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

2. 2 Baseball and Physics Where Albert Pujols meets Albert Einstein

3. 3 Albert Einstein and Baseball

4. 4 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.” Albert Einstein, Moe Berg, and baseball

5. 5 A good book to read…. “…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.” Prof. Bob Adair relativity

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

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

10. 10 1. Effective Bat Mass M eff  “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. 11 Is There an Advantage to “Corking” a Bat? Based on best experimental data available: …for “harder” hit: no …for frequency of good contact: probably Sammy Sosa, June 2003

12. 12 2.e = ball-bat coefficient of restitution (bbcor) 1 - e 2 = 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. 13 Vibrations and the ball-bat collision outside“sweet spot”

14. 14 Studying the Vibrations of a Baseball Bat www.kettering.edu/~drussell/bats.html frequency time f 1 = 179 Hz f 2 = 582 Hz f 3 = 1181 Hz f 4 = 1830 Hz

15. 15 20 y z y Dynamics of the Bat-Ball Collision AMN, AJP 68, 979-990 (2000) 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 F=kx n COR

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

17. 17 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 Independence of End Conditions Batter could drop bat just before contact and it would have no effect on ball!!!

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

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

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

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

22. 22 What do we know about C D ? (mainly from pitch tracking) Depends on …. v 0 (Reynold’s Number) surface “roughness”? seam orientation? spin? Dedicated TrackMan experiment@Safeco, Oct. 2008 StL, Sept. 2009 PITCHf/x TrackMan Good approximation: C d = 0.35±0.05 in range 60-100 mph No steep “drag crisis” More dedicated experiments in progress

23. 23 What do we know about C L ? (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: C L  S  R  /v in range 0.05-0.30

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

25. 25 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. Image, courtesy of Sportvision Marv White, Physics, UIUC, 1969 Marv White, Physics, UIUC, 1969

26. 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. 27 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 So what good is a physicist in all this?

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

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

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

31. 31 Josh Kalk, THT, 5/22/08 Ex 2a: What makes an effective slider 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. 32 Ex 3: A Pitcher’s Repertoire Catcher’s View 4-seam fastball 2-seam fastball changeup curveball slider/cutter

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

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

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

37. 37 What Constitutes a Well-Hit Ball? w/o home runs home runs HR BABIP V 0 >90

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

39. 39 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 friction normal force v ???

40. 40 Paradoxical Popups AJP 76, 723-729 (2008)

41. 41 Combining HITf/x with Hittracker HITf/x  v 0, ,  Hittracker (Greg Rybarczyk, hittrackeronline.com) –Landing point –Flight time Together these constrain the full trajectory

42. 42 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 (379,20,5.2)

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

44. 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. 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. 46 HITf/x + hittracker Analysis: 4354 HR from 2009

47. 47 C D : One Final Thought Correlations suggestive of variations in baseball PFXTM PFX-TM

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

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

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