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1927 Solvay Conference: Greatest physics team ever assembled

1927 Yankees: Greatest baseball team ever assembled. 1927 Solvay Conference: Greatest physics team ever assembled. MVP’s. Baseball and Physics. As smart as he was, Albert Einstein could not figure out how to handle those tricky bounces at third base. Philosophical Notes:.

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1927 Solvay Conference: Greatest physics team ever assembled

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  1. 1927 Yankees: Greatest baseball team ever assembled 1927 Solvay Conference: Greatest physicsteam ever assembled MVP’s Baseball and Physics

  2. As smart as he was, Albert Einstein could not figure out how to handle those tricky bounces at third base.

  3. Philosophical Notes: “…the physics of baseball is not the clean, well-defined physics of fundamental matters but the ill-defined physics of the complex world in which we live, where elements are not ideally simple and the physicist must make best judgments on matters that are not simply calculable…Hence conclusions about the physics of baseball must depend on approximations and estimates….But estimates are part of the physicist’s repertoire…a competent physicist should be able to estimate anything ...” ---Bob Adair in “The Physics of Baseball”, May, 1995 issue of Physics Today “The physicist’s model of the game must fit the game.” “Our aim is not to reform baseball but to understand it.”

  4. #521, September 28, 1960 Hitting the Baseball “...the most difficult thing to do in sports” --Ted Williams: 1918-2002 BA: .344 SA: .634 OBP: .483 HR: 521

  5. Introduction: Description of Ball-Bat Collision • forces large (>8000 lbs!) • time short (<1/1000 sec!) • ball compresses, stops, expands • kinetic energy  potential energy • lots of energy lost • bat is flexible • hands don’t matter • to hit a home run... • large hit ball speed • optimum take-off angle • backspin

  6. “Lab” Frame Bat Rest Frame vrel vball vbat vf eAvrel The Ball-Bat Collision: Kinematics vf = eA vball + (1+eA) vbat • eA  “Collision Efficiency” • property of ball & bat • weakly dependent on vrel • Superball-wall: eA 1 • Ball-Bat near “sweet spot”: eA 0.2 •  vf0.2 vball + 1.2 vbat Conclusion: vbat matters much more than vball

  7. Kinematics: recoil of bat (r) • Dynamics: energy dissipation (e) = + . . . CM • Small r is best • r  0.25 typical…depends on…. • mass of bat • mass distribution of bat • impact location b What Does eA Depend On? Heavier bat is better but….

  8. What is Ideal Bat Weight? Actually, Scaling with Iknob better Note: Batters seem to prefer lighter bats!

  9. vbat I-0.3 vbat I-0.5 • vBAT(6”) = 1.2 mph/(1000 oz-in2)(vf=1.5  0.3 mph)

  10. Energy Dissipation: the ball-bat COR (e) • Coefficient Of Restitution • in CM frame: Ef/Ei = e2 • ball on hard floor:e2 = hf/hi  0.25 • e  0.5 (note: r=0.25, e=0.5  eA =0.2) • ~3/4 CM energy dissipated! • depends (weakly) on impact speed • the bat matters too! • vibrations • “trampoline” effect

  11. Aside:Effect of “Juiced” Ball • MLB:e = 0.546  0.032 @ 58 mph on massive rigid surface 10% increase in COR  ~30-35 ft increase in distance

  12. Accounting for Energy Dissipation: Dynamic Model for Ball-Bat Colllision • Collision excites bending vibrations in bat • Ouch!! Thud!! Sometimes broken bat • Energy lost  lower e, vf • Find lowest mode by tapping • Reduced considerably if • Impact is at a node • Collision time (~0.6 ms) > TN see AMN, Am. J. Phys, 68, 979 (2000)

  13. y 20 • Step 1: Solve eigenvalue problem for free vibrations • Step 2: Nonlinear lossy spring for F • Step 3: Expand in normal modes and solve y z Dynamic Model

  14. f1 = 177 Hz f3 = 1179 Hz f2 = 583 Hz f4 = 1821 Hz Normal Modesof the Bat Louisville Slugger R161 (33”, 31 oz) Can easily be measured: Modal Analysis

  15. Measurements via Modal Analysis Louisville Slugger R161 (33”, 31 oz) FFT frequencybarrel node ExptCalcExptCalc 17917726.526.6 58258327.828.2 1181117929.029.2 1830182130.029.9 Conclusion: free vibrations of bat can be well characterized

  16. Theory vs. Experiment: Louisville Slugger R161 33-inch/31-oz. wood bat only lowest mode excited lowest 4 modes excited Conclusion:essential physics understood

  17. T= 0-1 ms T= 1-10 ms Time evolution of the bat •  0.6 ms  hands don’t matter

  18. Effect of Bat on COR: Vibrations COR maximum near 2nd node

  19. CM Putting Everything Together... vf = eA vball + (1+eA) vbat • “sweet spot” depends on • collision efficiency • recoil factor • COR • how bat is swung

  20. Conclusion: ideal ball-bat collision can be simulated

  21. Wood versus Aluminum • Kinematics • Length, weight, MOI “decoupled” • shell thickness, added weight • fatter barrel, thinner handle • weight distribution more uniform • CM closer to handle • less mass at contact point  • easier to swing Dynamics Stiffer for bending Less vibrational energy  More compressible COR larger 

  22. The “Trampoline” Effect • Compressional energy shared between ball and bat • PEbat/PEball = kball/kbat << 1 • PEball mostly dissipated (75%) • Wood Bat • hard to compress • little effect on COR: “BPF”  1 • Aluminum Bat • compressible through “shell” modes • kball/kbat ~ 0.10 (more or less) • PEbatmostly restored (more on this later) • COR larger: “BPF”  1.1 (more or less)

  23. The Trampoline Effect: A Closer Look Bending Modes vs. Shell Modes • k  R4: large in barrel •  little energy stored • f (170 Hz, etc) > 1/ •  energy goes into • vibrations • k  (t/R)3: small in barrel •  more energy stored • f (2-3 kHz) < 1/  •  energy mostly restored

  24. Wood versus Aluminum: Dynamics of “Trampoline” Effect “bell” modes: “ping” of bat • Want k small to maximize stored energy • Want >>1 to minimize retained energy • Conclusion: there is an optimum 

  25. Where Does the Energy Go?

  26. “Corking” a Wood Bat (illegal!) Drill ~1” diameter hole along axis to depth of ~10” • Smaller mass • larger recoil factor (bad) • higher bat speed (good) • Is there a trampoline effect?

  27. Baseball Research Center, UML, Sherwood & amn, Aug. 2001 Not CorkedDATACorked COR:0.445  0.0050.444  0.005 • Conclusions: • no tramopline effect! • corked bat is WORSE • even with higher vbat calculation

  28. Aerodynamics of a Baseball Forces on Moving Baseball • No Spin • Boundary layer separation • DRAG! • FD=½ CDAv2 • With Spin • Ball deflects wake ==>”lift” • FM ~ RdFD/dv • Force in direction front of ball is turning Drawing courtesty of Peter Brancazio

  29. approxlinear: The Flight of the Ball:Real Baseball vs. Physics 101 Baseball

  30. Summary of Aerodynamics • 108 mph  ~400 ft • each mph  ~5 ft • optimum angle ~350 • 2000 rpm backspin • Increases range ~27 ft • Decreases optimum angle ~30 • these number are only estimates!

  31. Oblique Collisions:The Role of Friction • Friction halts vT •  spin, “lift” • Results • Balls hit to left/right break toward foul line • Backspin keeps fly ball in air longer • Topspin gives tricky bounces in infield • Pop fouls behind the plate curve back toward field

  32. vT| vN| vN vT Model for Oblique Collisions: • vN treated as before vNf = eA(vball+vbat)N + vbat,N • Angular momentum conserved about contact point (!) • Friction reduces vT, increases  • Rolls when vT = R • Horizontal: vTf (5/7)vT • Vertical: a bit more complicated • Not the way a superball works!

  33. down the line power alley Oblique Collisions: Horizontal Plane Initial takeoff angle

  34. Ball100 downward D = center-to-center offset Bat 100 upward Oblique Collisions: Vertical Plane • optimum: • D  0.75” •  3000 rpm   330

  35. Ball100 downward D = center-to-center offset Bat 100 upward Typical Trajectories

  36. Some Practical/Interesting Questions • Does more friction help? • Can a curveball be hit further than a fastball?

  37. Summary and Conclusions • Some aspects of baseball are amenable to physics analysis • Kinematic and dynamics of ball-bat collision • Trajectory of a ball with drag and lift • Can understanding these things improve our ability to play the game? • Almost surely NOT • Can understanding these things enhance our own enjoyment of the game • For me, a resounding YES • I hope for you also

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