MCMTeam8008paperWord文件下载.docx

MCMTeam8008paperWord文件下载.docx

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Summary

Thechosenofball-pointhavedirectlyinfluenceontheoutputvelocityofballsandthereactionforcesonthehandofbatters.Agoodball-pointistheplaceonthebatbarrelwherethecontactbetweenbatandballresultsinthebesthit-theballleavesthebatwiththegreatestspeedandtheplayer'

shandsfeelverylittlevibrationfromtheimpact.Inthispaper,myprojectusesaPhysicsknowledge,MATLABaswellasSimulationTechnologysoftwaretodeterminewhereabaseballbathittingabaseballwouldresultintheleastvibration,asingle“sweetspot”oralarger“sweetzone”.

Asforthefirstproblem,inordertodevelopamodeltoexplainwhythesweetspotisn’tattheendofthebat,weutilizethreeequations:

conservationoflinearmomentum,conservationofangularmomentum,andthedefinitionofcoefficientofrestitution,andconsideraspecialcircumstancethatthereisnoenergylossduringthecollisionbetweenthebatandball.Thenbysimplification,wecanderivethemodelaboutthelocationofsweetspot

andwewillverifytherationalityofthismodelbyMATLABSimulationTechnology.

Thenforthesecondone,byamelioratingthemodeldevelopedabove,itrequiresustojudgewhether“corking”abatcanenhancethe“sweetspot”effect.Onthebaseofthemodelabove,wetakerecoilfactorofthebat,COR,BPFandrelationsbetweenthemintoconsideration.Thenweobtainanewmodelwhichreflectstheaffecttothe“sweetspot”by“corking”abat.

.Wewillconfirmthatthemodelisreasonablebyqualitativeanalysis,andwewillcometoconclusionthat“corking”abatcanenhancethe“sweetspot”effect.

Astothethirdproblem,ourtaskistoanswerthequestionwhetherthematerialoutofwhichthebatisconstructedmatterthesweetzone.Throughthedeeplyexplainfortheimprovedmodel,wetendtothinkthatthemetalbatsoutperformwoodones.

Finally,becauseofthestrongpracticalsignificanceoftheissue,wecollectsomecertainexistedmodelforustoinfertoandindirectlyvalidatethemodel.

Keywords:

sweetspot,coefficientofrestitution,simulation,thelossofenergy,thebaseballbat,recoilfactor

Content

Introduction……………………………………………….3

background……………………..…………………………3

Statementoftheproblems…………………………….3

Assumptionsofthemodels……………………..……..4

Variabledefinition……………………..……………….4

Steptosolvetheproblem……………………..……………4

Stepone…………………………………………………4

Steptwo………………………………………………...6

Stepthree……………………………………………….6

Stepfour………………………………………………..7

Stepfive………………………………………………...8

Thepromotiontothemodel……………………..…………9

Theevaluationtothemodel……………………..…………9

StrengthsandWeaknesses………………..……………….13

TheReferences……………………………………………14

Appendix……………………..……………………………15

ExploretheSweetspotoftheBaseballbat

Introduction

1.1Background

Doyouknowthesweetspotofbaseballbat?

Duringabaseballgame,everybatterwantstomaketheballtotravelasfaraspossible.Asweknow,thechosenofball-pointhavedirectlyinfluenceontheoutputvelocityofballsandthereactionforcesonthehandofbatters.Soitisnecessaryforustofindagoodball-point.Therearemanydefinitionsforwhatconstitutesthe"

SweetSpot"

onabaseballbat.Fromaplayer'

sviewpoint,thesweetspotistheplaceonthebatbarrelwherethecontactbetweenbatandballresultsinthebesthit-theballleavesthebatwiththegreatestspeedandtheplayer'

shandsfeelverylittlevibrationfromtheimpact.Mostofteninthepublishedresearchthesweetspotisusuallyreferedtoaseitherthecenterofpercussion（COP）orthenodeofthefirstbendingmode.

Whilealmosteverybatonthemarket（especiallyneweraluminumbats）isclaimedtohavea"

wider"

sweetspot.Theamountofcontroversyoverthemetalversuswoodbatissue,therehavebeensurprisinglyfewscientificstudiescomparingtheperformanceofwoodandmetalbaseballbats.Inthispaper,wedevelopamodeltodescribethatthemetalbathasa"

sweetspotcomparedtowoodone.

1.2Statementoftheproblems

Thenextquestionsshouldbesolved:

1.Developamodeltovalidatethefindingthatthesweetspotisn’tattheendofthebat.

2.Makeyourchosentoaffirmornegativetheversionthat“corking”abatcanenhancethe“sweetspot”effectandgiveyourreasonbyamelioratingthemodeldevelopedabove.

3.Forfurtherdetails,judgeifthebats’materialmattersthelocationofthesweetspot.

4.Discusswhethermetalbatshavea“wider”sweetzone.

5.AndthendepicttherationalityofwhyMajorLeagueBaseballprohibitsmetalbats.

1.3Assumptionsofthemodel

1.3.1Supposethatthebaseballbatishomogeneousandthesurfaceofitissmooth.

1.3.2Supposethatthebaseballbatissincere.

1.33Ignoretheimpactofairresistancewhentheballtravelsintheair.

1.4Variabledefinitions

:

Thebatmomentofinertia（abouttheCM）.

Thequalityofbaseballbat.

Thequalityoftheball.

Theball’sinitialvelocity.

Thefinalvelocityofball.

Theinitialvelocityofbat.

Thefinalvelocityofbat.

Theinitialangularvelocityofbat.

Thefinalangularvelocityofbat.

Thedistancefromthecentroidtosweetspot.

Thedistancefromfulcrumtocentroid.

Restitutioncoefficient.

Thedistancefromfulcrumtothetopofthebat.

Theball-wallCOR.

Thebatrecoilfactor.

Steptosolvetheproblems

Step1

DesignIssuesfortheSweetspotoftheBaseballbat

Fig.1.Stuctureofthebaseballbat

Fig.2.Thesystemofthebatandball

（Vfamongthesystemrepresents

Vballamongthesystemrepresents

Vbatamongthesystemrepresents

）

Intheball-batsystem,astheinteractiontimeofcollisionisveryshortwhilethesignificantchangesinmotionstateaftercollision,sointernaleffectandtheothereffectcanbeignored.ThenweconsiderthatthesystemisConservationofMomentum.

.

Wepurposethebatandballtobeasystem.ThenthissystemwillsatisfyConservationofAngularMomentumtotheCM,

（1）

Wecanknowfromthedefinitionoftherestitutioncoefficientthat,

.

（2）

Iftherestitutioncoefficientequalstoone,knownfromConservationofenergytheorem,itsuggestthatit’snotcausethelosstothetotalofthemechanicalenergybeforeandaftercollision.Thencombiningformula

（1）,

（2）withe=1（3）（Iftherewasnolossofenergyduringthebouncethenewouldbe1）,wecanreceivethenextformula:

（4）

Asallweknown,itwillproduceenormousenergywhentheballandthebatviolentcollision.Energycan’tnotbedestroyed,onlycanbetransmittedfromonetoanother.Alltheenergycannotbepassedtotheballactuallyiswasted.Asthebatwillhaverecoilforceandrotationaboutanaxisperpendiculartotheplaneoftheswing,whiletheybothcanreducetheenergywhatshouldbepassedtotheball,andthendecreasetheoutputvelocityofball.Thuswhentheimpactspotofballisthespotwheretheenergytransmittedfromthebattoballutmost,thebathasnofinalrotationalenergy.Thentheangularmomentummustbezero,thatis

.Sotheformula（4）willbelistsystematicallytobe

Thenweknowthat,

while

initcanbeobtaininthelab.

Step2

Amelioratingthemodeldevelopedabove

The“corking”ofabatresultintheReboundcoefficientincrease.

So

Basedonphysicalknowledgewecanseethatwhentheballhitthesweetspot,reboundcoefficientequaltoone.

Step3

Theanswertothequestion3

Fromtheformulaabove,wecanknowthatwhenthereboundcoefficientincreases,thenitwillresultinthedecreaseofthemechanicalenergy.Atthesametime,wecanreceivethatthefinalvelocityoftheballdecreasesandmakethesweetzonenarrowatlast.Thenindirectlyitwilllowertheaudiences’enthusiasmtoappreciateabaseballgamebecauseitwillbetoodifficultforthemtowatchawinningball.Inaword,“corking”abatcanenhancethe“sweetspot”effect,andwhattobeworseisthatitcanresultinthedecreaseofthequalityofappreciatingabaseballgame.

Step4

Doesthematerialoutofwhichthebatisconstructedmatter?

Wecanobtainthelocationofthesweetspot

frommodel1.ItisclearthatthispointisnottheCOPlocation,becausethepositionisafunctionoftheballandbatvelocityinadditiontothepropertiesofthebat.Thevalueof

and

areeasytoobtaininthelab,butthevaluesof

and

aredeterminedbythehitterswingingthebatandthepitcherthrowingtheball.

Thevalueof

forarangeoftheseparameterscanbeobtained,butitisinstructivetofirstseehow

varieswitheachofthesevariable.If

Islessthanone,thesquarerootcanbeexpandedandtheresultis

Where

hasbeenreplacedby

Throughtheformulaabove,weknowthat

thedistancefromtheCMofthebattotheimpactpointoftheball,increasesasthemassofthebatincreases,andincreasesasthemomentofinertiaofthebatincreases,andincreasesthemore”wristy”istheswing.Asdifferentmaterialhasdifferentmomentofinertia,whilethroughtheformulaaboveweknowthatthemomentofinertiacanaffectthedistancefromtheCMofthebattotheimpactpointoftheball,therefore,thematerialoutofwhichthebatisconstructedmatters.Atthesametime,themassofabatcanalsoinfluenthedistancefromtheCMofthebattotheimpactpointoftheball.Thatis,themodelcanpredictthedifferent