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

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Baseball and PhysicsWhere Albert Pujols meets
Albert Einstein---Alan Nathan, University of
Illinois
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Baseball and PhysicsWhere Albert Pujols meets
Albert Einstein
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Albert Einstein, Moe Berg, and baseball
Einstein--Mr. Berg, you teach me baseball and
Ill teach you the theory of relativity. Then
after some thought. No, we must not. You will
learn about relativity faster than I learn
baseball.
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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

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You can observe a lot by watching---Yogi Berra

• forces large, time short
• gt8000 lbs, lt1 ms
• ball compresses, stops, expands
• like a spring KE?PE?KE
• bat recoils
• lots of energy dissipated
• distortion of ball
• vibrations in bat

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What Determines Batted Ball Speed?

• pitch speed
• bat speed
• collision efficiency a property of the ball
  and bat
• BBS q vpitch (1q) vbat
• typical numbers q 0.2 1q 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

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Kinematics of Ball-Bat Collision
BBS q vpitch (1q) 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 ltlt1 and
e?1, q?1
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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)
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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

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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!

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Vibrations and the ball-bat collision

outside
sweet spot
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Studying the Vibrations of a Baseball
Bat www.kettering.edu/drussell/bats.html
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Vibrations, BBCOR, and the Sweet Spot

at node 2 vibrations minimized COR
maximized BBS maximized best feel
e
vf
Evib
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Independence of End Conditions

• strike bat on barrellook 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!!!
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BBCOR and the Trampoline Effect(hollow bats)
The Ping!
Lowest Hoop (or wineglass) Mode
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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 (!)

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Energy Flow
wood
aluminum
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Forces on a Spinning Baseball in Flight

• Drag slows ball down
• Magnus mg deflects ball from straight line

CD 0.2-0.5
CM 1
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Real vs. Physics 101 Trajectory Effect of
Drag and Magnus
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PITCHf/x and HITf/x
Marv White, Physics, UIUC, 1969

• Two video cameras _at_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.

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Baseball AnalysisUsing PITCHf/x to discover
how pitchers do what they do
Hitting is timing. Pitching is upsetting
timing.
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Ex 1 Mariano Rivera Why is he so good??
Three Reasons Location, Location,
Location Images, courtesy of BaseballAnalytics.org
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Ex 2 Late Break Truth or MythMariano
Riveras Cut Fastball
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Ex 3 A Pitchers Repertoire
Catchers View
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Ex 4 Jon Lester vs. Brandon Webb
15 inches
Brandon Webb is a sinkerball pitcher Almost no
rise on his fastball
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Ex 5 The Knuckleball
Tim Wakefield is a knuckleball pitcher Chaotic
Movement
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Learning About Batted Balls

• Experiments to measure spin of batted ball
• HITf/x extension of PITCHf/x
• Initial part of trajectory
• TrackMan
• Full trajectory

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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)
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Some Results
Final spin is large and nearly independent of
initial spin (for given ?)
?
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More Results
Gripping ?gtVx/r
final surface speed
Rolling ?Vx/r
Sliding ?ltVx/r
Initial surface speed
Data suggest ball grips surface, creating
overspin
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• 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

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Paradoxical PopupsAJP 76, 723-729 (2008)
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Extract sidespin vs. ? from trajectory
CF
RF
LF
RF
LF
RF
RHH
LHH
?

• Balls break toward foul pole
• Break increases with angle
• Ball hit to CF slices
• LHH/RHH asymmetry
• Tilt in bat

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What Constitutes a Well-Hit Ball?
w/o home runs
home runs
V0gt90
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Combining HITf/x with Hittracker

• HITf/x ? v0,?,?
• Hittracker (Greg Rybarczyk, hittrackeronline.com)
• Landing point
• Flight time
• Together these constrain the full trajectory

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HITf/xhittracker 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

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HITf/x hittracker Analysis4354 HR from 2009
Denver
Cleveland
Yankee Stadium
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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

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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_at_illinois.edu
• I am living proof that knowing the physics
  doesnt help you play the game better!

_at_ Red Sox Fantasy Camp, Feb. 1-7, 2009