Corked Bats and Rising Fastballs:

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

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

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

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

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

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

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, 30o d  400 ft • each additional mph  ~5 ft

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

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

13. Experiments to Determine vbat • Use high-speed video • Measure dependence of vbat 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. 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. What does e depend on? 2. Bounciness of ball • “coefficient of restitution” or COR • COR2 = rebound ht/initial ht • ~0.5 for baseball demo

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

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

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

19. Vibrations and Broken Bats pitcher catcher movie

20. Does Aluminum Outperform Wood? 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” demo

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

22. Does Aluminum Outperform Wood? YES!

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. FLift  Fdrag mg Forces on a Baseball in Flight • Gravity • Drag (“air resistance”) • Lift (or “Magnus”) demo

25. Effect of Drag and Lift on Trajectories FL(Magnus)  Fd mg • drag effect is huge • lift effect is smaller but significant

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 ~30o-35o

27. FL(Magnus)  Fd mg Some Effects of Lift • 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. FL(Magnus)  Fd mg Does a Fastball Rise? • Can a ball thrown horizontally rise? • Is there a net upward acceleration? • Can Magnus force exceed gravity? • For this to happen… • backspin must exceed 4000 rpm • >25 revolutions • not physically possible

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. 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

31. Ball100 downward D = center-to-center offset Bat 100 upward Undercutting the ball  backspin trajectories “vertical sweet spot”

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

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

34. Can Curveball Travel Farther than Fastball? • 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!

35. 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!