Baseball & Physics: An Intersection of Passions

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

2. In my younger days…. Is this heaven? No, it’s …. Iowa Dyersville, home of the Field of Dreams

3. But now I just watch and enjoy… 2004 2007 …and there’s been a lot to enjoy lately….

4. A good book to read…. My mentor, Prof. Bob Adair “Our goal is not to reform the game but to understand it.” “The physicist’s model of the game must fit the game.”

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

6. The Physics of Hitting a Home Run • How does a baseball bat work? • The flight of a baseball. • Leaving the no-spin zone. • Putting it all together. • And what’s the deal with steroids?

7. “Hitting is timing; pitching is upsetting timing” “Hitting is fifty percent above the shoulders” Hitting the Baseball: the most difficult feat in sports 1955 Topps cards from my personal collection

8. Hitting and Pitching, Thinking and Guessing Graphic courtesy of Bob Adair and NYT

9. Champaign News-Gazette “You can observe a lot by watching” --Yogi Berra Easton Sports UMass/Lowell

10. 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

11. What Determines BBS? • pitch speed • bat speed • “collision efficiency”: a property of the ball and bat • my only formula 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

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

13. Is There an Advantage to “Corking” a Bat? Sammy Sosa, June 2003 Based on best experimental data available: …for home run distance: no …for home run frequency: maybe

14. What does q depend on? 2. Bounciness of ball • “coefficient of restitution” or COR • COR2 = rebound ht/initial ht • ~0.5 for baseball demo

15. What does q depend on? • Impact location on bat sweet spot inside outside

16. Vibrations and Broken Bats pitcher catcher movie

17. Does Aluminum Outperform Wood? Aluminum has thin shell • Less mass in barrel • --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” YES! demo

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

19. FMagnus  Fdrag mg Aerodynamics of Baseball in Flight • Gravity • Drag (“air resistance”) • “Magnus” force on spinning baseball

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-35o

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. FMagnus  Fdrag 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

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

24. What’s the Deal with Denver? • High altitude, reduced air density (80% of sea level) • Reduced drag: increases distance • Reduced lift: decreases distance • Net effect: • Fly balls travel ~5% farther

25. Leaving the No-Spin Zone

26. 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

27. Another familiar result: bat hits under ball: popup to opposite field bat tilted downward Catcher’s View bat hits over ball: grounder to pull field

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

29. 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 • Aerodynamics • A ball hit faster will travel farther • Backspin increases distance • Which effect wins? • Curveball, by a hair! • But I wouldn’t bet the farm on it!

30. Steroids and Home Run Productonsee Roger Tobin, AJP, Jan. 2008 • 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

31. To have 10% HR’s, there must be a lot of near-HR’s Elite hitters: HR/BBIP = ~10% Thanks to Roger Tobin

32. Change in range distribution when batted ball speed increased by 3%: Baseline 3% change in BBS gives 50% increase in HR rate! 3% speed increase Thanks to Roger Tobin

33. 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!