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1、ProblemB.TableTennisBallSizes-team412Abstract0.AbstractIntabletennisgame,theexistenceofairresistanceandMagnuseffectslowingdownthemotionoftheball,aswellasthehitfromtheracket,makethegamemorefascinatingandappealingtotheaudience.InthisessaywesettravelingtimeTasthemajorst
2、andardtoevaluatethevisualeffectsofthegame,i.e.thelongertheballstaysintheair,themoreexcitationtheaudiencereceivesfromthegame.Thisessaymainlyfocusesonthemechanismoftheseaddedforcesandtheirresponsetothedivergenceofthesizeoftheball.Inthesecondsection,wemanagedtosimplifyt
3、hetheoryofcalculatingtheMagnusforceandtheairassistancebasedontheworkofanumberofvariousreferences.WeadoptPrandtl’sboundary-layertheorywhenanalyzingtheflowfieldaroundtheball,andfinallyprovidetheexpressionsofliftcoefficientCanddragcoefficientCoftheballafterafewDLprocedu
4、resofapproximation,which,however,hashardlybeenmentionedinthesereferences.Inthethirdsectionwedidresearchintheinteractionbetweentheballandtheracketandestablishedaseriesofequationstodescribetheball’smovement.Thestudyinthispartsuggestshowangularvelocityoftheballreliesoni
5、tssize.Aswehaverevealedinsection1,theairflowhashighReynoldsnumber,whichleadstosmallerinfluencefromtheviscosity.Weneglectedtheviscousforceandestablishedthedynamicalequationwithonlylifeforceandairresistanceinvolved.Withtheequationtogetherwiththeinitialconditionsprovide
6、dinsection3,weareabletonumericallycalculatetheball’stravellingtimeintheairapplyingbothMATLABandMATHEMETICA.1.IntroductionInordertoslowdownthecompetition,theInternationalTableTennisFederationchangedthesizeoftheball.Ourgoalistoshowthatthisactionwouldworkandthenfindapro
7、perdiametertomakethisgameasfunaspossible.Variables:v:Velocityofthetabletennisbat,relativetothetable0v:Velocityoftheball,inframeaav:Velocityoftheball,inframebbv:Velocityoftheball,inframecc:AngularvelocityoftheracketI:ImpactofnormalforcefromtheracketNF:liftforcecaused
8、byMagnuseffectLF:DragforcefromtheairdR:Radiusofthetabletennisballm:Massofthetabletennisballe:Therestitutioncoefficientoftheballandg