1. 1 How a Physicist Analyzes the Game of Baseball Alan M. Nathan a-nathan@uiuc.edu webusers.npl.uiuc.edu/~a-nathan/pob Department of Physics University of Illinois

2. 2 1927 Solvay Conference: Greatest physics team ever assembled Baseball and Physics 1927 Yankees: Greatest baseball team ever assembled MVP’s

3. 3 A great book to read…. “Our goal is not to reform the game but to understand it. “The physicist’s model of the game must fit the game.”

4. 4 Some Topics I Will Cover How does a baseball bat work? The flight of a baseball Leaving the no-spin zone Putting it all together

5. 5 “You can observe a lot by watching” Champaign News-Gazette CE Composites --Yogi Berra Easton Sports

6. 6 Description of Ball-Bat Collision forces large, time short – >8000 lbs, <1 ms ball compresses, stops, expands – KE  PE  KE – bat recoils lots of energy dissipated (“COR”) – distortion of ball – vibrations in bat to hit home run…. –large batted ball speed 100 mph  ~400 ft, each additional mph ~ 5-6’ –optimum take-off angle (30 0 -35 0 ) –lots of backspin

7. 7 BBS = q v ball + (1+q) v bat Conclusion: v bat matters much more than v ball q  “Collision Efficiency” Joint property of ball & bat  independent of reference frame  ~independent of “end conditions”—more later  weakly dependent on v rel Superball-wall: q  1 Ball-Bat near “sweet spot”: q  0.2  BBS  0.2 v ball + 1.2 v bat Kinematics of Ball-Bat Collision v ball v bat BBS

8. 8 Kinematics of Ball-Bat Collision e: “coefficient of restitution”  0.50 (energy dissipation—mainly in ball, some in bat) r = m ball /M bat,eff : bat recoil factor =  0.25 (momentum and angular momentum conservation) ---heavier is better but… q=0.20 BBS = q v ball + (1+q) v bat v ball v bat BBS

9. 9 wood aluminum Batting cage study show how bat speed depends on MOI for college/semipro baseball players

10. 10 Collision Efficiency q Can Be Measured Air cannon fires ball onto stationary bat q = v out /v in Used by NCAA, ASA, … to regulate/limit performance of bats Sports Sciences Lab @ WSU

11. 11 Regulating Performance of Non- Wood Bats (NCAA) Specify maximum q (“BESR”=q+1/2) –relative to wood –implies bats swung alike will perform alike Specify minimum MOI to limit bat speed –smaller than wood Together, these determine a maximum BBS –gap between wood and aluminum  5% BBS = q v ball + (1+q) v bat

12. 12 aluminum-5 rule BESR MOI

13. 13 Accounting for COR: Dynamic Model for Ball-Bat Collision AMN, Am. J. Phys, 68, 979 (2000) Collision excites bending vibrations in bat –hurts! breaks bats –dissipates energy lower COR, BBS Dynamic model of collision –Treat bat as nonuniform beam –Treat ball as damped spring

14. 14 Modal Analysis 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 Vibrations, COR, and the “Sweet Spot” E vib vfvf e + Strike bat here best performance & feel @ ~ node 2

16. 16 strike bat in barrel—look at response in handle handle moves only after ~0.6 ms delay collision nearly over by then nothing on knob end matters size, shape boundary conditions hands! confirmed experimentally Independence of End Conditions

17. 17 q independent of end conditions: experimental proof Conclusion: mass added in knob has no effect on collision efficiency (q)

18. 18 Vibrations and Broken Bats movie pitcher catcher

19. 19 Aluminum has thin shell –Less mass in barrel --lower MOI, higher bat speed, easier to control --but less effective at transferring energy  --for many bats  cancels »just like corked wood bat –“Hoop modes” trampoline effect “ping” Why Is Aluminum Better Than Wood? demo

20. 20 Two springs mutually compress each other KE  PE  KE PE shared between “ball spring” and “bat spring” PE in ball mostly dissipated (~80%!) PE 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

21. 21 Aerodynamics of a 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 direction leading edge is turning

22. 22 Measuring drag and Magnus forces by high-speed tracking Magnus force is much easier to measure than drag force drag/wt  0.8 Magnus/wt=0.58

23. 23 Typical values of drag and lift “Drag crisis?”

24. 24 Effect of Drag and Lift on Trajectories drag effect is huge lift effect is smaller but significant mg FdFd FMFM 

25. 25 Some Effects of Drag Reduced distance on fly ball Reduction of pitched ball speed by ~10% Asymmetric trajectory: –Total Distance  1.7 x distance at apex Optimum home run angle ~30 o -35 o

26. 26 Some Effects of Magnus 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 FdFd FMFM 

27. 27 The PITCHf/x Tracking System A New Tool to Study Baseball Flight

28. 28 How Does PITCHf/x Work? Two video cameras track baseball in 1/60-sec intervals –usually “high home” and “high first” –third CF camera used establises ht. of strike zone for each batter Pattern-recognition software to identify “blobs” Camera calibration to convert pixels to (x,y,z) 9- parameter fit to trajectory –constant acceleration for x(t),y(t),z(t) Use fit to calculate lots of stuff –The full trajectory –The “break” –Drag and Magnus forces

29. 29 Pitch Classification Jon Lester, Aug 3, 2007 @ Seattle I: Nearly overhand fastball II: Cut Fastball III: ¾ Fastball IV: Curveball LHP Catcher’s View

30. 30 What’s the Deal with the Gyroball? Courtesy, The New York TImes Courtesy, Ryutaro Himeno Daisuke Matsuzaka: Does he or doesn’t he?

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32. 32 Barry Bond’s 756 th Home Run PITCHf/x data tracked hit ball over first 20 ft Precision measurement of endpoint and time Inferred: v 0 =112 mph;  =27 o up;  =16 o to right of dead center;  =1186 rpm (backspin) and 189 rpm (sidespin, breaking to center)

33. 33 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/lift on seam orientation Is the spin constant?

34. 34 Oblique Collisions: Leaving the No-Spin Zone Oblique  friction  spin Familiar Results: 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 demo

35. 35 Undercutting the ball  backspin Ball10 0 downward Bat 10 0 upward D = center-to-center offset trajectories “vertical sweet spot” What’s going on here??

36. 36

37. 37 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

38. 38 Bat-Ball Collision Dynamics – A fastball will be hit faster – A curveball will be hit with more backspin Putting it all Together: Can curveball be hit farther than fastball?

39. 39 Net effect: backspin larger for curveball Fastball: spin must reverse curveball can be hit with more backspin: WHY? Fastball with backspin Curveball: spin doesn’t reverse Curveball with topspin

40. 40 Bat-Ball Collision Dynamics – A fastball will be hit faster – A curveball will be hit with more backspin Aerodynamics – A ball hit faster will travel farther – Backspin increases distance Which effect wins? Curveball, by a hair! Can Curveball Travel Farther than Fastball?

41. 41 Work in Progress Collision experiments & calculations to elucidate trampoline effect New studies of aerodynamics using Doppler radar Experiments on high-speed oblique collisions A book, with Aussi Rod Cross

42. 42 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@uiuc.edu Thanks for your attention and go Red Sox!