Published on August 1, 2007
A Comparative Study ofWood and Aluminum Baseball BatsAlan M. NathanUniversity of Illinois at [email protected]://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 [email protected] 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!