AAPT v3

Download
Share  Add to  Flag Embed
Uploaded from authorPOINTLite
Views:
 
Category: Education
     
 
License:   All Rights Reserved

Presentation Description

No description available.

Comments

Presentation Transcript

A Comparative Study of Wood and Aluminum Baseball Bats Alan M. Nathan University of Illinois at Urbana-Champaign a-nathan@uiuc.edu http://www.npl.uiuc.edu/~a-nathan/pob : 

A Comparative Study of Wood and Aluminum Baseball Bats Alan M. Nathan University of Illinois at Urbana-Champaign a-nathan@uiuc.edu http://www.npl.uiuc.edu/~a-nathan/pob Introduction Some Basics Wood vs. Aluminum Some Examples Summary/Conclusions

Slide2: 

Introduction: Description 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

Slide3: 

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

Recoil Energy of Bat: m/Meff: 

Recoil Energy of Bat: m/Meff Bat recoil depends on…. mass M mass distribution location of CM MOI ICM impact location (z)

Energy Dissipation: The COR: 

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!

Slide6: 

Effect of Bat on COR: Vibrations COR depends strongly on impact location

Slide7: 

Putting Everything Together... “sweet spot” depends on collision efficiency recoil factor COR how bat is swung vf = eA vball + (1+eA) vbat

Slide8: 

Aluminum vs. Wood Inertial Effects: mass and mass distribution recoil bat swing Dynamic Effects COR: the trampoline effect

Slide9: 

Generic Wood-Aluminum Comparison Conclusion: Inertial effects seem to favor wood

Slide10: 

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

Slide11: 

Generic Wood-Aluminum Comparison Conclusion: Trampoline effect favors aluminum

The Trampoline Effect: A Closer Look: 

The 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

Slide13: 

Tracking the Energy

Example 1: Effect of Wall Thickness: 

Example 1: Effect of Wall Thickness k  t3   t make wall thinner add mass to keep CM, ICM fixed Conclusion: thinner is better!

Example 2: Redistributing the Mass: 

Example 2: Redistributing the Mass make wall thinner add mass at different locations Conclusion: barrel loading better!

Example 3: “Corking” a Wood Bat (illegal!): 

Example 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?

Slide17: 

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 calculation

Example 4: Ash vs. Maple (legal!) : 

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!

Summary and Conclusions: 

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!