1. 1 Corked Bats and Rising Fastballs: Using Physics to Debunk Some Myths of Baseball September 23, 2006 Thanks to J. J. Crisco & R. M. Greenwald Medicine & Science in Sports & Exercise 34(10): 1675-1684; Oct 2002 Alan M. Nathan Department of Physics University of Illinois

2. 2 Corked Bats and Rising Fastballs: Using Physics to Debunk Some Myths of Baseball October 27, 2004: the day the curse was broken

3. 3 References “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 References “The book is written for the inquiring layperson…” “…many controversial claims about the game are addressed and…resolved by this book.”

5. 5 References http://www.npl.uiuc.edu/~a-nathan/pob Is this heaven? No, it’s …. Iowa Dyersville, home of the Field of Dreams

6. 6 Outline How does a baseball bat work? The flight of a baseball. Leaving the no-spin zone. Putting it all together.

7. 7 Issues I Will Address What matters more: pitch speed or bat speed? Is the ball “juiced”? What/where is the “sweet spot”? Is corking the bat effective? Does aluminum outperform wood? Does a fastball rise? What’s the deal with Denver? Can a curveball be hit farther than a fastball?

8. 8 “You can observe a lot by watching” Champaign News-Gazette CE Composites --Yogi Berra Easton Sports

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10. 10 When Ash Meets Cowhide A violent collision! –forces large (>8000 lbs!); time short (<1/1000 sec!) –ball compresses, stops, expands like a spring: kinetic energy  potential energy inefficient: lots of energy dissipated bat recoils, vibrates –bat recoils, vibrates GOAL: maximize batted ball speed ( BBS) –BBS  105 mph, 30 o  d  400 ft –each additional mph  ~5 ft

11. 11 What Determines BBS? pitch speed, bat speed, “collision efficiency” my only formula BBS = e v pitch + (1+e) v bat typical numbers: e = 0.2 1+e = 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

12. 12 What does e depend on? 1. Weight and weight distribution of bat –Heavier bat more efficient larger e; less recoil to bat –Heavier bat has smaller v bat (usually) –What is ideal bat weight? effect of bat weight on e is easy effect of bat weight on v bat harder BBS = e v pitch + (1+e) v bat

13. 13 Experiments to Determine v bat Use high-speed video Measure dependence of v bat on … --bat weight W --“swing weight” or MOI Conclusion: MOI matters more than W Observation: Batters prefer lighter bats—31-34 oz --control vs. power

14. 14 Is There an Advantage to “Corking” a Bat? Based on best experimental data available: …for home run distance: no …for home run frequency: maybe

15. 15 What does e depend on? 2. Bounciness of ball –“coefficient of restitution” or COR –COR 2 = rebound ht/initial ht –~0.5 for baseball demo

16. 16 Is the Baseball “Juiced”? Is COR larger than it used to be? MLB rules allow ~ 10% range of COR  35 ft 1975 and 2004 equal to few % No evidence for juiced ball Measurements with high-speed cannon COR=rebound speed/initial speed 1975 vs. 2004 MLB specs

17. 17 demos What does e depend on? 3.Impact location on bat: the “sweet spot” Minimize recoil to bat—at Center of Gravity Maximize bat speed—at tip Minimize vibrations which… sting! sometimes break the bat reduce COR  lower BBS

18. 18 The “Sweet Spot Zone” computer simulation …which agrees with experiments nodes CG

19. 19 Vibrations and Broken Bats movie pitcher catcher

20. 20 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” Does Aluminum Outperform Wood? demo

21. 21 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

22. 22 Does Aluminum Outperform Wood? YES!

23. 23 Additional Remarks on e can be measured in the lab – regulate non-wood bats (NCAA, ASA, …) “end conditions” don’t matter –Not even the batter’s hands!

24. 24 Forces on a Baseball in Flight Gravity Drag (“air resistance”) Lift (or “Magnus”) mg F drag F Lift  demo

25. 25 Effect of Drag and Lift on Trajectories drag effect is huge lift effect is smaller but significant mg FdFd F L (Magnus) 

26. 26 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

27. 27 Some Effects of Lift mg FdFd F L (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.

28. 28 Does a Fastball Rise? Can a ball thrown horizontally rise? Is there a net upward acceleration? Can Magnus force exceed gravity? mg FdFd F L (Magnus)  For this to happen… backspin must exceed 4000 rpm >25 revolutions not physically possible

29. 29 What’s the Deal with Denver? High altitude, reduced air pressure –80% of sea level –Reduced drag –Reduced lift Net effect: –Fly balls travel ~5% farther

30. 30 How Do We Know What We Know? Measuring the Magnus Force Two-wheel pitching machine Baseball with reflecting dot High-Speed Motion Capture System

31. 31 Joe Hopkins ~15 ft Motion Capture Geometry

32. 32 Motion Capture System: 10 cameras 700 frames/sec 1/2000 shutter very fancy software www.motionanalysis.com Pitching Machine: project horizontally 50-110 mph 1500-4500 rpm movie

33. 33 Typical Data Note: topspin  a y > g

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”

36. 36 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?

37. 37 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

38. 38 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?

39. 39 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 –www.npl.uiuc.edu/~a-nathan/pob –a-nathan@uiuc.edu Thanks for your attention and go Red Sox!