1 Baseball and Physics: Where Albert Pujols meets Albert Einstein ---Alan Nathan, University of Illinois

2 Baseball and Physics Where Albert Pujols meets Albert Einstein

3 Einstein--“Mr. Berg, you teach me baseball and I’ll teach you the theory of relativity.” Then after some thought…. “No, we must not. You will learn about relativity faster than I learn baseball.” Albert Einstein, Moe Berg, and baseball

4 Topics I Will Cover The ball-bat collision –How a bat works –Wood vs. aluminum The flight of the baseball –Drag, lift, and all that New tools for baseball analysis –PITCHf/x and HITf/x

5 “You can observe a lot by watching” ---Yogi Berra forces large, time short – >8000 lbs, <1 ms ball compresses, stops, expands – like a spring: KE  PE  KE – bat recoils lots of energy dissipated – distortion of ball – vibrations in bat

6 pitch speed bat speed “collision efficiency”: a property of the ball and bat BBS = q v pitch + (1+q) v bat typical numbers: q = q = 1.2 example: gives 101 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 What Determines Batted Ball Speed?

7 Kinematics of Ball-Bat Collision 1. m/M eff = ball mass/effective bat mass  0.25 bat recoil 2. e = elasticity of collision  0.50 energy dissipation For m/M eff <<1 and e  1, q  1 BBS = q vpitch + (1+q) vbat

8 1. Effective Bat Mass M eff  “Swing Weight”: related to MOI about the handle Larger  less recoil to bat  larger q Larger  smaller swing speed Batters seem to prefer lower MOI bats sacrificing power for “quickness” Cross and AMN, Sports Technology 2, 7-15 (2009)

9 2.e = ball-bat coefficient of restitution (bbcor) 1 - e 2 = fraction of CM energy dissipated –~75%! Joint property of ball and bat –Most of energy loss is in ball –But the bat matters Vibrations decrease e Trampoline effect increase e

10 What about that humidor? increasing RH from 30 to 50% --decrease COR by ~4.5% --decreases BBS by ~2.5 mph --decreases fly ball distance by ~14 ft --reduces home run probability by ~25%!

11 Vibrations and the ball-bat collision outside“sweet spot”

12 Studying the Vibrations of a Baseball Bat frequency time f 1 = 179 Hz f 2 = 582 Hz f 3 = 1181 Hz f 4 = 1830 Hz

13 Vibrations, BBCOR, and the “Sweet Spot” E vib vfvf e + at ~ node 2 vibrations minimized COR maximized BBS maximized best “feel”

14 strike bat on barrel—look at movement in handle handle moves only after ~0.6 ms delay collision nearly over by then nothing on knob end matters size, shape, hands, grip boundary conditions confirmed experimentally Independence of End Conditions Batter could drop bat just before contact and it would have no effect on ball!!!

15 BBCOR and the Trampoline Effect (hollow bats) The Ping! Lowest Hoop (or wineglass) Mode

16 BBCOR increases with …  elasticity of ball (~0.5)  elasticity of bat (~1)  relative stiffness ~ k ball /k bat BBCOR(Al)/BBCOR(wood)  unregulated, can be very large  Little League  1.15  NCAA  1.0 (!) The “Trampoline” Effect: A Simple Physical Picture

17 Energy Flow woodaluminum

18 Forces on a Spinning Baseball in Flight Drag slows ball down Magnus + mg deflects ball from straight line mg FDFD FMFM C M ~ 1 C D ~

19 Real vs. “Physics 101” Trajectory: Effect of Drag and Magnus

20 PITCHf/x and HITf/x Two video fps –“high home” and “high first” –tracks every pitch in every MLB ballpark all data publicly available on web! –tracks initial trajectory of batted ball Used for analysis, TV broadcasts, MLB Gameday, etc. Image, courtesy of Sportvision Marv White, Physics, UIUC, 1969 Marv White, Physics, UIUC, 1969

21 Baseball Analysis: Using PITCHf/x to discover how pitchers do what they do “Hitting is timing. Pitching is upsetting timing.”

22 Ex 1: Mariano Rivera: Why is he so good? ? Three Reasons: Location, Location, Location Images, courtesy of BaseballAnalytics.org

23 Ex 2: “Late Break”: Truth or Myth Mariano Rivera’s Cut Fastball View from above: actual trajectory linear extrapolation

24 Ex 3: A Pitcher’s Repertoire Catcher’s View 4-seam fastball 2-seam fastball changeup curveball slider/cutter

25 Ex 4 Jon Lester vs. Brandon Webb Brandon Webb is a “sinkerball” pitcher: Almost no rise on his fastball 15 inches

26 Ex 5 The Knuckleball Tim Wakefield is a knuckleball pitcher: Chaotic Movement

27 Learning About Batted Balls Experiments to measure spin of batted ball HITf/x: extension of PITCHf/x –Initial part of trajectory TrackMan –Full trajectory

28 A New Experiment Project balls with spin using 2- wheel machine (~100 mph) Scatter from cylinder bolted to wall Record at 1000 fps Analyze to get final spin, speed, angle Ben Thoren (UIUC physics UG) Jonas Cantakos (UIUC kinesiology GS) normal force friction

29 Some Results Final spin is large and nearly independent of initial spin (for given  ) 

30 More Results Data suggest ball grips surface, creating overspin Sliding:  <V x /r Rolling:  =V x /r Gripping:  >V x /r final surface speed Initial surface speed

31 undercutting/overcutting  backspin/topspin Magnus force is up/down Topspin makes line drives nose-dive Backspin keeps fly ball in air longer Tricky popups to infield friction normal force v ???

32 Paradoxical Popups AJP 76, (2008)

33 RHH LHH CF LFRF  Extract sidespin vs.  from trajectory CF RF break to right break to leftLF Balls break toward foul pole Break increases with angle Ball hit to CF slices LHH/RHH asymmetry Tilt in bat RF RHH LHH LFRF friction normal force

34 What Constitutes a Well-Hit Ball? w/o home runs home runs HR BABIP V 0 >90

35 Combining HITf/x with Hittracker HITf/x  v 0, ,  Hittracker (Greg Rybarczyk, hittrackeronline.com) –Landing point –Flight time Together these constrain the full trajectory

36 HITf/x+hittracker Analysis: The “carry” of a fly ball Motivation: does the ball carry especially well in the new Yankee Stadium? “carry” ≡ (actual distance)/(vacuum distance) for same initial conditions (379,20,5.2)

37 HITf/x + hittracker Analysis: 4354 HR from 2009 Denver ClevelandYankee Stadium

38 Work in Progress Collision experiments & calculations to elucidate trampoline effect New studies of drag and Magnus Experiments on high-speed oblique collisions to quantify spin on batted ball

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 –go.illinois.edu/physicsofbaseball I am living proof that knowing the physics doesn’t help you play the game Red Sox Fantasy Camp, Feb. 1-7, 2009