Experimental Baseball Physics

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Experimental Baseball Physics
Alan M. Nathan a-nathan_at_uiuc.edu webusers.npl.uiuc
.edu/a-nathan/pob Department of
Physics University of Illinois
Courtesy, Trey Crisco
Courtesy, Dan Russell
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The Baseball/Physics Connection
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Some Topics I Will Cover

• The ball-bat collision
• The flight of the baseball

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The 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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Studies of the Collision Efficiency q

• Independent of reference frame
• Measure in bat rest frame qvf/vi
• Use q to predict field performance

Sports Sciences Laboratory, Washington State
University
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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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Studies of the Collision Efficiency q

• Independent of end conditions

Vf (mph)
Courtesy, Keith Koenig
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q Field Study vs. Laboratory
Crisco, Smith, AMN

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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
at node 2 vibrations minimized COR
maximized BBS maximized best feel

e
vf
Evib
Note COP is irrelevant to feel and performance
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Aluminum Bats and 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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Softball Data and Model
Russell, Smith, AMN
Wood
change kbat
change kball

• Conclusions
• COR of Al bat can be significantly higher
• essential physics is understood

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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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Batting cage study show how bat speed depends on
I for college baseball players

• 1/I6n
• 0ltnlt0.5
• n ? 0.3

aluminum
wood
Crisco, Greenwald, AMN
Other studies show bat speed independent of M for
fixed I
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Example 34 Bats
q1/2
All bats below horizontal line and to right of
vertical line are allowed
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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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Putting spin on the ball Low speeds
no spin
topspin
backspin
Cross AMN

• Conclusions
• slide-then-roll model approximately works
• curveball is hit with more backspin than fastball

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High-Speed VersionWork in Progress
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Flight of the Baseball

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

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Measuring Magnus Force Using High-Speed Motion
Analysis
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Motion Analysis Geometry
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• Motion Capture System
• 10 Eagle-4 cameras
• 700 frames/sec
• 1/2000 shutter
• EVaRT 4.0 software
• www.motionanalysis.com

• Pitching Machine
• project horizontally
• 50-110 mph
• 1500-4500 rpm

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Typical Data and Fit
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Results for Lift Coefficient
FL 1/2?ACLv2 Sr?/v 100 mph, 2000
rpm ?S0.17
Conclusions --data qualitatively consistent
(20) --RKA model inconsistent with data
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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 Bonds 756
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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 4-seam fastball II Slider (?) III 2-seam
fastball IV Curveball
break direction ?-90o
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How Far Did That Home Run Travel?

• Ball leaves bat
• Hits stands D from home plate, H above ground
• How far would it have gone if no obstruction?

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Calculations
400 ft/30 ft Range415-455 Time can resolve
See www.hittrackeronline.com
4 s
5 s
7 s
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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 ?270 up ?160 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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Trackman Radar

• Monopulse Principle (Phase)

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thanks to Fredrik Tuxen, CTO of Trackman
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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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Elite hitters HR/BBIP 10
Thanks to Roger Tobin
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Change in range distribution when batted ball
speed increased by 3
Baseline
3 change in BBS gives 50 increase in HR rate!
3 speed increase
Thanks to Roger Tobin
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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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Work in Progress

• Collision experiments calculations to elucidate
  trampoline effect
• New studies of aerodynamics using Trackman and
  PITCHf/x
• Experiments on high-speed oblique collisions
• A book, with Aussi Rod Cross

Thanks for the invitation and your attention