Baseball & Physics: An Intersection of Passions

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

2. A good book to read…. My friend and mentor, 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.” “Our goal is not to reform the game but to understand it.” “The physics of baseball is not rocket science. It’s much harder”

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

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

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 much does a ball “carry”?

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

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 (300-350) • lots of backspin

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: 90 + 70 gives 102 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. What does q depend on? • BBS = q vpitch + (1+q) vbat • “Swing Weight”: MOI about the handle • Larger MOI: • less recoil to bat  larger q • smaller swing speed (usually) • What is ideal swing weight? • effect of swing weight on q is easy • effect of swing weight on vbat is harder

10. The Ideal Bat Weight (or MOI) BBS (mph) Batters seem to prefer lower MOI bats, sacrificing power for “quickness”

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. What does q depend on? 2. Bounciness of ball • “coefficient of restitution” or COR • COR= vf/vi • ~0.5 for baseball • 75% of energy dissipated

13. What does q depend on? • Impact location on bat 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. Vibrations, COR, and the “Sweet Spot” Strike bat here at ~ node 2 vibrations minimized COR maximized BBS maximized best “feel” + e vf Evib Note: COP is irrelevant to feel and performance

16. 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!!!

17. Does Aluminum Outperform Wood? Aluminum has thin shell • Less mass in barrel—lower MOI • --higher bat speed and quickness  • --but smaller q  • --for many bats  nearly cancels  • just like corked wood bat • “Hoop modes” • trampoline effect  • “ping” YES!

18. The “Trampoline” Effect: A Simple Physical Picture • 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, … demo

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

20. 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 ~30o

21. FMagnus  Fdrag mg 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.

22. Oblique Collisions and Spin Movie clip

23. normal force v friction

24. friction velocity Some Familiar Effects • Balls hit to left/right break toward foul line • Topspin makes line drives nose-dive • Backspin keeps fly ball in air longer • Tricky popups to infield View from above

25. Another familiar result: Balls hit to CF slice Spin axis From LHH, ball will curve toward LF

26. Ball100 downward D = center-to-center offset Bat 100 upward What’s this all about? Undercutting the ball  backspin trajectories “vertical sweet spot”

27. Paradoxical Popups

28. 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 This section prepared with help from John Walsh, Mike Fast, Josh Kalk, Dan Brooks, and the good folks at Sportvison, mainly Marv White. webusers.npl.uiuc.edu/~a-nathan/pob/pitchtracker.html sportvision.com/events/pfx.html

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

30. 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

31. 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 these data are freely available online!

32. Example: Pitch Speed--PITCHf/x vs. the gun • Pitched ball loses about 10% of speed between pitcher and batter • Average speed <v> is ~95% of release speed vf PITCHf/x is almost surely more accurate than the gun v0

33. 10% 7.5% loss of velocity total movement 12” 8” Example: Pitching at High Altitude:Higher <v>, less movement in Denver vs.Toronto PITCHf/x data contain a wealth of information about drag and lift!

34. Drag Coefficient from Pitchf/x Cd vs. v0 <Cd> vs. v0 in 2 mph bins Example--20k pitches from Anaheim, 2007:

35. Drag Coefficient:no evidence for “drag crisis” Good approximation: Cd = 0.35±0.05 in range 70-100 mph

36. Pitch Classification: LHP Jon Lester, Aug. 3, 2007 4-seam fastball 2-seam fastball >90 mph 80-90 mph <80 mph cutter/slider curveball

37. What makes an effective slider?—C. C. Sabathia 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

38. 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 PITCHf/x tackles the knuckleball – John Walsh http://www.hardballtimes.com fastball knuckler slider change curve

39. New Tools to Study Trajectories of Batted Balls • Hitf/x • Uses Pitchf/x cameras to track initial trajectory • v0,, • Hittracker (www.hittrackeronline.com) • Measure landing point and flight time for home runs • Trackman • Phased array Doppler radar • Measure full trajectory and spin

40. Example of Hitf/x Analysis:Batting Average for Balls in Play w/o home runs home runs only  V0  V0  V0  V0 V0

41. Example of Hitf/x Analysis:Batting Average for Balls in Play BABIP: V0>90 mph w/o home runs home runs Goal: Establish “outcome-independent” hitting metrics

42. Tracking Everything Movie clip

43. Combining HITf/x with Hittracker • Full trajectory is constrained by • initial velocity vector • landing point • flight time

44. Final example:The “carry” of a fly ball

45. The “carry” of a fly ball

46. 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, … • What is the time constant for spin decay?

47. 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

48. 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