Alan M. Nathan,University of Illinois

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Some Topics in the Physics of Baseball

• Alan M. Nathan,University of Illinois
• a-nathan _at_uiuc.edu

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Some Topics in the Physics of Baseball

• Can a curveball be hit farther than a fastball?
• Some aerodynamics
• Physics of the ball-bat collision
• Why does aluminum outperform wood?
• How does a baseball bat work?

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1. Can a curveball be hit farther than a
fastball?Some Aerodynamics
(in direction leading edge is turning)
CD, CM 0.2-0.5
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Measurements of Lift and DragJoe Hopkins, Lance
Chong, Hank Kaczmarski, AMN
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Experiment MoCap Data
y ½ ayt2
topspin?aygtg
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Effect of Spin on Baseball Trajectory

• Lift
• scales approx. linearly with ?
• has major effect on trajectory

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Oblique CollisionsPutting Spin on the Ball

• Sliding friction
• reduces transverse velocity
• increases ?
• sliding-to-rolling transition
• Results
• Balls hit to left/right break toward foul line
• Topspin gives tricky bounces in infield
• Pop fouls behind the plate curve back toward
  field
• Backspin keeps fly ball in air longer

f
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Undercutting the ball ? backspin
trajectories
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? ? larger for curveball
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In summary.Can a curveball be hit farther than
a fastball?

• Higher pitch speed ? higher hit ball speed on
  fastball
• Butmore backspin on curve ball
• Net result curveball goes farther
• by a little bit
• Mont Hubbard, AJP 71, 1152-1162 (2003)
• See also February 2005 issue of AJP for a debate
  Hubbard vs. Adair

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Physics Description of Ball-Bat Collision

• forces large (gt8000 lbs!)
• time is short (lt1/1000 sec!)
• ball compresses, stops, expands
• bat compresses ball
• ball bends/compresses bat
• lots of energy dissipated
• distortion of ball
• vibrations in bat
• ball-bat COR related to energy dissipation
• why is aluminum better?

Courtesy of CE Composites
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Wood versus Aluminum

• Aluminum has thin shell
• Less mass in barrel
• easier to swing and control ?
• but less effective at transferring energy ?
• Hoop modes
• trampoline effect
• larger COR ??

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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
• PE in ball mostly dissipated (80!)
• PE in bat mostly restored
• Net effect less overall energy dissipated
• ...and therefore higher ball-bat COR
• more bounce

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Trampoline Effect
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Experimental Modal Analysis
Impact hammer (force transducer) 35 points along
length
Accelerometer fixed location on barrel
FFT Analyzer
Frequency Response Function (accel / force)
Dan Russell, Kettering U.
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Hoop Modes of Hollow Bats
Lowest hoop mode --that annoying ping
--trampoline effect
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COR correlated with fhoop
Wood bat
30 on long fly ball
Courtesy of Dan Russell www.kettering.edu/druss
ell/bats
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SummaryWhy Does Aluminum Outperform Wood?

• Trampoline effect reduces energy dissipation
• More pop
• Longer fly 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
• www.npl.uiuc.edu/a-nathan/pob
• a-nathan_at_uiuc.edu
• Go Red Sox!