1. 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 of Illinois at Urbana-Champaign a-nathan@uiuc.edu http://www.npl.uiuc.edu/~a-nathan/pob l Introduction l Some Basics l Wood vs. Aluminum l Some Examples l Summary/Conclusions

2. AAPT Philadelphia Meeting: The Science of Sports January 23, 2002 Page 2 Introduction: Description of Ball-Bat Collision l violent collision ­forces large (>8000 lbs!) ­time is short (<1/1000 sec!) l bat compresses ball ­kinetic energy  potential energy ­lots of energy dissipated l ball deforms bat ­vibrations! l performance metric: ­ball exit speed v f

3. AAPT Philadelphia Meeting: The Science of Sports January 23, 2002 Page 3 v ball and v bat “Collision efficiency” (e A ) * For superball on massive, rigid bat … e A  1 * For baseball on typical bat … e A  0.2 + Recoil of bat + Energy dissipated in ball and bat v ball v bat vfvf What Does v f Depend On? v f = e A v ball + (1+e A ) v bat

4. AAPT Philadelphia Meeting: The Science of Sports January 23, 2002 Page 4 Recoil Energy of Bat: m/M eff Bat recoil depends on…. mass M mass distribution * location of CM * MOI I CM impact location (z) Translation: Rotation: 1/M eff = 1/M + z 2 /I CM.. CM z.

5. AAPT Philadelphia Meeting: The Science of Sports January 23, 2002 Page 5 Energy Dissipation: The COR Coefficient Of Restitution: “bounciness” of ball in CM frame: E f /E i = COR 2 massive rigid surface: COR 2 = h f /h i  0.25  COR  0.5  ~3/4 CM energy dissipated! depends (weakly) on impact speed depends on surface  the bat matters too!

6. AAPT Philadelphia Meeting: The Science of Sports January 23, 2002 Page 6 f 1 = 177 Hz f 2 = 583 Hz Effect of Bat on COR: Vibrations nodes COR depends strongly on impact location

7. AAPT Philadelphia Meeting: The Science of Sports January 23, 2002 Page 7 Putting Everything Together... “sweet spot” depends on collision efficiency *recoil factor *COR how bat is swung CM v f = e A v ball + (1+e A ) v bat

8. AAPT Philadelphia Meeting: The Science of Sports January 23, 2002 Page 8 Aluminum vs. Wood Inertial Effects: mass and mass distribution * recoil * bat swing Dynamic Effects * COR: the trampoline effect

9. AAPT Philadelphia Meeting: The Science of Sports January 23, 2002 Page 9 direct comparision 3.6% larger v bat Generic Wood-Aluminum Comparison Conclusion: Inertial effects seem to favor wood

10. AAPT Philadelphia Meeting: The Science of Sports January 23, 2002 Page 10 l Compressional energy shared between ball and bat l Ball very inefficient (~25% restored) l Wood Bat ­hard to compress ­little effect on COR l Aluminum Bat ­compressible through “shell” modes ­COR larger The “Trampoline” Effect

11. AAPT Philadelphia Meeting: The Science of Sports January 23, 2002 Page 11 direct comparision 3.6% larger v bat + 10% larger COR Generic Wood-Aluminum Comparison Conclusion: Trampoline effect favors aluminum

12. AAPT Philadelphia Meeting: The Science of Sports January 23, 2002 Page 12 The Trampoline Effect: A Closer Look Bending Modes vs. Shell Modes k  R 4 : 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

13. AAPT Philadelphia Meeting: The Science of Sports January 23, 2002 Page 13 Tracking the Energy

14. AAPT Philadelphia Meeting: The Science of Sports January 23, 2002 Page 14 Example 1: Effect of Wall Thickness k  t 3   t l make wall thinner l add mass to keep CM, I CM fixed Conclusion: thinner is better!

15. AAPT Philadelphia Meeting: The Science of Sports January 23, 2002 Page 15 Example 2: Redistributing the Mass l make wall thinner l add mass at different locations Conclusion: barrel loading better!

16. AAPT Philadelphia Meeting: The Science of Sports January 23, 2002 Page 16 “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?

17. AAPT Philadelphia Meeting: The Science of Sports January 23, 2002 Page 17 Not Corked DATA Corked COR: 0.445  0.005 0.444  0.005 Conclusions: no tramopline effect! corked bat is WORSE even with higher v bat Bat Research Center, UML, Sherwood & amn, Aug. 2001 calculation

18. AAPT Philadelphia Meeting: The Science of Sports January 23, 2002 Page 18 Ash vs. Maple (legal!) Example 4: Ash vs. Maple (legal!)  (maple)  1.085  (ash) equal mass  R maple = R ash /1.042 k ~ R 4  k maple = 0.92 k ash more compression energy stored in maple Conclusion: B 2 had no real advantage!

19. AAPT Philadelphia Meeting: The Science of Sports January 23, 2002 Page 19 Summary and Conclusions l The physics of ball-bat collision is well understood l There are significant differences between wood and aluminum ­mass distribution ­trampoline effect l Wood bats cannot easily duplicate trampoline effect l Aluminum bats work better!