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. A Brief Intoduction • My day job… • experimental nuclear/particle physics • high-speed collisions between subatomic particles • Nights and weekends... • physics of baseball • high-speed collision between baseball and bat • Many similarities • And I get to watch/play baseball and call it work • A true intersection of passions

3. 1927 Yankees: Greatest baseball team ever assembled 1927 Solvay Conference: Greatest physics team ever assembled MVP’s The Baseball-Physics Connection

4. A good book to read…. My friend and mentor, Prof. Bob Adair “…the physics of baseball is not the clean, well-defined physics of fundamental matters. Hence conclusions must depend on approximations and estimates. But estimates are part of the physicist’s repertoire...” “Our goal is not to reform the game but to understand it.” “The physics of baseball is not rocket science. It’s much harder” “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. Topics I Will Cover • The ball-bat collision • How a bat works • Wood vs. aluminum • Putting spin on the ball • The flight of the baseball • Drag, lift, and all that • New tools to study ballball trajectories • How far did that home run go?

7. “You can observe a lot by watching” Daily Illini --Yogi Berra Easton Sports UMass/Lowell

8. 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

9. What Determines Batted Ball Speed? • 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

10. What does q depend on? • BBS = q vpitch + (1+q) vbat • Weight of bat in the barrel—Moment of Inertia (MOI) about a point in the handle (“swing weight”) • Heavier bat more efficient • less recoil to bat  larger q • But….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

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

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

13. What does q depend on? • Impact location on bat: the “sweet spot” sweet spot inside outside

14. The Sweet Spot

15. Vibrations and Broken Bats pitcher catcher movie

16. 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

17. More on the trampoline effect… • Trampoline effect increased by stiffer ball or more compliant bat • Also see in tennis, golf, …

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

19. Independence of End Conditions • hit bat at barrel—measure movement at handle • handle moves only after ~0.6 ms delay • collision nearly over by then • nothing on knob end matters • size, shape • boundary conditions • hands, grip • who is holding it • Confirmed experimentally Batter could drop bat just before contact and it would have no effect on ball!!!

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

21. 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

22. 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.

23. 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

24. What can we learn from PITCHf/x?PITCHf/x is a pitch-tracking system installed in every MLB venue—a joint venture of Sportvision & MLBAM ESPN K-Zone MLB Gameday MLB Gameday Screen Fox Trak

25. How Does PITCHf/x Work? • Two video cameras track baseball in 1/60-sec intervals • usually “high home” and “high first” • Software to identify and track pitch frame-by- frame in real time  full trajectory  lots of other stuff Image, courtesy of Sportvision

26. The PITCHf/x pitch-tracking system: LHP Jon Lester, Aug. 3, 2007 4-seam fastball 2-seam fastball >90 mph 80-90 mph <80 mph cutter/slider curveball

27. Jon Lester vs. sinkerball pitcher Brandon Webb Brandon Webb • Comparing FB upward movement: • Lester ~ 11” • Webb ~ 3” Jon Lester Plots, courtesy of Dan Brooks

28. What makes an effective slider?—C. C. Sabathia Josh Kalk, THT, 5/22/08 This slider is very effective since it looks like a fastball for over half the trajectory, then seems to drop at the last minute (“late break”).

29. Classify pitches using vertical and horizontal break plus speed Compare “normal” pitcher (C.C. Sabathia) with k-baller (Tim Wakefield) “Randomness” of k-ball break is evident in PITCHf/x data Example analysis: What happens when knuckleball does not “knuckle”? Split k-balls into 3 groups – small, medium, large break PITCHf/x tackles the knuckleball – John Walsh http://www.hardballtimes.com fastball knuckler slider change curve (small sample size, though)

30. 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—a pitcher’s nightmare! • Fly balls travel ~5% farther • Pitches don’t break as much

31. 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

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

33. Paradoxical Popups

34. The aerodynamics of batted balls:How far did that home run travel? • Ball leaves bat • Ball hits horizontal distance D from home plate, H above ground • How far would it have gone if no obstruction? • There is no unique answer

35. Calculations 400 ft/30 ft Range=415-455 Use time-of-flight to resolve Bob Brown, CWRU Greg Rybarczk, www.hittrackeronline.com 4 s 5 s 7 s

36. The famous Mantle Home RunGriffith Stadium, April 17, 1953Publicized as 565 ft

37. Two Plausible Trajectories 2000 rpm Range: 520-540 ft 4000 rpm sign house How far did it really go? • Ball hit sign 460 ft (horizontal) and 60 ft (vertical) from home plate • It was supposedly retrieved behind a house with a 22-ft roof • Wind was blowing out at ~20 mph • Is there a plausible set of conditions consistent with all these facts? Answer: Maybe!

38. 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?

39. Work in Progress • Collision experiments & calculations to elucidate trampoline effect • New studies of aerodynamics • Experiments on high-speed oblique collisions • To quantify spin on batted ball • A book, with Aussi Rod Cross

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@illinois.edu • I am living proof that knowing the physics doesn’t help you play the game better! @ Red Sox Fantasy Camp, Feb. 1-7, 2009

41. Example: Bond’s 756th home run • tracking data from PITCHf/x video determines first 20 ft of trajectory • landing point and time of flight determined precisely from HD video • together, these are sufficient to determine the full trajectory, with very little uncertainty

42. An example:Barry Bond’s 756th Home Run Results: • v0=112 mph • =270 up • =160to right of dead center • =1186 rpm (backspin) and 189 rpm (sidespin, breaking to center) • Total range: 442 ft