1 Baseball & Physics: An Intersection of Passions Alan M. Nathan Department of Physics University of Illinois

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

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

4 A good book to read…. “…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.” My friend and mentor, Prof. Bob Adair

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” UMass/Lowell --Yogi Berra Easton Sports Daily Illini

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 ( ) –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 v pitch + (1+q) v bat typical numbers: q = q = 1.2 example: 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

10 What does q depend on? 1.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 v bat (usually) –What is ideal bat weight? effect of bat weight on q is easy effect of bat weight on v bat is harder BBS = q v pitch + (1+q) v bat

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

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

13 Is the Baseball “Juiced”? Is COR larger than it used to be? 1975 and 2004 equal to few % No evidence for juiced ball Measurements with high-speed cannon COR=rebound speed/initial speed 1975 vs. 2004

14 What does q depend on? outside inside sweet spot 3.Impact location on bat: the “sweet spot”

15 The Sweet Spot

16 Vibrations and Broken Bats movie pitcher catcher

17 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” Does Aluminum Outperform Wood? demo YES!

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

19 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!

20 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 Independence of End Conditions Batter could drop bat just before contact and it would have no effect on ball!!!

21 Aerodynamics of Baseball in Flight Gravity Drag (“air resistance”) “Magnus” force on spinning baseball mg F drag F Magnus 

22 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 ~30 o -35 o

23 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. mg F drag F Magnus 

24 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 mg F drag F Magnus 

25 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 MLB Gameday ESPN K-Zone Fox Trak MLB Gameday Screen

26 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

27 >90 mph mph <80 mph 4-seam fastball 2-seam fastball cutter/slider curveball The PITCHf/x pitch-tracking system: LHP Jon Lester, Aug. 3, 2007

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

29 Josh Kalk, THT, 5/22/08 What makes an effective slider?—C. C. Sabathia 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”).

30 PITCHf/x tackles the knuckleball – John Walsh 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 fastball curve slider change knuckler Amount of Break Pitches put in play OPS against Small Medium Large (small sample size, though)

31 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

32 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

33 Undercutting the ball  backspin Ball10 0 downward Bat 10 0 upward D = center-to-center offset trajectories “vertical sweet spot” What’s this all about?

34 Paradoxical Popups

35 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

ft/30 ft Range= Use time-of-flight to resolve 4 s 5 s 7 s Calculations Bob Brown, CWRU Greg Rybarczk,

37 The famous Mantle Home Run Griffith Stadium, April 17, 1953 Publicized as 565 ft

38 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? sign house 2000 rpm 4000 rpm Range: ft Two Plausible Trajectories Answer: Maybe!

39 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?

40 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

41 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 I am living proof that knowing the physics doesn’t help you play the game Red Sox Fantasy Camp, Feb. 1-7, 2009

42 Example: Bond’s 756 th 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

43 An example: Barry Bond’s 756 th Home Run Results: v 0 =112 mph  =27 0 up  =16 0 to right of dead center  =1186 rpm (backspin) and 189 rpm (sidespin, breaking to center) Total range: 442 ft