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Physics and Baseball: Understanding the Game with Science

Delve into the intriguing intersection of physics and baseball with Alan M. Nathan's book. Explore topics like ball-bat collision dynamics, bat technologies, and the correlation between physics principles and the game. Discover insights on aluminum versus wood bats, aerodynamics, and more. Gain knowledge on controversies like corked bats, juiced balls, and the impact of steroid use. Uncover the science behind bat speed, ball trajectories, and the sweet spot. This engaging read offers a fascinating perspective on our favorite sport through a physicist's lens.

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Physics and Baseball: Understanding the Game with Science

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  1. Physics and Baseball:Having Your Cake and Eating it Too Alan M. Nathan a-nathan@uiuc.edu webusers.npl.uiuc.edu/~a-nathan/pob Department of Physics University of Illinois

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

  3. A great book to read…. “Our goal is not to reform the game but to understand it. “The physicist’s model of the game must fit the game.”

  4. A Physicist’s Approach to Current Issues in Baseball • Should aluminum bats be banned? • Corked bats and juiced balls—do they matter? • What the deal with the gyroball? • Can steroid use increase home run production? • Is the game different in Denver? • and what about that humidor?

  5. Some Experimental Tools • Bat testing facility • High-speed video or motion analysis “You can observe a lot by watching” ---Yogi • swinging the bat • ball-bat collision 1 • ball-bat collision 2 • PITCHf/x tracking system • Trackman radar more on these later See http://webusers.npl.uiuc.edu/~a-nathan/pob/video.html for some nifty videos.

  6. Some Physics Background • Physics of ball-bat collision • Aerodynamics of a baseball • Oblique collisions and spin

  7. Description of Ball-Bat Collision • forces large, time short • >8000 lbs, <1 ms • ball compresses, stops, expands • KEPEKE • bat recoils • lots of energy dissipated (“COR”) • distortion of ball • vibrations in bat • to hit home run…. • large batted ball speed • 100 mph~400 ft, each additional mph ~ 5-6’ • optimum take-off angle (300-350) • lots of backspin

  8. Kinematics of 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…

  9. 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

  10. Accounting for COR: Dynamic Model for Ball-Bat Collision AMN,Am. J. Phys, 68, 979 (2000) • Collision excites bending vibrations in bat • hurts! breaks bats • dissipates energy • lower COR, BBS • Dynamic model of collision • Treat bat as nonuniform beam • Treat ball as damped spring

  11. 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

  12. Vibrations, COR, and the “Sweet Spot” Strike bat here + best performance & feel @ ~ node 2 e vf Evib

  13. 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

  14. Why Is Aluminum Better Than Wood? Aluminum has thin shell • Less mass in barrel • --lower MOI, higher bat speed, easier to control  • --but lower collision efficiency  • --partially canceling effects • “Hoop modes” • trampoline effect  • “ping” (~2000 Hz) demo

  15. 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

  16. 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

  17. 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

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

  19. FM  Fd Fd=½ CDAv2 mg FM= ½ CMARv Courtesy, Popular Mechanics direction leading edge is turning Aerodynamics of a Baseball • Gravity • Drag (“air resistance”) • Lift (or “Magnus”)

  20. “Drag crisis?” Typical values of drag and lift

  21. Effect of Drag and Lift on Trajectories FM  Fd mg • drag effect is huge • lift effect is smaller but significant

  22. Some Effects of Drag • Reduced distance on fly ball • Reduction of pitched ball speed by ~10% • Asymmetric trajectory: • Total Distance  1.7 x distance at apex • Optimum home run angle ~30o-35o

  23. FM  Fd mg Some Effects of Magnus • 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.

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

  25. 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

  26. Example: Drag and Drag Coefficients20k pitches from Anaheim, 2007

  27. Using PITCHf/x to Classify PitchesJon Lester, Aug 3, 2007 @ Seattle spin axis LHP Catcher’s View I: Nearly overhand fastball II: Slider or cut fastball III: ¾ Fastball IV: Curveball break direction = -90o

  28. Courtesy, Ryutaro Himeno Daisuke Matsuzaka: Does he or doesn’t he? What’s the Deal with the Gyroball?

  29. 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; =27o up; =16o to right of dead center; =1186 rpm (backspin) and 189 rpm (sidespin, breaking to center)

  30. 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?

  31. 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

  32. thanks to Fredrik Tuxen, CTO of Trackman

  33. Oblique Collisions:Leaving the No-Spin Zone Oblique  friction  spin still need a good collision model my model: slide, then roll Familiar Results: Balls hit to left/right break toward foul line Topspin gives tricky bounces in infield Backspin keeps fly ball in air longer Tricky popups to infield

  34. Ball100 downward D = center-to-center offset Bat 100 upward What’s going on here?? Undercutting the ball  backspin trajectories “vertical sweet spot”

  35. Another familiar result: bat hits under ball: popup to opposite field bat tilted downward Catcher’s View bat hits over ball: grounder to pull field

  36. 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

  37. 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%!

  38. Steroids and Bat Speed • Batter supplies energy proportional to M • Energy shared between bat and some fraction 2of M • Roughly: 2 ~ 0.01 • So roughly, 10% increase in M gives • ~2.5% increase in vbat • ~2 mph increase in BBS • ~12 additional ft. on long fly ball • ~20% (Adair) -50% (Tobin) more home runs!

  39. 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—does slide-then-roll model work? • A book, with Aussi Rod Cross

  40. 2004 2007 Final Summary • Physics of baseball is a fun application of basic (and not-so-basic) physics • Check out my web site if you want to know more • webusers.npl.uiuc.edu/~a-nathan/pob • a-nathan@uiuc.edu • Thanks for your attention and go Red Sox!

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