如何設(shè)計(jì)棒球棒

HowWouldaPhysicist

DesignaBat?

ThePhysicsoftheBaseball-BatCollision

AlanM.Nathan

UniversityofIllinoisatUrbana-Champaign

a-nathan@

IntroductionHowDoesaBatWork?ImplicationsforBatDesignWoodAluminumSummary#521,September28,1960see/~a-nathan/pobIntroduction:DescriptionofBall-BatCollisionforceslarge(>8000lbs!)timeisshort(<1/1000sec!)ballcompresses,stops,expandskineticenergypotentialenergybataffectsball….ballaffectsbatGOAL:maximizevfvf

105mphx400ftx/vf=5ft/mphWhataspectsofcollisionleadtolargevf?vfdependsoninitialballandbatspeed

vf=P

vball

+(1+P)vbat

batspeedmuchmoreimportant!collisionveryinefficientWheredoestheenergygo?recoil/rotationofbatdissipationinballvibrationsinbatHowDoesaBatWork?

MaximizingvfTypicalnumbers:P=.22(1+P)=1.2290+70105mphWhereDoestheEnergyGo?1.Recoil/RotationofBat.Translation:Mball/Mbat.Rotation:Mball

z2/ICM.zNote:BatspeeddependsontheseSeeTerryBahill’sTalkImportantBatParameters:mass(inertia)locationofCMdistributionaboutCM(“rotationalinertia”)WhereDoestheEnergyGo?2.DissipationinBallCoefficientOfRestitution:“bounciness”ofballBounceballoffmassivehardsurfaceCOR2=hf/hiForbaseball,COR.5

3/4energylost!ChangingCORby.05changesVby7mph

(35ft!)

ImportantPoint:thebatmatterstoo!

WhereDoestheEnergyGo?2.DissipationinBallEnergysharedbetweenballandbatdependsonrelativecompressibilities

Ballisinefficient:25%returnedWoodBatEbat/Eball

~0.0280%restoredCOReff

=0.50-0.51

AluminumBatEbat/Eball

~0.1080%restoredCOReff

=0.55-0.58

“trampolineeffect”~10%larger!tennisball/racketImportantBatParameters:compressibilityelasticityCollisionexcitesbendingvibrationsinbatOuch!!Thud!!SometimesbrokenbatEnergylostlowervfLowestmodeseasytofindbytappingReducedconsiderablyif

collisionatnode

fn<1/collisiontimeWhereDoestheEnergyGo?3.VibrationsinBatFundamental:170Hz1stovertone:560HznodesImportantBatParameters:stiffnessshapePuttingitalltogether...1m/scollisionwithstationarywoodbatLouisvilleSluggerR161(33”,31oz)calculation…amndata…RodCross

Conclusions:rigidmodelworkspoorlyvf=rigidvalueatnodeEssentialphysicsunderstoodPuttingitalltogether...Underrealisticconditions…90mph,70mphat28”nodatayet…..CMnodes24”27”30”

Possible“sweetspots”1.Maximumofvf

(28”)2.Nodeoffundamental(27”)3.CenterofPercussion(27”)Handlebarelymovesbytimeballleavesbat!DesigningaBatvf=Pvball

+(1+P)vbatGoalsvflargeatmaximum

vf

vs.impactlocationbroadOpposingtendencies…tooptimizeP

massfarfromhandstooptimizevbat

massclosetohandsFromouranalysis….vfinsensitivetosize,shapeofbatfarfromimpactTherefore….makebarrelfatandlongmakehandlefeelcomfortableadjusttapertomoveCMOptimizingaWoodBat-2024681012051015202530R161(33”,31oz)ModifiedbatswithsamemassPreliminaryConclusions:

1.Can’tdomuchtoaffectwoodbatwithinconstraintsallowedbyrules,weight2.Long,fatbarrel;thinhandleseemsbestWoodversusAluminumLengthandweight“decoupled”CanadjustshellthicknessFatterbarrel,thinnerhandleMorecompressibleCORlargerWeightdistributionmoreuniformEasiertoswingLessrotationalrecoilMoreforgivingoninsidepitchesStifferforbendingLessenergylostduetovibrationsSummary/ConclusionsPhysicsofball-batcollisionlargelyunderstoodbatcanbewellcharac