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Introduction How Does a Bat Work? Implications for Bat Design Wood Aluminum Summary

#521, September 28, 1960. How Would a Physicist Design a Bat? The Physics of the Baseball-Bat Collision Alan M. Nathan University of Illinois at Urbana-Champaign a-nathan@uiuc.edu. Introduction How Does a Bat Work? Implications for Bat Design Wood Aluminum Summary.

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Introduction How Does a Bat Work? Implications for Bat Design Wood Aluminum Summary

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  1. #521, September 28, 1960 How Would a PhysicistDesign a Bat?The Physics of the Baseball-Bat CollisionAlan M. NathanUniversity of Illinois at Urbana-Champaigna-nathan@uiuc.edu • Introduction • How Does a Bat Work? • Implications for Bat Design • Wood • Aluminum • Summary see http://www.npl.uiuc.edu/~a-nathan/pob

  2. Introduction: Description of Ball-Bat Collision • forces large (>8000 lbs!) • time is short (<1/1000 sec!) • ball compresses, stops, expands • kinetic energy  potential energy • bat affects ball….ball affects bat • GOAL: maximize vf vf 105 mph  x  400 ft x/vf = 5 ft/mph What aspects of collision lead to large vf?

  3. How Does a Bat Work?Maximizing vf • vf depends on initial ball and bat speed • vf = Pvball+ (1+P)vbat • bat speed much more important! • collision very inefficient • Where does the energy go? • recoil/rotation of bat • dissipation in ball • vibrations in bat Typical numbers: P = .22 (1+P) = 1.22 90 + 70  105 mph

  4. . . . CM z Translation: Mball/Mbat Rotation: Mball z2/I Where Does the Energy Go? 1. Recoil/Rotation of Bat • Important Bat Parameters: • mass (inertia) • location of CM • distribution about CM • (“rotational inertia”) • Note: • Bat speed depends on these • See Terry Bahill’s Talk

  5. Where Does the Energy Go? 2. Dissipation in Ball • Coefficient Of Restitution: “bounciness” of ball • Bounce ball off massive hard surface • COR2 = hf/hi • For baseball, COR  .5 •  3/4 energy lost! • Changing COR by .05 changes V by 7 mph(35 ft!) Important Point: the bat matters too!

  6. tennis ball/racket ~10% larger! Where Does the Energy Go? 2. Dissipation in Ball • Energy shared between ball and bat • depends on relative compressibilities • Ball is inefficient:  25% returned • Wood Bat • Ebat/Eball~0.02 • 80% restored • COReff = 0.50-0.51 • Aluminum Bat • Ebat/Eball~0.10 • 80% restored • COReff = 0.55-0.58 • “trampoline effect” • Important Bat Parameters: • compressibility • elasticity

  7. Fundamental: 170 Hz nodes 1st overtone: 560 Hz Where Does the Energy Go? 3. Vibrations in Bat • Collision excites bending vibrations in bat • Ouch!! Thud!! • Sometimes broken bat • Energy lost  lower vf • Lowest modes easy to find by tapping • Reduced considerably if • collision at node • fn < 1/collision time • Important Bat Parameters: • stiffness • shape

  8. Putting it all together... • 1 m/s collision with • stationary wood bat • Louisville Slugger R161 • (33”, 31 oz) • calculation…amn • data…Rod Cross • Conclusions: • rigid model works poorly • vf = rigid value at node • Essential physics understood

  9. CM nodes 24” 27” 30” Putting it all together... • Under realistic conditions… • 90 mph, 70 mph at 28” • no data yet….. Possible “sweet spots” 1. Maximum of vf (28”) 2. Node of fundamental (27”) 3. Center of Percussion (27”) Handle barely moves by time ball leaves bat!

  10. Designing a Bat vf = P vball + (1+P)vbat • Goals • vf large at maximum • vf vs. impact location broad • Opposing tendencies… • to optimize P mass far from hands • to optimize vbat  mass close to hands • From our analysis…. • vf insensitive to size, shape of bat far from impact • Therefore…. • make barrel fat and long • make handle feel comfortable • adjust taper to move CM

  11. 12 10 8 6 4 2 0 -2 0 5 10 15 20 25 30 Optimizing a Wood Bat Modified bats with same mass R161 (33”, 31 oz) Preliminary Conclusions: 1. Can’t do much to affect wood bat within constraints allowed by rules, weight 2. Long, fat barrel; thin handle seems best

  12. Wood versus Aluminum • Length and weight “decoupled” • Can adjust shell thickness • Fatter barrel, thinner handle • More compressible • COR larger • Weight distribution more uniform • Easier to swing • Less rotational recoil • More forgiving on inside pitches • Stiffer for bending • Less energy lost due to vibrations

  13. Summary/Conclusions • Physics of ball-bat collision largely understood • bat can be well characterized • ball is less well understood • Essential parameters for bat design known • mass and mass distribution • compressibility and elasticity • stiffness and shape • Hillerich & Bradsby probably know this already!

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