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1、ParachuteJumping,Falling,andLanding1DavidC.Arney,BarbraS.Melendez,DebraSchnelleIntroductionItisextremelyimportantthatleadersofairborneunitsunderstandthesafety,medical,andoperationalissuesinvolvedinparachutejumping.Mathematicalmodelingoftheflightandthelanding
2、ofeitherapersonoracargopackagecanhelpwiththisunderstanding.Inthissection,wedescribe,analyze,andmodelseveralcomponentsofparachutejumping.Thesearebasicmodelsusingsimplifieddatainordertobeginthestudyoftheseissuesandshouldnotbeusedforactualairborneoperations.The
3、Armyhasnumeroustechnicalmanualsthatgovernthetechnicalissuesassociatedwithairborneoperations.TheSituationAnairbornejumper,whosemassis103kg,leapswithavelocityof0.555m/sstraightout(directionofthex-axis)fromthesideofanairplanewhichismovingatavelocityof115m/s(dir
4、ectionofthey-axis).Theairplaneisflyingatanaltitude(heightonthez-axis)of4000meters.Whenthejumperleavestheaircraft,heishighenoughinaltitudethattheairresistancecanbeconsiderednegligible,andhefallsasafreelyfallingbodyfor11.5secondsuntilhepullstheparachutecord.Af
5、terthatpoint,thefallbecomesathreedimensionalprojectilemotionproblemwithnon-constantaccelerationalongeachaxisasairresistancemustnowbetakenintoaccount.Thereferenceaxesareestablishedasfollows(x-axisindirectionofjumperleavingplane,y-axisindirectionofplanewhenthe
6、jumperexits,z-axisisvertical,andtheoriginisonthegrounddirectlyundertheplanethemomentthejumperexits).Whentheparachutecordispulled,weassumethattheparachutedeploysimmediatelyandexertsacombineddragandairresistanceforceofmagnitudeD=dv2,wheredisthedragcoefficientd
7、uetotheparachuteandairresistance,andvisthevelocityofthejumper.Inthiscase,weused=20,butnormallythevalueofdisdifficulttodetermine,sinceitdependsonsomanyvariables.Assumethedragforceisexertedonlyalongtheverticaldirection(z-axis),andthattheeffectofairresistanceal
8、ongthey-directioncanbemodeledasaforceofmagnitudeF=-bv,wheretheminussignindicatesthattheforceopposesthe1FormerlyinDepartmentofPhysics,USMA61directionofmotionandbisthedragcoefficientduetoairresist
