Physics and Baseball: Having Your Cake and Eating it Too

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Physics and BaseballHaving Your Cake and Eating
it Too
Alan M. Nathan a-nathan_at_uiuc.edu webusers.npl.uiuc
.edu/a-nathan/pob Department of
Physics University of Illinois
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Baseball and Physics
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A great book to read.
Our goal is not to reform the game but to
understand it. The physicists model of the
game must fit the game.
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A Physicists Approach to Current Issues in
Baseball

• Should aluminum bats be banned?
• Corked bats and juiced ballsdo they matter?
• What the deal with the gyroball?
• Can steroid use increase home run production?
• Is the game different in Denver?
• and what about that humidor?

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Some Experimental Tools

• Bat testing facility
• High-speed video or motion analysis
• You can observe a lot by watching ---Yogi
• swinging the bat
• ball-bat collision 1
• ball-bat collision 2
• PITCHf/x tracking system
• Trackman radar

more on these later
See http//webusers.npl.uiuc.edu/a-nathan/pob/vid
eo.html for some nifty videos.
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Some Physics Background

• Physics of ball-bat collision
• Aerodynamics of a baseball
• Oblique collisions and spin

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Description of Ball-Bat Collision

• forces large, time short
• gt8000 lbs, lt1 ms
• ball compresses, stops, expands
• KE?PE?KE
• bat recoils
• lots of energy dissipated (COR)
• distortion of ball
• vibrations in bat
• to hit home run.
• large batted ball speed
• 100 mph?400 ft, each additional mph 5-6
• optimum take-off angle (300-350)
• lots of backspin

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Kinematics of Ball-Bat Collision
BBS q vball (1q) vbat
z
e coefficient of restitution ? 0.50
(energy dissipationmainly in
ball, some in bat) r ? mballz2/I6 bat recoil
factor ? 0.25 (momentum and angular momentum
conservation) ---heavier is better but
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Batting cage study show how bat speed depends on
I for college baseball players

• 1/I6n
• 0ltnlt0.5
• n ? 0.3

aluminum
wood
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Accounting for COR Dynamic Model for Ball-Bat
Collision AMN, Am. J. Phys, 68, 979 (2000)

• Collision excites bending vibrations in bat
• hurts! breaks bats
• dissipates energy
• lower COR, BBS
• Dynamic model of collision
• Treat bat as nonuniform beam
• Treat ball as damped spring

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Modal Analysis of a Baseball Bat www.kettering.edu
/drussell/bats.html
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Vibrations, COR, and the Sweet Spot
Strike bat here

best performance feel _at_ node 2
e
vf
Evib
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Independence of End Conditions

• strike bat in barrellook at response in handle
• handle moves only after 0.6 ms delay
• collision nearly over by then
• nothing on knob end matters
• size, shape
• boundary conditions
• hands!
• confirmed experimentally

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Why Is Aluminum Better Than Wood?

• Aluminum has thin shell
• Less mass in barrel
• --lower MOI, higher bat speed, easier to control
  ?
• --but lower collision efficiency ?
• --partially canceling effects
• Hoop modes
• trampoline effect ? ?
• ping (2000 Hz)

demo
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The Trampoline Effect A Simple Physical
Picture

• Two springs mutually compress each other
• KE ? PE ? KE
• PE shared between ball spring and bat spring
• sharing depends on kball/kbat
• PE in ball mostly dissipated (80!)
• PE in bat mostly restored
• Net effect less overall energy dissipated
• ...and therefore higher ball-bat COR
• more bounceconfirmed by experiment
• and higher BBS
• Also seen in golf, tennis,

demo
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Regulating Performance of Non-Wood BatsA
Science-Based Approach Used by NCAA

• Specify maximum q
• approx. same as for wood bats of similar wt.
• implies bats swung alike will perform alike
• Specify minimum MOI to limit bat speed
• smaller than wood
• Together, these determine a maximum BBS
• gap between wood and aluminum ? 5
• does that mean aluminum should be banned?
• an issue many are struggling with

BBS q vball (1q) vbat
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What About Corked Bats?or..What was Sammy
thinking?
no trampoline effect!

• Conclusion
• No increase in BBS
• increase in swing speed
• decrease in collision efficiency

• 1/I6n
• 0ltnlt0.5

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What About Juiced Baseballs?
Conclusion No evidence for juiced ball
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Aerodynamics of a Baseball

• Gravity
• Drag (air resistance)
• Lift (or Magnus)

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Typical values of drag and lift
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Effect of Drag and Lift on Trajectories

• drag effect is huge
• lift effect is smaller but significant

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Some Effects of Drag

• Reduced distance on fly ball
• Reduction of pitched ball speed by 10
• Asymmetric trajectory
• Total Distance ? 1.7 x distance at apex
• Optimum home run angle 30o-35o

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Some Effects of Magnus

• 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.

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The PITCHf/x Tracking SystemA Quantitative Tool
to Study Pitched Baseball Trajectories
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How Does PITCHf/x Work?

• Two video cameras track baseball in 1/60-sec
  intervals
• usually high home and high first
• third CF camera used establishes ht. of strike
  zone
• Pattern-recognition software to identify blobs
• Camera calibration to convert pixels to (x,y,z)
• 9-parameter fit to trajectory
• constant acceleration for x(t),y(t),z(t)
• Use fit to calculate lots of stuff
• The full trajectory
• The break
• Drag and Magnus forces

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Example Drag and Drag Coefficients20k pitches
from Anaheim, 2007
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Using PITCHf/x to Classify PitchesJon Lester,
Aug 3, 2007 _at_ Seattle
spin axis
LHP Catchers View
I Nearly overhand fastball II Slider or cut
fastball III ¾ Fastball IV Curveball
break direction ?-90o
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Whats the Deal with the Gyroball?
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From PITCHf/x to HITf/xBarry Bonds 756th Home
Run

• PITCHf/x data tracked hit ball over first 20 ft
• Precision measurement of endpoint and
  time-of-flight
• Inferred v0112 mph ?27o up ?16o to right
  of dead center ?1186 rpm (backspin) and 189 rpm
  (sidespin, breaking to center)

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Baseball AerodynamicsThings I would like to
know better

• Better data on drag
• drag crisis?
• spin-dependent drag?
• drag for vgt100 mph
• Dependence of drag Magnus on seam orientation,
  surface roughness,
• Is the spin constant?

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Trackman The Wave of the Futuresee
www.trackmangolf.com

• Doppler radar to measure radial velocity
• 3-detector array to measure phase
• two angles
• Sidebands gives spin magnitude
• Result
• in principle, full trajectory can be
  reconstructed, including spin and spin axis
• already in use for golf, currently being adapted
  for baseball

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thanks to Fredrik Tuxen, CTO of Trackman
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Oblique CollisionsLeaving the No-Spin Zone

• Oblique ? friction ? spin
• still need a good collision model
• my model slide, then roll
• 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

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Undercutting the ball ? backspin
trajectories
vertical sweet spot
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Another familiar result
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Steroids and Home Run Productonsee Roger Tobin,
AJP, Jan. 2008

• Steroids increases muscle mass
• Increased muscle mass increases swing speed
• Increased swing speed increase BBS
• Increased BBS means longer fly balls
• Longer fly balls means more home runs

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Home Run Distances, 2007 www.hittrackeronline.com
4 per foot
Tobins Conclusion increase of BBS by few mph
can increase HR rate by 30-50!
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Steroids and Bat Speed

• Batter supplies energy proportional to M
• Energy shared between bat and some fraction ?2 of
  M
• Roughly ?2 0.01
• So roughly, 10 increase in M gives
• 2.5 increase in vbat
• 2 mph increase in BBS
• 12 additional ft. on long fly ball
• 20 (Adair) -50 (Tobin) more home runs!

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Work in Progress

• Collision experiments calculations to elucidate
  trampoline effect
• New studies of aerodynamics using Trackman and
  PITCHf/x
• Experiments on high-speed oblique collisionsdoes
  slide-then-roll model work?
• A book, with Aussi Rod Cross

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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
• webusers.npl.uiuc.edu/a-nathan/pob
• a-nathan_at_uiuc.edu
• Thanks for your attention and go Red Sox!