Baseball and Physics: Where Albert Pujols meets Albert Einstein ---Alan Nathan

1. Baseball and Physics:Where Albert Pujols meets Albert Einstein---Alan Nathan

2. Baseball and PhysicsWhere Albert Pujols meets Albert Einstein

3. Albert Einstein and Baseball

4. Albert Einstein, Moe Berg, and baseball Einstein--“Mr. Berg, you teach me baseball and I’ll teach you the theory of relativity.” Then after some thought…. “No, we must not. You will learn about relativity faster than I learn baseball.”

5. A good book to read…. relativity Prof. Bob Adair “…the physics of baseball is not the clean, well-defined physics of fundamental matters. Hence conclusions must depend on approximations and estimates. But estimates are part of the physicist’s repertoire...” “The physicist’s model of the game must fit the game.” “Baseball is not rocket science. It’s much harder.”

6. Topics I Will Cover • The ball-bat collision • How a bat works • Wood vs. aluminum • The flight of the baseball • Drag, lift, and all that • New tools for baseball analysis

7. “You can observe a lot by watching”---Yogi Berra • forces large, time short • >8000 lbs, <1 ms • ball compresses, stops, expands • like a spring: KEPEKE • bat recoils • lots of energy dissipated • distortion of ball • vibrations in bat

8. What Determines Batted Ball Speed? • pitch speed • bat speed • “collision efficiency”: a property of the ball and bat BBS = q vpitch + (1+q) vbat • typical numbers: q = 0.2 1+q = 1.2 example: 85 + 70 gives 101 mph(~400’) • vbat matters much more than vpitch! • Each mph of bat speed worth ~6 ft • Each mph of pitch speed worth ~1 ft

9. Kinematics of Ball-Bat Collision BBS = q vpitch + (1+q) vbat 1. m/Meff = ball mass/effective bat mass  0.25 bat recoil 2. e = elasticity of collision  0.50 energy dissipation For m/Meff<<1 and e1, q1

10. 1. Effective Bat Mass Meff “Swing Weight”: related to MOI about the handle Larger  less recoil to bat  larger q Larger  smaller swing speed Batters seem to prefer lower MOI bats sacrificing power for “quickness” Cross and AMN, Sports Technology 2, 7-15 (2009)

11. Is There an Advantage to “Corking” a Bat? Sammy Sosa, June 2003 Based on best experimental data available: …for “harder” hit: no …for frequency of good contact: probably

12. e = ball-bat coefficient of restitution(bbcor) • 1 - e2 = fraction of CM energy dissipated • ~75%! • Joint property of ball and bat • Most of energy loss is in ball • But the bat matters • Vibrations decrease e • Trampoline effect increase e

13. Vibrations and the ball-bat collision outside “sweet spot”

14. f1 = 179 Hz f3 = 1181 Hz f2 = 582 Hz f4 = 1830 Hz frequency time Studying the Vibrations of a Baseball Bat www.kettering.edu/~drussell/bats.html

15. Dynamics of the Bat-Ball Collision AMN, AJP 68, 979-990 (2000) y F=kxn y z COR 20 • Solve eigenvalue problem for normal modes • Model ball-bat force F • Expand y in normal modes • Solve coupled equations of motion for ball, bat • Energy budget: • KE of ball (batted ball speed) • recoil of bat • dissipation in ball • vibrations in bat

16. Vibrations, BBCOR, and the “Sweet Spot” + at ~ node 2 vibrations minimized COR maximized BBS maximized best “feel” e vf Evib

17. Independence of End Conditions • strike bat on barrel—look at movement in handle • handle moves only after ~0.6 ms delay • collision nearly over by then • nothing on knob end matters • size, shape, hands, grip • boundary conditions • confirmed experimentally Batter could drop bat just before contact and it would have no effect on ball!!!

18. BBCOR and the Trampoline Effect(hollow bats) The Ping! Lowest Hoop (or wineglass) Mode

19. The “Trampoline” Effect: A Simple Physical Picture Change kball alum wood • BBCOR increases with … • elasticity of ball (~0.5) • elasticity of bat (~1) • relative stiffness ~ kball/kbat • BBCOR(Al)/BBCOR(wood) • unregulated, can be very large • Little League <1.15 • NCAA < 1.0 (!) change kbat

20. Forces on a Spinning Baseball in Flight FM • Drag slows ball down • Magnus + mg deflects ball from straight line FD mg

21. Real vs. “Physics 101” Trajectory: Effect of Drag and Magnus

22. StL, Sept. 2009 PITCHf/x TrackMan Dedicated TrackMan experiment@Safeco, Oct. 2008 What do we know about CD?(mainly from pitch tracking) Depends on …. • v0(Reynold’s Number) • surface “roughness”? • seam orientation? • spin? • Good approximation: • Cd = 0.35±0.05 in range 60-100 mph • No steep “drag crisis” • More dedicated experiments in progress

23. What do we know about CL?(mainly from high-speed motion analysis) Depends on …. • spin parameter S  R/v • v @ fixed S? • best evidence is “no”, in region of 50-100 mph • seam orientation? Good approximation: CL S  R/v in range 0.05-0.30

24. New tools to study flight of baseball • PITCHf/x and HITf/x • Video tracking • TrackMan • Doppler radar tracking

25. Marv White, Physics, UIUC, 1969 Marv White, Physics, UIUC, 1969 Image, courtesy of Sportvision PITCHf/x and HITf/x • Two video cameras @60 fps • “high home” and “high first” • tracks every pitch in every MLB ballpark • all data publicly available on web! • tracks initial trajectory of batted ball • Used for analysis, TV broadcasts, MLB Gameday, etc.

26. TrackMan • Doppler radar to measure radial velocity • dr/dt  r(t) • 3-detector array to measure phase • two angles (t), (t) • Together these give full 3D trajectory • Spin modulates to give sidebands • spin frequency 

27. So what good is a physicist in all this? • Minimal parametrization of the trajectory • Constant acceleration works very well for pitched ball • Constant “jerk” works for most batted balls • Determining Magnus acceleration • “spin movement” important for studying pitching • Keeping everyone honest • Laws of physics cannot be violated • Recognizing errors • Measurements have uncertainties! • Dealing with imperfect data

28. Baseball Analysis:Using PITCHf/x to discover how pitchers do what they do “Hitting is timing. Pitching is upsetting timing.”

29. Home Runs home plate Ex 1: Mariano Rivera: Why is he so good?? Three Reasons: Location, Location, Location

30. View from above: actual trajectory -------- linear extrapolation - - - - Ex 2: “Late Break”: Truth or MythMariano Rivera’s Cut Fastball

31. Ex 2a: What makes an effective slider Josh Kalk, THT, 5/22/08 This slider is very effective since it looks like a fastball for over half the trajectory, then seems to drop at the last minute (“late break”). side view

32. 4-seam fastball slider/cutter 2-seam fastball changeup curveball Ex 3: A Pitcher’s Repertoire Catcher’s View

33. Ex 4 Jon Lester vs. Brandon Webb 15 inches Brandon Webb is a “sinkerball” pitcher: Almost no rise on his fastball

34. Ex 5 The Knuckleball Tim Wakefield is a knuckleball pitcher: Chaotic Movement

35. Learning About Batted Balls • HITf/x • Initial part of trajectory • All April 2009 data available • TrackMan • Full trajectory • Limited data from StL, Sept. 2009

36. TrackMan Data from StL, 2009 R vs. v0 R vs. 0 USEFUL BENCHMARK 400 ft @ 103 mph ~5 ft per mph peaks @ 25o-35o

37. BABIP HR What Constitutes a Well-Hit Ball? w/o home runs home runs V0>90

38. normal force friction Putting Spin on Batted Balls • in front or behind  sidespin • sideways Magnus force • fly balls break toward foul pole

39. v normal force ??? friction • undercutting/overcutting  backspin/topspin Magnus force is up/down Topspin makes line drives nose-dive Backspin keeps fly ball in air longer Tricky popups to infield

40. Paradoxical PopupsAJP 76, 723-729 (2008)

41. Combining HITf/x with Hittracker • HITf/x  v0,, • Hittracker (Greg Rybarczyk, hittrackeronline.com) • Landing point • Flight time • Together these constrain the full trajectory

42. (379,20,5.2) HITf/x+hittracker Analysis: The “carry” of a fly ball • Motivation: does the ball carry especially well in the new Yankee Stadium? • “carry” ≡ (actual distance)/(vacuum distance) • for same initial conditions

43. HITf/x + hittracker Analysis:4354 HR from 2009 Denver Cleveland Yankee Stadium

44. Work in Progress • Collision experiments & calculations to elucidate trampoline effect • New studies of drag and Magnus • Experiments on high-speed oblique collisions • To quantify spin on batted ball

45. 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 • go.illinois.edu/physicsofbaseball • a-nathan@illinois.edu • I am living proof that knowing the physics doesn’t help you play the game better! @ Red Sox Fantasy Camp, Feb. 1-7, 2009

46. HITf/x + hittracker Analysis:4354 HR from 2009

47. CD: One Final Thought PFX TM PFX-TM Correlations suggestive of variations in baseball

48. break to right break to left Extract sidespin vs.  from trajectory CF LF RF RF LF RF LHH RHH  • Balls break toward foul pole • Break increases with angle • Ball hit to CF slices • LHH/RHH asymmetry • Tilt in bat

49. Is the Baseball “Juiced”? Is COR larger than it used to be? • Measurements with high-speed cannon • COR=rebound speed/initial speed • 1975 vs. 2004 • 1975 and 2004 equal to few % • No evidence for juiced ball

50. 10% 7.5% loss of velocity total movement 12” 8” Example: Pitching at High Altitude Denver Toronto Toronto Denver PITCHf/x data contain a wealth of information about drag and lift!