1. 1 Baseball & Physics: An Intersection of Passions Alan M. Nathan Department of Physics University of Illinois a-nathan@illinois.edu

2. 2 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...” “ Our goal is not to reform the game but to understand it.” “ The physics of baseball is not rocket science. It’s much harder ” “The physicist’s model of the game must fit the game.” My friend and mentor, Prof. Bob Adair

3. 3 And check out my web site… webusers.npl.uiuc.edu/~pob/a-nathan

4. 4 1927 Solvay Conference: Greatest physics team ever assembled The Baseball/Physics Connection 1927 Yankees: Greatest baseball team ever assembled MVP’s

5. 5 Topics I Will Cover The ball-bat collision –How a bat works –Wood vs. aluminum –Putting spin on the ball The flight of the baseball –Drag, lift, and all that –New tools –How far did that home run go?

6. 6 “You can observe a lot by watching” UMass/Lowell --Yogi Berra Easton Sports Daily Illini

7. 7 When ash meets cowhide…. forces large, time short – >8000 lbs, <1 ms ball compresses, stops, expands – like a spring: KE  PE  KE – bat recoils lots of energy dissipated (“COR”) – distortion of ball – vibrations in bat to hit home run…. –large batted ball speed 105 mph  ~400 ft, each additional mph ~ 5-6’ –optimum take-off angle (30 0 -35 0 ) –lots of backspin

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: 90 + 70 gives 102 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 What does q depend on? 1.Weight of bat near the impact region (MOI about the handle) –Heavier bat more efficient less recoil to bat  larger q –Heavier bat has smaller v bat (usually) –What is ideal bat weight (or MOI) ? effect of bat weight on q is easy effect of bat weight on v bat is harder BBS = q v pitch + (1+q) v bat

10. 10 The Ideal Bat Weight (or MOI) Batters seem to prefer lower MOI bats, sacrificing control for power corked bats?

11. 11 Is There an Advantage to “Corking” a Bat? Based on best experimental data available: …for home run distance: no …for home run frequency: maybe Sammy Sosa, June 2003

12. 12 What does q depend on? 2. Bounciness of ball –“coefficient of restitution” or COR –COR 2 = rebound ht/initial ht –~0.5 for baseball

13. 13 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

14. 14 What does q depend on? 3.Impact location on bat outside inside sweet spot

15. 15 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

16. 16 Vibrations, COR, and the “Sweet Spot” E vib vfvf e + Strike bat here at ~ node 2 vibrations minimized COR maximized BBS maximized best “feel” Note: COP is irrelevant to feel and performance

17. 17 handle moves only after ~0.6 ms delay collision nearly over by then nothing on knob end matters size, shape boundary conditions hands, grip who is holding it Confirmed experimentally Independence of End Conditions Batter could drop bat just before contact and it would have no effect on ball!!!

18. 18 Measuring collision efficiency –Sport Sciences Lab @ Washington State –Baseball Research Center @ UMass/Lowell Regulating bat performance Independence of end conditions and ref. frame crucial

19. 19 Aluminum has thin shell –Less mass in barrel—lower MOI --higher bat speed, easier to control --but smaller q  --for many bats nearly cancels  »just like corked wood bat –“Hoop modes” trampoline effect “ping” Does Aluminum Outperform Wood? YES!

20. 20 Hoop (cylinder) modes First hoop mode  “ping” and “trampoline effect” Hoop Modes and the “ping” Thanks to Dan Russell for this slide

21. 21 Two springs mutually compress Energy shared between “ball spring” and “bat spring” Sharing depends on relative “stiffnesses” of springs Energy stored in ball mostly dissipated (~80%!) Energy stored 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, … The “Trampoline” Effect: A Simple Physical Picture demo

22. 22 Softball Data and Model Conclusions: COR of Al bat can be significantly higher essential physics is understood Russell, Smith, AMN change k ball change k bat Wood wood alum

23. 23 Trivia Timeout Why is this famous? Last pitch, perfect game in WS Year? 1956 Pitcher? Don Larsen 2B? Billy Martin Batter? Dale Mitchell Hitting for Sal Maglie Bonus deep trivia: Who was the home plate umpire? Babe Pinelli, in his last game

24. 24 Flight of the Baseball Gravity Drag (“air resistance”) Lift (or “Magnus”) mg FdFd FMFM  Courtesy, Popular Mechanics F d =½ C D  Av 2 F M = ½ C L  Av 2 C L = C M R  /v direction leading edge is turning

25. 25 Real vs. “Physics 101” Trajectory: Effect of Drag Reduced distance on fly ball Reduction of pitched ball speed by 8-10 mph Asymmetric trajectory: –Total Distance  1.7 x distance at apex Optimum home run angle ~30 o -35 o

26. 26 Some Effects of Spin 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. mg F drag F Magnus 

27. 27 Oblique Collisions and Spin friction

28. 28

29. 29 Some Familiar Effects 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 View from above friction velocity

30. 30 Another familiar result: Catcher’s View bat hits under ball: popup to opposite field bat hits over ball: grounder to pull field bat tilted downward

31. 31 Undercutting the ball  backspin Ball10 0 downward Bat 10 0 upward D = center-to-center offset trajectories “vertical sweet spot” What’s this all about?

32. 32 Paradoxical Popups

33. 33 What are we learning from the PITCHf/x system? A report from the summit What is PITCHf/x and how does it work? What are we learning from it? Outlook for future webusers.npl.uiuc.edu/~a-nathan/pob/pitchtracker.html sportvision.com/events/pfx.html This section prepared with help from John Walsh, Mike Fast, Josh Kalk, Dan Brooks, and the good folks at Sportvison, mainly Marv White.

34. 34 PITCHf/x is a pitch-tracking system installed in every MLB venue—a joint venture of Sportvision & MLBAM MLB Gameday ESPN K-Zone Fox Trak MLB Gameday Screen

35. 35 How Does PITCHf/x Work? Two video cameras track baseball in 1/60-sec intervals –usually “high home” and “high first” Software to identify and track pitch frame-by- frame in real time  full trajectory  lots of other stuff Image, courtesy of Sportvision

36. 36 What kind of “stuff” can one learn? Pitch speed to ~0.5 mph –at release and at home plate (they are different!) Pitch location to ~0.5 inches –at release and at home plate “movement” to ~2.0 inches –both magnitude and direction Initial velocity direction Type of pitch –more on this later And all of this can be correlated with what the batter does! –a complete digital record exists!

37. 37 And the good news is…. …all these data are freely available online! For info on how to download, establish data base, etc., see … –mvn.com/mlb-stats/2008/01/14/a-pitchfx-primer/ Mike Fast –http://brooksbaseball.net/pfx/ Dan Brooks –http://blog.stealingfirst.com/2008/03/07/how-to-link-pitchfx- to-retrosheet/ Dan Turkenkopf

38. 38 What can we potentially learn from these data? Things of interest to physicists –Effect of air drag and spin How much does a ball break? Is there “late break”? Can the effects of drag be quantified? How does drag depend on atmospheric conditions? Does drag depend on spin? Is there a “drag crisis”? –The mysteries of the knuckleball

39. 39 Pitched ball loses about 10% of speed between pitcher and batter Average speed is ~95% of release speed Example: Pitch Speed--PITCHf/x vs. the gun PITCHf/x is almost surely more accurate than the gun

40. 40 Example: Pitching at High Altitude: Higher, less movement in Denver vs. Toronto 10% loss of velocity total movement 12” 7.5% 8” PITCHf/x data contain a wealth of information about drag and lift!

41. 41 Compare to sinkerball pitcher Brandon Webb Jon Lester Brandon Webb Plots, courtesy of Dan Brooks Comparing FB upward movement: Lester ~ 11” Webb ~ 3”

42. 42 Josh Kalk, THT, 5/22/08 What makes an effective slider?—C. C. Sabathia 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”).

43. 43 PITCHf/x tackles the knuckleball – John Walsh Classify pitches using vertical and horizontal break plus speed Compare “normal” pitcher (C.C. Sabathia) with k-baller (Tim Wakefield) “Randomness” of k-ball break is evident in PITCHf/x data Example analysis: What happens when knuckleball does not “knuckle”? Split k-balls into 3 groups – small, medium, large break http://www.hardballtimes.com/main/article/butterflies-are-not-bullets/ fastball curve slider change knuckler Amount of Break Pitches put in play OPS against Small47.979 Medium71.873 Large79.684 http://www.hardballtimes.com (small sample size, though)

44. 44 The aerodynamics of batted balls: How far did that home run travel? Ball leaves bat Ball hits horizontal distance D from home plate, H above ground How far would it have gone if no obstruction?

45. 45 400 ft/30 ft Range=415-455 Use time-of-flight to resolve 4 s 5 s 7 s Calculations Bob Brown, CWRU Greg Rybarczk, www.hittrackeronline.com

46. 46 Example: Bond’s 756 th home run tracking data from PITCHf/x video determines first 20 ft of trajectory landing point and time of flight determined precisely from HD video together, these are sufficient to determine the full trajectory, with very little uncertainty

47. 47 An example: Barry Bond’s 756 th Home Run Results: v 0 =112 mph  =27 0 up  =16 0 to right of dead center  =1186 rpm (backspin) and 189 rpm (sidespin, breaking to center) Total range: 442 ft

48. 48 The famous Mantle Home Run Griffith Stadium, April 17, 1953 Publicized as 565 ft

49. 49 How far did it really go? Ball hit sign 460 ft (horizontal) and 60 ft (vertical) from home plate It was supposedly retrieved behind a house with a 22-ft roof Wind was blowing out at ~20 mph Is there a plausible set of conditions consistent with all these facts? sign house 2000 rpm 4000 rpm Range: 520-540 ft Two Plausible Trajectories Answer: Maybe!

50. 50 Sci-Fly: The Wave of the Future …another toy for me to play with! 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 –originally developed for golf (Trackman) –now adapted for baseball

51. 51 Safeco Field Experiment, October 2008 The goal: study fly ball trajectories and check the validity of SciFly Project fly balls with pitching machine Track with Sci-Fly and measure spin Measure initial velocity & spin with high- speed video Measure time of flight with camcorder Measure total distance with tape measure Many thanks to the M’s management and to Rawlings for making this happen

52. 52 Typical Sci-Fly Trajectory initial parameters: 81.7 mph, 30.8 0, 2004 rpm backspin TOF=4.62 sec D=317 ft. Data still being analyzed

53. 53 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?

54. 54 Work in Progress Collision experiments & calculations to elucidate trampoline effect New studies of aerodynamics Experiments on high-speed oblique collisions –To quantify spin on batted ball A book, with Aussi Rod Cross

55. 55 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@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