A Comparative Study of Wood and Aluminum Baseball Bats Alan M' Nathan University of Illinois at Urba

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A Comparative Study ofWood and Aluminum Baseball
BatsAlan M. NathanUniversity of Illinois at
Urbana-Champaigna-nathan_at_uiuc.eduhttp//www.npl.
uiuc.edu/a-nathan/pob

• Introduction
• Some Basics
• Wood vs. Aluminum
• Some Examples
• Summary/Conclusions

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Introduction Description of Ball-Bat Collision

• violent collision
• forces large (gt8000 lbs!)
• time is short (lt1/1000 sec!)
• bat compresses ball
• kinetic energy ? potential energy
• lots of energy dissipated
• ball deforms bat
• vibrations!
• performance metric
• ball exit speed vf

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What Does vf Depend On?
vf eA vball (1eA) vbat

• vball and vbat
• Collision efficiency (eA)
• For superball on massive, rigid bat eA ? 1
• For baseball on typical bat eA ? 0.2
• Recoil of bat
• Energy dissipated in ball and bat

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Recoil Energy of Bat m/Meff

• Bat recoil depends on.
• mass M
• mass distribution
• location of CM
• MOI ICM
• impact location (z)

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Energy Dissipation The COR

• Coefficient Of Restitution bounciness of ball
• in CM frame Ef/Ei COR2
• massive rigid surface COR2 hf/hi ? 0.25
• COR ? 0.5
• 3/4 CM energy dissipated!
• depends (weakly) on impact speed
• depends on surface
• the bat matters too!

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Effect of Bat on COR Vibrations
COR depends strongly on impact location
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Putting Everything Together...
vf eA vball (1eA) vbat

• sweet spot depends on
• collision efficiency
• recoil factor
• COR
• how bat is swung

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Aluminum vs. Wood

• Inertial Effects mass and mass distribution
• recoil
• bat swing
• Dynamic Effects
• COR the trampoline effect

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Generic Wood-Aluminum Comparison
Conclusion Inertial effects seem to favor wood
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The Trampoline Effect

• Compressional energy shared between ball and bat
• Ball very inefficient (25 restored)
• Wood Bat
• hard to compress
• little effect on COR
• Aluminum Bat
• compressible through shell modes
• COR larger

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Generic Wood-Aluminum Comparison
Conclusion Trampoline effect favors aluminum
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The Trampoline Effect A Closer Look

• Bending Modes vs. Shell Modes

k ? R4 large in barrel ? little energy
stored f (170 Hz, etc) gt 1/? ? energy goes
into vibrations
k ? (t/R)3 small in barrel ? more energy
stored f (2-3 kHz) lt 1/ ? ? energy mostly
restored
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Tracking the Energy
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Example 1 Effect of Wall Thickness

• k ? t3 ? ? t
• make wall thinner
• add mass to keep CM, ICM fixed

Conclusion thinner is better!
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Example 2 Redistributing the Mass

• make wall thinner
• add mass at different locations

Conclusion barrel loading better!
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Example 3 Corking a Wood Bat (illegal!)
Drill 1 diameter hole along axis to depth of
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• Smaller mass
• larger recoil factor (bad)
• higher bat speed (good)
• Is there a trampoline effect?

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Bat Research Center, UML, Sherwood amn, Aug.
2001
Not Corked DATA Corked COR
0.445 ? 0.005 0.444 ? 0.005

• Conclusions
• no tramopline effect!
• corked bat is WORSE
• even with higher vbat

calculation
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Example 4 Ash vs. Maple (legal!)

• ?(maple) ? 1.085 ?(ash)
• equal mass ? Rmaple Rash/1.042
• k R4 ? kmaple 0.92 kash
• more compression energy stored in maple

Conclusion B2 had no real advantage!
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Summary and Conclusions

• The physics of ball-bat collision is well
  understood
• There are significant differences between wood
  and aluminum
• mass distribution
• trampoline effect
• Wood bats cannot easily duplicate trampoline
  effect
• Aluminum bats work better!