How Would a Physicist Design a Bat? The Physics of the Baseball-Bat Collision Alan M. Nathan University of Illinois at Urbana-Champaign [e-mail]

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How Would a PhysicistDesign a Bat?The Physics
of the Baseball-Bat Collision Alan M.
NathanUniversity of Illinois at
Urbana-Champaigna-nathan_at_uiuc.edu

• Introduction
• How Does a Bat Work?
• Implications for Bat Design
• Wood
• Aluminum
• Summary

see http//www.npl.uiuc.edu/a-nathan/pob
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Introduction Description of Ball-Bat Collision

• forces large (gt8000 lbs!)
• time is short (lt1/1000 sec!)
• ball compresses, stops, expands
• kinetic energy ? potential energy
• bat affects ball.ball affects bat
• GOAL maximize vf
• vf ? 105 mph ? x ? 400 ft ?x/?vf 5 ft/mph

What aspects of collision lead to large vf?
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How Does a Bat Work?Maximizing vf

• vf depends on initial ball and bat speed
• vf P vball (1P)vbat
• bat speed much more important!
• collision very inefficient
• Where does the energy go?
• recoil/rotation of bat
• dissipation in ball
• vibrations in bat

Typical numbers P .22 (1P) 1.22 90
70 ? 105 mph
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Where Does the Energy Go? 1. Recoil/Rotation of
Bat

• Important Bat Parameters
• mass (inertia)
• location of CM
• distribution about CM
• (rotational inertia)

• Note
• Bat speed depends on these
• See Terry Bahills Talk

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Where Does the Energy Go? 2. Dissipation in Ball

• Coefficient Of Restitution bounciness of ball
• Bounce ball off massive hard surface
• COR2 hf/hi
• For baseball, COR ? .5
• ? 3/4 energy lost!
• Changing COR by .05 changes V by 7 mph (35 ft!)
• Important Point the bat matters too!

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Where Does the Energy Go? 2. Dissipation in Ball

• Energy shared between ball and bat
• depends on relative compressibilities
• Ball is inefficient ? 25 returned
• Wood Bat
• Ebat/Eball 0.02
• ?80 restored
• COReff 0.50-0.51
• Aluminum Bat
• Ebat/Eball 0.10
• ?80 restored
• COReff 0.55-0.58
• trampoline effect

• Important Bat Parameters
• compressibility
• elasticity

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Where Does the Energy Go? 3. Vibrations in Bat

• Collision excites bending vibrations in bat
• Ouch!! Thud!!
• Sometimes broken bat
• Energy lost ? lower vf
• Lowest modes easy to find by tapping
• Reduced considerably if
• collision at node
• fn lt 1/collision time

• Important Bat Parameters
• stiffness
• shape

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Putting it all together...

• 1 m/s collision with
• stationary wood bat
• Louisville Slugger R161
• (33, 31 oz)
• calculationamn
• dataRod Cross

• Conclusions
• rigid model works poorly
• vf rigid value at node
• Essential physics understood

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Putting it all together...

• Under realistic conditions
• 90 mph, 70 mph at 28
• no data yet..

Possible sweet spots 1. Maximum of vf
(28) 2. Node of fundamental (27) 3. Center of
Percussion (27)
Handle barely moves by time ball leaves bat!
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Designing a Bat vf P vball (1P)vbat

• Goals
• vf large at maximum
• vf vs. impact location broad
• Opposing tendencies
• to optimize P ? mass far from hands
• to optimize vbat ? mass close to hands
• From our analysis.
• vf insensitive to size, shape of bat far from
  impact
• Therefore.
• make barrel fat and long
• make handle feel comfortable
• adjust taper to move CM

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Optimizing a Wood Bat
Modified bats with same mass
R161 (33, 31 oz)
Preliminary Conclusions 1. Cant do much to
affect wood bat within constraints allowed by
rules, weight 2. Long, fat barrel thin handle
seems best
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Wood versus Aluminum

• Length and weight decoupled
• Can adjust shell thickness
• Fatter barrel, thinner handle
• More compressible
• COR larger
• Weight distribution more uniform
• Easier to swing
• Less rotational recoil
• More forgiving on inside pitches
• Stiffer for bending
• Less energy lost due to vibrations

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Summary/Conclusions

• Physics of ball-bat collision largely understood
• bat can be well characterized
• ball is less well understood
• Essential parameters for bat design known
• mass and mass distribution
• compressibility and elasticity
• stiffness and shape
• Hillerich Bradsby probably know this already!