AAPT Philadelphia Meeting: The Science of Sports January 23, 2002 Page 1 A Comparative Study of Wood and Aluminum Baseball Bats Alan M. Nathan University

AAPT Philadelphia Meeting: The Science of Sports January 23, 2002 Page 1

A Comparative Study ofA Comparative Study ofWood and Aluminum Baseball BatsWood and Aluminum Baseball Bats

Alan M. NathanAlan M. NathanUniversity of Illinois at Urbana-ChampaignUniversity of Illinois at Urbana-Champaign

[email protected]@uiuc.eduhttp://www.npl.uiuc.edu/~a-nathan/pobhttp://www.npl.uiuc.edu/~a-nathan/pob

Introduction

Some Basics

Wood vs. Aluminum

Some Examples

Summary/Conclusions


Introduction: Introduction: Description of Ball-Bat CollisionDescription of Ball-Bat Collision

violent collision forces large (>8000 lbs!)

time is short (<1/1000 sec!)

bat compresses ball kinetic energy potential energy

lots of energy dissipated

ball deforms bat vibrations!

performance metric: ball exit speed vf


• 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

vball vbat

vf

What Does vf Depend On?

vf = eA vball + (1+eA) vbat


Recoil Energy of Bat: m/MRecoil Energy of Bat: m/Meffeff

Bat recoil depends on….

• mass M

• mass distribution

* location of CM

* MOI ICM

• impact location (z)

Translation: Rotation:

1/Meff = 1/M + z2/ICM

. .CM

z

.


Energy Dissipation: The COREnergy 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!


0 5 10 15 20 25 30 35

f1 = 177 Hz

f2 = 583 Hz

Effect of Bat on COR: Vibrations

nodes

0

0.1

0.2

0.3

0.4

0.5

0 2 4 6 8 10 12 14distance from tip (inches)

CORCM

COR depends strongly on impact location


Putting Everything Together...

“sweet spot” depends on•collision efficiency

*recoil factor*COR

•how bat is swung

20

40

60

80

100

0.00

0.05

0.10

0.15

0.20

0.25

0 2 4 6 8 10 12 14

eAv (mph)

distance from tip (inches)

vf

eA

vbat

CM

vf = eA vball + (1+eA) vbat


Aluminum vs. Wood

• Inertial Effects: mass and mass distribution* recoil* bat swing

• Dynamic Effects* COR: the trampoline effect


direct comparision

3.6% larger vbat

Generic Wood-Aluminum Comparison

60

70

80

90

100

2 3 4 5 6 7 8 9

vf (mph)

distance from knob (inches)

woodaluminum

Conclusion: Inertial effects seem to favor wood


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

The “Trampoline” Effect


direct comparision

3.6% larger vbat

3.6% larger vbat + 10% larger COR

Generic Wood-Aluminum Comparison

60

70

80

90

100

2 3 4 5 6 7 8 9

vf (mph)


woodaluminum

Conclusion: Trampoline effect favors aluminum


The Trampoline Effect: A Closer LookThe Trampoline Effect: A Closer Look

Bending Modes vs. Shell Modes

k R4: large in barrel little energy stored

f (170 Hz, etc) > 1/ energy goes into

vibrations

k (t/R)3: small in barrel

more energy stored

f (2-3 kHz) < 1/ energy mostly restored


Tracking the Energy

0

50

100

150

200

250

300

350

400

0 0.2 0.4 0.6 0.8 1

Wood Bat

Ball KE

Ball PE

Bat Recoil KE

Bat Vibrational E

Energy (J)

t (ms)

0

50

100

150

200

250

300

350

400

0 0.2 0.4 0.6 0.8 1

Aluminum Bat

Ball KE

Ball PE

Bat Recoil KE

Bat Vibrational E

Energy (J)

t (ms)


Example 1: Effect of Wall Thicknessk t3 t

make wall thinner add mass to keep CM, ICM fixed

100

105

110

115

0.08 0.09 0.10 0.11 0.12

vf (mph)

t (in)

Conclusion:thinner is better!


Example 2: Redistributing the Mass

make wall thinner add mass at different locations

Conclusion:barrel loading better!

80

85

90

95

100

105

2 3 4 5 6 7 8 9 10

vf (mph)

distance from barrel (inches)

d=6"

d=0"

d=33"

d=12"


Example 3:

“Corking” a Wood Bat “Corking” a Wood Bat (illegal!)(illegal!)

Drill ~1” diameter hole along axis to depth of ~10”

• Smaller mass• larger recoil factor (bad)• higher bat speed (good)

• Is there a trampoline effect?


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

Bat Research Center, UML, Sherwood & amn, Aug. 2001

70

80

90

2 3 4 5 6 7 8 9

vf (mph)


uncorked

corked

calculation


Example 4: Ash vs. Maple Ash vs. Maple (legal!)(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!

70

75

80

85

90

95

100

2 3 4 5 6 7 8 9

vf (mph)

z (inches)

Ash

Maple


Summary and ConclusionsSummary 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!

Documents

AAPT Philadelphia Meeting: The Science of Sports January 23, 2002 Page 1 A Comparative Study of Wood and Aluminum Baseball Bats Alan M. Nathan University