Baseball and Physics Where Albert Pujols meets Albert

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

Baseball and Physics Where Albert Pujols meets Albert Einstein 2

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

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 4

“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 5

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 6

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 7

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” Cross and AMN, Sports Technology 2, 7 -15 (2009) 8

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 9

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%! 10

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

Studying the Vibrations of a Baseball Bat www. kettering. edu/~drussell/bats. html f 1 = 179 Hz f 2 = 582 Hz f 3 = 1181 Hz f 4 = 1830 Hz frequency time 12

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

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!!! 14

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

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 (!) 16

Energy Flow wood aluminum 17

Forces on a Spinning Baseball in Flight FM • Drag slows ball down CD ~ 0. 2 -0. 5 FD mg • Magnus + mg deflects ball from straight line CM ~ 1 18

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

PITCHf/x and HITf/x 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 20

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

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

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

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

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

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

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

A New Experiment friction normal force • 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) 28

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

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

• 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 v normal force friction ? ? ? 31

Paradoxical Popups AJP 76, 723 -729 (2008) 32

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

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

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

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 36

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

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 38

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 39