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MathproblemsaboutBaseballSummaryBaseballisapopularbat-and-ballgameinvolvingbothathleticsandwisdom.Therearestrictrestrictionsonthematerial,sizeandmanufactureofthebat.Itisvitalimportanttotransferthemaximumenergytotheballinordertogiveitthefastestbattedspeedduringthehittingprocess.Firstly,thispaperlocatesthecenter-of-percussion(COP)andtheviberationalnodebasedonthesinglependulumtheoryandtheanalysisofbatvibration.Withthehelpofthesynthesizingoptimizationapproach,amathematicalmodelisdevelopedtoexecutetheoptimizedpositioningforthe“sweetspot”,andthebesthittingspotturnsoutnottobeattheendofthebat.Secondly,basedonthebasicmodelhypothesis,takingthephysicalandmaterialattributesofthebatasparameters,themomentofinertiaandthehighestbattedballspeed(BBS)ofthe“sweetspot”areevaluatedusingdifferentparametervalues,whichenablesaquantifiedcomparisontobemadeontheperformanceofdifferentbats.ThusfinallyexplainedwhyMajorLeagueBaseballprohibits“corking”andmetalbats.InproblemI,takingtheCOPandtheviberationalnodeastwodecisivefactorsofthe“sweetzone”,modelsaredevelopedrespectivelytostudythehittingeffectfromtheangleofenergyconversion.Becausethedifferent“sweetspots”decidedbyCOPandtheviberationalnodereflectdifferentformofenergyconversion,the“space-distance”conceptisintroducedandthe“TechniqueforOrderPreferencebySimilaritytoIdealSolution(TOPSIS)isusedtolocatethe“sweetzone”stepbystep.Andthus,itisprovedthatthe“sweetspot”isnotattheendofthebatfromthetwoanglesofspecificquantitativerelationshipofthehittingeffectsandtheinferenceofenergyconversion.InproblemII,applyingnewphysicalparametersofacorkedbatintothemodeldevelopedinProblemI,themomentofinertiaandtheBBSofthecorkedbatandtheoriginalwoodbatunderthesameconditionsarecalculated.TheresultshowsthatthecorkingbatreducestheBBSandthecollisionperformanceratherthanenhancingthe“sweetspot”effect.Ontheotherhand,thecorkingbatreducesthemomentofinertiaofthebat,whichmakesthebatcanbecontrolledeasier.BycomparingthetwoTeam#8038Page2of20conflictingimpactscomprehensively,theconclusionisdrawnthatthecorkedbatwillbeadvantageoustothesameplayerinthegame,forwhichMajorLeagueBaseballprohibits“corking”.InproblemIII,adoptingthesimilarmethodusedinProblemII,thatis,applyingdifferentphysicalparametersintothemodeldevelopedinProblemI,calculatethemomentofinertiaandtheBBSofthebatsconstructedbydifferentmaterialtoanalyzetheimpactofthebatmaterialonthehittingeffect.ThedatasimulationofmetalbatsperformanceandwoodbatsperformanceshowsthattheperformanceofthemetalbatisimprovedforthemomentofinertiaisreducedandtheBBSisincreased.OurmodelandmethodsuccessfullyexplainwhyMajorLeagueBaseball,forthesakeoffaircompetition,prohibitsmetalbats.Intheend,anevaluationofthemodeldevelopedinthispaperisgiven,listingitsadvantagessandlimitations,andprovidingsuggestionsonmeasuringtheperformanceofabat.RestatementoftheProblemExplainthe“sweetspot”onabaseballbat.Everyhitterknowsthatthereisaspotonthefatpartofabaseballbatwheremaximumpoweristransferredtotheballwhenhit.Whyisn’tthisspotattheendofthebat?Asimpleexplanationbasedontorquemightseemtoidentifytheendofthebatasthesweetspot,butthisisknowntobeempiricallyincorrect.Developamodelthathelpsexplainthisempiricalfinding.Someplayersbelievethat“corking”abat(hollowingoutacylinderintheheadofthebatandfillingitwithcorkorrubber,thenreplacingawoodcap)enhancesthe“sweetspot”effect.Augmentyourmodeltoconfirmordenythiseffect.DoesthisexplainwhyMajorLeagueBaseballprohibits“corking”?Doesthematerialoutofwhichthebatisconstructedmatter?Thatis,doesthismodelpredictdifferentbehaviorforwood(usuallyash)ormetal(usuallyaluminum)bats?IsthiswhyMajorLeagueBaseballprohibitsmetalbats?2.1AnalysisofProblemIFirstexplainthe“sweetspot”onabaseballbat,andthendevelopamodelthathelpsexplainwhythisspotisn’tattheendofthebat.[1]Thereareamultitudeofdefinitionsofthesweetspot:1)thelocationwhichproducesleastvibrationalsensation(sting)inthebatter'shands2)thelocationwhichproducesmaximumbattedballspeed3)thelocationwheremaximumenergyistransferredtotheball4)thelocationwherecoefficientofrestitutionismaximum5)thecenterofpercussionFormostbatsallofthesesweetspotsareatdifferentlocationsonthebat,sooneisoftenforcedtodefinethesweetspotasaregion.Ifexplainedbasedontorque,this“sweetspot”mightbeattheendofthebat,whichisknowntobeempiricallyincorrect.Thispaperisgoingtoexplainthisempiricalparadoxbyexploringthelocationofthesweetspotfromareasonableangle.Basedonnecessaryanalysis,itcanbeknownthatthesweetzone,whichisdecidedbythecenter-of-percussion(COP)andthevibrationalnode,producesthehittingeffectabidingbythelawofenergyconversion.ThetwodifferentsweetspotsrespectivelydecidedbytheCOPandtheviberationalnodereflectdifferentenergyconversions,whichformsatwo-factorinfluence.2.2AnalysisofProblemIIProblemIIistoexplainwhether“corking”abatenhancesthe“sweetspot”effectandwhyMajorLeagueBaseballprohibits“corking”.[4]Inordertofindoutwhatchangeswilloccuraftercorkingthebat,thechangesofthebat’sparametersshouldbeanalyzedfirst:1)Themassofthecorkedbatreducesslightlythanbefore;2)Lessmass(lowermomentofinertia)meansfasterswingspeed;3)Them