Title: A Comparative Study of Wood and Aluminum Baseball Bats Alan M' Nathan University of Illinois at Urba
1A 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
2Introduction 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
3What 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
4Recoil Energy of Bat m/Meff
- Bat recoil depends on.
- mass M
- mass distribution
- location of CM
- MOI ICM
- impact location (z)
5Energy 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!
6Effect of Bat on COR Vibrations
COR depends strongly on impact location
7Putting Everything Together...
vf eA vball (1eA) vbat
- sweet spot depends on
- collision efficiency
- recoil factor
- COR
- how bat is swung
8Aluminum vs. Wood
- Inertial Effects mass and mass distribution
- recoil
- bat swing
- Dynamic Effects
- COR the trampoline effect
9Generic Wood-Aluminum Comparison
Conclusion Inertial effects seem to favor wood
10The 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
11Generic Wood-Aluminum Comparison
Conclusion Trampoline effect favors aluminum
12The 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
13Tracking the Energy
14Example 1 Effect of Wall Thickness
- k ? t3 ? ? t
- make wall thinner
- add mass to keep CM, ICM fixed
Conclusion thinner is better!
15Example 2 Redistributing the Mass
- make wall thinner
- add mass at different locations
Conclusion barrel loading better!
16Example 3 Corking a Wood Bat (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?
17Bat 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
18Example 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!
19Summary 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!