标准大气参数推算

1TheInternationalStandardAtmosphere(ISA)MustafaCavcar*AnadoluUniversity,26470Eskisehir,TurkeyNomenclaturea=speedofsound,m/secg=accelerationofgravity,m/sec2h=altitude,morftp=pressure,N/m2orhPaR=realgasconstantforair,287.04m2/°Ksec2T=temperature,°Kor°Cρ=density,kg/m3Subscripts0=standardsealevelconditions11=tropopausecaonditionsAbbreviationsICAO=InternationalCivilAviationOrganizationISA=InternationalStandardAtmosphereMSL=MeanSeaLevelPA=PressureAltitude1.StandardAtmosphereModelingForpurposesofpressurealtimetercalibrations,aircraftandrocketperformanceandtheirdesign,andsoforth,knowledgeoftheverticaldistributionofsuchquantitiesaspressure,temperature,density,andspeedofsoundisrequired.Sincetherealatmosphereneverremainsconstantatanyparticulartimeorplace,ahypotheticalmodelmustbeemployedasanapproximationtowhatmaybeexpected.Thismodelisknownasthestandardatmosphere.Theairinthemodelisassumedtobedevoidofdust,moisture,andwatervaporandtobeatrestwithrespecttotheEarth(thatis,nowindsorturbulence).[1]Thefirststandardatmosphericmodelsweredevelopedinthe1920'sinbothEuropeandtheUnitedStates.Theslightdifferencesbetweenthemodelswerereconciledandaninternationallyacceptedmodelwasintroducedin1952bytheInternationalCivilAviationOrganization(ICAO).[1]TheInternationalStandardAtmosphereisdefinedinICAODocument7488/2.TheISAassumesthemeansealevel(MSL)conditionsasgiveninTable1.*Professor,SchoolofCivilAviation;[e-mail].2Table1InternationalStandardAtmosphere,MeanSeaLevelConditionsPressure=0p101325N/m2=1013.25hPaDensity=0ρ1.225kg/m3Temperature=0T288.15°K(15°C)Speedofsound=0a340.294m/secAccelerationofgravity=0g9.80665m/sec21.1.TemperatureModelingThefollowingdiagram(Figure1)illustratesthetemperaturevariationsinthestandardatmosphere:Figure1InternationalStandardAtmospheretemperaturevariation[2].Temperaturedecreaseswithaltitudeataconstantrateof-6.5°C/1000m(-1.98°C/1000ft)uptothetropopause.Thestandardtropopausealtitudeis11,000m(36,089ft).Therefore,theairwhichisconsideredasaperfectgasintheISAmodelpresentsthefollowingcharacteristicswithinthetroposphere:1000(m)5.60hTT−=(1)or31000(ft)98.10hTT−=(2)Forsimpleestimations,Equation(2)canbeassumed1000(ft)20hTT−=(3)Thetemperatureremainsataconstantvalueof-56.5°C(216.65°K)fromthetropopauseupto20,000m(65,600ft).ThisISAmodelisusedasareferencetocomparerealatmosphericconditionsandthecorrespondingengine/aircraftperformance.TheatmosphericconditionswillthereforebeexpressedasISA+/-∆ISAatagivenflightlevel[2].Example:Let’sconsideraflightinthefollowingconditions:Altitude=31,000feetActualTemperature=-37ºCThestandardtemperatureat31,000feetis:4731215−=×−=TºC,whereastheactualtemperatureis-37ºC,i.e.10ºCabovethestandard.Conclusion:TheflightisoperatedinISA+10conditions1.2.PressureModelingTocalculatethestandardpressurepatagivenaltitude,thetemperatureisassumedstandard,andtheairisassumedasaperfectgas.Thealtitudeobtainedfromthemeasurementofthepressureiscalledpressurealtitude(PA).BothTable2andFigure2showvariationofthepressurealtitudeasafunctionofthepressure.ThelastcolumnofTable2showscorrespondingflightlevelsforthegivenpressurealtitudes.Theflightlevelisthealtitudeexpressedinhundredsoffeet.Table2Pressurealtitudeversuspressure[2].4Figure2Pressurealtitudeversuspressure[2].ThepressurevariationsfortheInternationalStandardAtmospherecanbecalculatedbyusingthehydrostaticequation,perfectgaslawandthetemperaturelapserateequation.Thehydrostaticequationforacolumnofair(Figure3):gdhdpρ−=(4)Figure3Asmallatmosphereelement.Theequationofstatefortheperfectgas:5RTpρ=(5)whereRistherealgasconstantfortheair.Dividingthehydrostaticequationbytheequationofstategives:dhRTgRTgdhpdp−=−=ρρ(6)Therelationshipbetweenthepressureatatropospherealtitudeandsealevelpressurecanbeobtainedbyintegratingequation(1)between00=handh:∫∫=−−=pphhhTdhRgpdp00000065.0Performingtheaboveintegration,weobtain:2561.5000065.01−=Thpp(7)Inequation(7),theunitof0Tis°K,andhisinmeters.PressureabovethetropopauseForthealtitudesabovethetropopause,thetemperatureisconstant,sothatintegratingequation(6)fromthetropopausetoanaltitudeabovethetropopause:∫∫=−=pphhdhRTgpdp11111100011resultsin)(111111hhRTgepp−−=(8)wheretheparameterswithsubscript“11”correspondtothevaluesatthetropopause,and=11p226.32hPa,=11T216.65°K,and=11h11,000m1.3.DensityModelingSincethepressureandstandardtemperatureareknownforagivenaltitude,thestandarddensitycaneasilybecalculatedfromtheperfectgasequation(5):6RTp=ρ(9)2.InternationalStandardAtmosphere(ISA)Table[2]TheInternationalStandardAtmosphereparameters(temperature,pressure,density)canbeprovidedasafunctionofthealtitudeunderatabulatedform,asgiveninTable3:Table3InternationalStandardAtmosphere[2]7References[1]Talay,T.A.,IntroductiontotheAerodynamicsofFlight,NASASP-367,NationalAeronauticsandSpaceAdministration,Washington,D.C.,1975,p.6-9.[2]Airbus,GettingtoGripswithAircraftPerformance,AirbusIndustrie,CustomerServices,Blagnac,2000,p.11-16.