# AAPT v3

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Sports

Published on August 1, 2007

Author: funnyside

Source: authorstream.com

A Comparative Study ofWood and Aluminum Baseball BatsAlan M. NathanUniversity of Illinois at Urbana-Champaigna-nathan@uiuc.eduhttp://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 (andgt;8000 lbs!) time is short (andlt;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) andgt; 1/  energy goes into vibrations k  (t/R)3: small in barrel  more energy stored f (2-3 kHz) andlt; 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 andamp; 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!

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