Physics and Baseball: A Report to Red Sox Nation Alan Nathan, University of Illinois

A good book to read…. Skip 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...” “The physicist’s model of the game must fit the game.” “Baseball is not rocket science. It’s much harder.” Skip

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

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

“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 Hold ball and bat Ball compresses to half its radius (nearly an inch!) Takes a lot of force to do that Well hit ball has large BBS If you want to optimize your chances of getting a hit, you want to maximize the speed of the hit ball. whether swing for fences or line drive through infield

What Determines Batted Ball Speed? pitch speed bat speed “collision efficiency”: a property of the ball and bat BBS = q vpitch + (1+q) vbat typical numbers: q = 0.2 1+q = 1.2 example: 85 + 70 gives 101 mph (~400’) vbat matters much more than vpitch! Each mph of bat speed worth ~6 ft Each mph of pitch speed worth ~1 ft Superball on massive wall: e~1.

Kinematics of Ball-Bat Collision BBS = q vpitch + (1+q) vbat 1. m/Meff = ball mass/effective bat mass  0.25 bat recoil 2. e = elasticity of collision  0.50 energy dissipation For m/Meff <<1 and e1, q1 Superball on massive wall: e~1.

1. Effective Bat Mass Meff  “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” Can transfer more energy to ball with heavier than lighter object—or, less recoil to bat. Ideal bat wt: Depends critically on how bat speed depends on bat weight. Not really a physics issue but a biomechanics issue. Power vs. control Cross and AMN, Sports Technology 2, 7-15 (2009)

Is There an Advantage to “Corking” a Bat? Sammy Sosa, June 2003 Gain in bat speed offset by reduction in collision efficiency Based on best experimental data available: …for “harder” hit: no …for frequency of good contact: probably

e = ball-bat coefficient of restitution (bbcor) 1 - e2 = 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 Bounce some balls: Golf ball Steel ball Baseball Happy ball Sad ball

Vibrations and the ball-bat collision Demo with… Tapping bat to listen for node outside “sweet spot”

Studying the Vibrations of a Baseball Bat www.kettering.edu/~drussell/bats.html f1 = 179 Hz f2 = 582 Hz f3 = 1181 Hz f4 = 1830 Hz time frequency Note: nodes stack up at barrel end-->”sweet spot zone”

COR Dynamics of the Bat-Ball Collision y z AMN, AJP 68, 979-990 (2000) F=kxn 20 Solve eigenvalue problem for normal modes Model ball-bat force F Expand y in normal modes Solve coupled equations of motion for ball, bat Energy budget: KE of ball (batted ball speed) recoil of bat dissipation in ball vibrations in bat Two “free” parameters…Young’s and shear modulus COR

Vibrations, BBCOR, and the “Sweet Spot” at ~ node 2 vibrations minimized COR maximized BBS maximized best “feel” + e vf COR vs impact location E-vib vs impact location Vf vs impact location Response in handle vs impact location Sweet spot (feel): close to node 2 (hands insensitive to higher modes; hands are already at node 1) Evib

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

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

The “Trampoline” Effect: A Simple Physical Picture BBCOR increases with … elasticity of ball (~0.5) elasticity of bat (~1) relative stiffness ~ kball/kbat BBCOR(Al)/BBCOR(wood) unregulated, can be very large Little League <1.15 NCAA < 1.0 (!) wood alum Change kball Ask question: Which give more “power”: tighter strings or looser strings on tennis racket? Then ask (if they get it wrong): can a person bounce higher from a hardwood floor or from a trampoline? change kbat

Forces on a Spinning Baseball in Flight FM Drag slows ball down Magnus + mg deflects ball from straight line FD mg Won’t discuss CM here except to say that data on golf balls suitably scaled for a baseball indicate that time constant for spin decay is large, in the 20’s of seconds or more, so that it is safe to ignore, at least until we get better data on it.

Real vs. “Physics 101” Trajectory: Effect of Drag and Magnus Drag reduces distance by a lot. Make trajectory asymmetric. Reduces optimum angle Magnus gives lift, keeps ball in air longer. Reduces optimum angle even further.

What do we know about CD? (mainly from pitch tracking) Depends on …. v0 (Reynold’s Number) surface “roughness”? seam orientation? spin? Dedicated TrackMan experiment@Safeco, Oct. 2008 StL, Sept. 2009 PITCHf/x TrackMan Skip Good approximation: Cd = 0.35±0.05 in range 60-100 mph No steep “drag crisis” More dedicated experiments in progress

What do we know about CL? (mainly from high-speed motion analysis) Depends on …. spin parameter S  R/v v @ fixed S? best evidence is “no”, in region of 50-100 mph seam orientation? Skip Good approximation: CL S  R/v in range 0.05-0.30

New tools to study flight of baseball PITCHf/x and HITf/x Video tracking TrackMan Doppler radar tracking

PITCHf/x and HITf/x Two video cameras @60 fps Marv White, Physics, UIUC, 1969 Marv White, Physics, UIUC, 1969 Two video cameras @60 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

TrackMan Skip Doppler radar to measure radial velocity dr/dt  r(t) 3-detector array to measure phase two angles (t), (t) Together these give full 3D trajectory Spin modulates to give sidebands spin frequency  Skip

So what good is a physicist in all this? Minimal parametrization of the trajectory Constant acceleration works very well for pitched ball Constant “jerk” works for most batted balls Keeping everyone honest Laws of physics cannot be violated Recognizing and dealing with imperfect data Measurements have uncertainties! Skip

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

Location, Location, Location Ex 1: Mariano Rivera: Why is he so good?? home plate Home Runs Three Reasons: Location, Location, Location

Ex 2: “Late Break”: Truth or Myth Mariano Rivera’s Cut Fastball View from above: actual trajectory -------- linear extrapolation - - - - Both pitches heading for ~same location. One seems to break at the last minute, the other doesn’t.

Ex 2a: What makes an effective slider 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”). side view

Ex 3: A Pitcher’s Repertoire 4-seam fastball slider/cutter 2-seam fastball changeup curveball Remove spin axis arrows. Try to find ball with spin axis showing. Catcher’s View

Ex 4 Jon Lester vs. Brandon Webb 15 inches Remove spin axis arrows. Try to find ball with spin axis showing. Brandon Webb is a “sinkerball” pitcher: Almost no rise on his fastball

Tim Wakefield is a knuckleball pitcher: Ex 5 The Knuckleball Remove spin axis arrows. Try to find ball with spin axis showing. Tim Wakefield is a knuckleball pitcher: Chaotic Movement

Ex 5 Ubaldo Jimenez Pitching at High Altitude San Diego Denver vf/v0 vf/v0 "Every time that I come here to San Diego, it's always good. Everything moves different. The breaking ball is really nasty, and my fastball moves a lot. So I love it here." Remove spin axis arrows. Try to find ball with spin axis showing. Denver Denver Denver Denver

Learning About Batted Balls HITf/x Initial part of trajectory All April 2009 data available TrackMan Full trajectory Limited data from StL, Sept. 2009

TrackMan Data from StL, 2009 R vs. v0 R vs. 0 USEFUL BENCHMARK 400 ft @ 103 mph ~5 ft per mph peaks @ 25o-35o

What Constitutes a Well-Hit Ball? w/o home runs HR BABIP home runs V0>90

Putting Spin on Batted Balls in front or behind  sidespin sideways Magnus force fly balls break toward foul pole friction normal force

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 ???

Paradoxical Popups AJP 76, 723-729 (2008)

Combining HITf/x with Hittracker HITf/x  v0,, Hittracker (Greg Rybarczyk, hittrackeronline.com) Landing point Flight time Together these constrain the full trajectory

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

HITf/x + hittracker Analysis: 4354 HR from 2009 Denver Cleveland Yankee Stadium

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

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 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

HITf/x + hittracker Analysis: 4354 HR from 2009

CD: One Final Thought PFX TM PFX-TM Correlations suggestive of variations in baseball

Extract sidespin vs.  from trajectory CF LF RF RF LF RF LHH break to right break to left RHH  Balls break toward foul pole Break increases with angle Ball hit to CF slices LHH/RHH asymmetry Tilt in bat

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 Mention v dependence of COR….better to measure at 150 mph than at 60 mph. 1975 and 2004 equal to few % No evidence for juiced ball

Example: Pitching at High Altitude 10% loss of velocity total movement 12” 7.5% 8” Denver Toronto Toronto Denver PITCHf/x data contain a wealth of information about drag and lift!