  23. 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

  24. Typical Data and Fit

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

  26. The PITCHf/x Tracking SystemA Quantitative Tool to Study Pitched Baseball Trajectories

  27. How Does PITCHf/x Work? • Two video cameras track baseball in 1/60-sec intervals • usually “high home” and “high first” • third CF camera used establishes ht. of strike zone • Pattern-recognition software to identify “blobs” • Camera calibration to convert pixels to (x,y,z) • 9-parameter fit to trajectory • constant acceleration for x(t),y(t),z(t) • Use fit to calculate lots of stuff • The full trajectory • The “break” • Drag and Magnus forces

  28. Example: Bonds’ 756

  29. drag/W=1@~90 mph Example: Drag and Drag Coefficients20k pitches from Anaheim, 2007

  30. Using PITCHf/x to Classify PitchesJon Lester, Aug 3, 2007 @ Seattle spin axis LHP Catcher’s View I: 4-seam fastball II: Slider (?) III: 2-seam fastball IV: Curveball break direction = -90o

  31. 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?

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

  33. From PITCHf/x to HITf/xBarry Bond’s 756th Home Run • PITCHf/x data tracked hit ball over first 20 ft • Precision measurement of endpoint and time-of-flight • Inferred: v0=112 mph; =270 up; =160to right of dead center; =1186 rpm (backspin) and 189 rpm (sidespin, breaking to center)

  34. Baseball Aerodynamics:Things I would like to know better • Better data on drag • “drag crisis”? • spin-dependent drag? • drag for v>100 mph • Dependence of drag & Magnus on seam orientation, surface roughness, … • Is the spin constant?

  35. Trackman: The Wave of the Futuresee www.trackmangolf.com • Doppler radar to measure radial velocity • 3-detector array to measure phase • two angles • Sidebands gives spin magnitude • Result: • in principle, full trajectory can be reconstructed, including spin and spin axis • already in use for golf, currently being adapted for baseball

  36. Monopulse Principle (Phase) Trackman Radar

  37. thanks to Fredrik Tuxen, CTO of Trackman

  38. Steroids and Home Run Productonsee Roger Tobin, AJP, Jan. 2008 • Steroids increases muscle mass • Increased muscle mass increases swing speed • Increased swing speed increase BBS • Increased BBS means longer fly balls • Longer fly balls means more home runs

  39. To have 10% HR’s, there must be a lot of near-HR’s Elite hitters: HR/BBIP = ~10% Thanks to Roger Tobin

  40. Change in range distribution when batted ball speed increased by 3%: Baseline 3% change in BBS gives 50% increase in HR rate! 3% speed increase Thanks to Roger Tobin

  41. Home Run Distances, 2007 www.hittrackeronline.com Delta = distance beyond fence (ft) ~4% per foot Tobin’s Conclusion: increase of BBS by few mph can increase HR rate by 30-50%!

  42. Work in Progress • Collision experiments & calculations to elucidate trampoline effect • New studies of aerodynamics using Trackman and PITCHf/x • Experiments on high-speed oblique collisions • A book, with Aussi Rod Cross Thanks for the invitation and your attention

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