1. 1 Physics and Baseball: Having Your Cake and Eating it Too 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 A Physicist’s Approach to Current Issues in Baseball Should aluminum bats be banned? Corked bats and juiced balls—do they matter? What the deal with the gyroball? Can steroid use increase home run production? Is the game different in Denver? –and what about that humidor?

5. 5 Some Experimental Tools Bat testing facility High-speed video or motion analysis “You can observe a lot by watching” ---Yogi –swinging the bat –ball-bat collision 1 –ball-bat collision 2 PITCHf/x tracking system Trackman radar more on these later See http://webusers.npl.uiuc.edu/~a-nathan/pob/video.html for some nifty videos.http://webusers.npl.uiuc.edu/~a-nathan/pob/video.html

6. 6 Some Physics Background Physics of ball-bat collision Aerodynamics of a baseball Oblique collisions and spin

7. 7 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

8. 8 Kinematics of Ball-Bat Collision e: “coefficient of restitution”  0.50 (energy dissipation—mainly in ball, some in bat) r  m ball z 2 /I 6 : 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 z

9. 9 wood aluminum Batting cage study show how bat speed depends on I for college baseball players  ~ [1/I 6 ] n 0<n<0.5 n  0.3

10. 10 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

11. 11 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

12. 12 Vibrations, COR, and the “Sweet Spot” E vib vfvf e + Strike bat here best performance & feel @ ~ node 2

13. 13 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

14. 14 Aluminum has thin shell –Less mass in barrel --lower MOI, higher bat speed, easier to control --but lower collision efficiency  --partially canceling effects –“Hoop modes” trampoline effect “ping” (~2000 Hz) Why Is Aluminum Better Than Wood? demo

15. 15 Two springs mutually compress each other KE  PE  KE PE shared between “ball spring” and “bat spring” …sharing depends on “k ball /k bat ” 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

16. 16 Regulating Performance of Non-Wood Bats: A Science-Based Approach Used by NCAA Specify maximum q –approx. same as for wood bats of similar wt. –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% –does that mean aluminum should be banned? an issue many are struggling with BBS = q v ball + (1+q) v bat

17. 17 What About Corked Bats? or..What was Sammy thinking? Conclusion: No increase in BBS  increase in swing speed  decrease in collision efficiency  ~ [1/I 6 ] n 0<n<0.5 no trampoline effect!

18. 18 What About Juiced Baseballs? Conclusion: No evidence for juiced ball

19. 19 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 M  AR  v direction leading edge is turning

20. 20 Typical values of drag and lift “Drag crisis?”

21. 21 Effect of Drag and Lift on Trajectories drag effect is huge lift effect is smaller but significant mg FdFd FMFM 

22. 22 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

23. 23 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 

24. 24 The PITCHf/x Tracking System A Quantitative Tool to Study Pitched Baseball Trajectories

25. 25 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 establishes ht. of strike zone 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

26. 26 Example: Drag and Drag Coefficients 20k pitches from Anaheim, 2007

27. 27 Using PITCHf/x to Classify Pitches Jon Lester, Aug 3, 2007 @ Seattle I: Nearly overhand fastball II: Slider or cut fastball III: ¾ Fastball IV: Curveball LHP Catcher’s View spin axis break direction =  -90 o

28. 28 What’s the Deal with the Gyroball? Courtesy, Ryutaro Himeno Daisuke Matsuzaka: Does he or doesn’t he?

29. 29 From PITCHf/x to HITf/x Barry Bond’s 756 th Home Run PITCHf/x data tracked hit ball over first 20 ft Precision measurement of endpoint and time-of-flight 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)

30. 30 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?

31. 31 Trackman: The Wave of the Future see www.trackmangolf.com 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 –already in use for golf, currently being adapted for baseball

32. 32 thanks to Fredrik Tuxen, CTO of Trackman

33. 33 Oblique Collisions: Leaving the No-Spin Zone Oblique  friction  spin still need a good collision model my model: slide, then roll 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

34. 34 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??

35. 35 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

36. 36 Steroids increases muscle mass Increased muscle mass increases swing speed Increased swing speed increase BBS Increased BBS means longer fly balls Longer fly balls means more home runs Steroids and Home Run Producton see Roger Tobin, AJP, Jan. 2008

37. Home Run Distances, 2007 www.hittrackeronline.com Delta = distance beyond fence (ft) ~4% per foot Tobin’s Conclusion: increase of BBS by few mph can increase HR rate by 30-50%!

38. 38 Steroids and Bat Speed Batter supplies energy proportional to M Energy shared between bat and some fraction  2 of M Roughly:  2 ~ 0.01 So roughly, 10% increase in M gives –~2.5% increase in v bat –~2 mph increase in BBS –~12 additional ft. on long fly ball –~20% (Adair) -50% (Tobin) more home runs!

39. 39 Work in Progress Collision experiments & calculations to elucidate trampoline effect New studies of aerodynamics using Trackman and PITCHf/x Experiments on high-speed oblique collisions—does slide-then-roll model work? A book, with Aussi Rod Cross

40. 40 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! 20042007