Post on 03-Oct-2018
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NATIONALADVISORYCOMMITTEi-------FORAERONAUTICS
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TECHNICALNOTE —
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.TENTATIVETABLESFORTHEPROPERTIES --
, OF THEUPPERATMOSPHERE. ‘“1 —
.* By CalvinN. Warfield ....
for the ..—..----
NACASpecialSubcommitteeon theUpperAtmosphere“--’”
LamzlevMemorialAeronauticalLaboratory
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LangleyField, Va..-. ... :.. .——
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Washington ““v:.-—.
N A CA lJIRARY-.” .....LANuwYnMmAi.A.m9N.AuikB?k
January,1947,,
J-w LABORATORY.,...,.
LangleyFkkLV8. . ,“
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https://ntrs.nasa.gov/search.jsp?R=19930081846 2018-10-03T08:52:29+00:00Z
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TECHNICALNUI’ENO.1.200
TENTATIVETABLESFORTHEFROFER’TIES
OFTHEUPPERATMXWHERE
By CalvinN.Warfielii
forthe
NACASpecialSubcommitteeontheUpperAtmosphere
SUMMARY
As a resultofrecentdevelopmentsInaeronauticsandordnance,a needhasarisenfortablesofpropertiesof theatmosphereataltitudesin excessof thosecoveredby theexistingstandardtables(NACAReportNo.ZI.8). In orderto satisfythisneed,theNationalAd\-iscryCommitteeforAeronauticshasadoptedthree-temperature-heightrelationshipsandonecomposition-heightrela-tionship,andtablesbaseduponttmmhavebeenpreparedforpertin-ent propertiesof theupperatmosphere(thatis,from20 to 120kilo-”matersinmetricunits,andfrom65,000to 393,7oOfeet.inBriti@units). In theabsenceof directdata,suchesmightbe obtainedby soundingswithhigh-altituderockets,thevaluesadoptedarebaseduponexistinginformationobtainedby indirectmeasurementsof certainquantities.As a consequence,thetablesareonlytentative.
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Two setsof tablesbasedupcntheadoptedtentativestandardspecificationsfortheupperatmospherearepresented.Onesetoftwotablesisbaseduponthesamearbitraryconstantvaluefortheaccelerationofgravityas wasusedin thepreparationoftheexistingstandardtablesforthelowerlevels(NACAReportNo.218).Thissetoftablesfortheupperlevelsof theatnmspheratherefore
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constitutesa consistentextensionoftheexistingstandardtables.Theothersetof twotablestakesintoconsiderationthedecreasein theaccelerationof gravitywithincreasingaltitudeandthere-foreismoreprecisethanthefirstset. Consequently,thisset
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ispresentedonlyto satisfytheneedforgreateraccuracythatmayexistIn somefieldsofresearch.
EachtableisdividedIntoseparatepartsforbothdayandnightconditionsataltitudesabove&lkilometers.ThenecessityforseparatetablesfordayendnightvaluGsisoccasioned_bythe
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NACATN No.1200 3.
InApril1946thisPanelwassupersededby theE@ecialSubcom-—-.
mitteeontheUpperAtmospherewhichwasalsoappointedby theNACA. ““””.-
2 ?,%:)~f;,gr~z:x,xThememerhi of-th~eSpecialSubcommitteeisas follows:.- ,
Dr.HarryWexler,U. S.WeatherBureau,ChairmanCol,D. N.YatesjChief,AirWeatherServiceCol.PaulH. Dane,A. C.,TSEAC,AAFAirMaterielCcmmandCapt,H.T. Orville,USN,OfficeofChiefofNavalOperations,
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NavyDepartmentCapt.WalterS.Diehl,USN,BureauofAeronautics,Navy”
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Departmentn.-Dr. CalvinN.Warfield,LangleyMemorialAeronauticalLeborato~
Dr.E.H. Krause,NavalResearchLaboratoryDr.W. G.Brombacher,NationalBureauofStandartiDr.L.V. Berkner,CarnegieInstitutionofWashingtonDr.B. Gutenberg,CaliforniaInstituteofTechnolo~ .—— -
Dr.FredL. Whipple,HarvardObservatory,HarvardUti-versftyDr.O.R. Wuif,GatesandCrelljnLaboratories,California
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InstituteofTechnology.Mr.JeromeTeplitz,NACA,Secretary.
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ThisSubcommitteehasconsideredthe”informationavailablecon-cerningtemperatureandcompositionin theupperatmmphere.Onthebasisof existindataobtainedby ball~onsat altitudesUYto.
?about32kilometersreferences6 and7),of Indirectmeasurementsobtainedat greaterheightssuchas thosediscussedinreferences8to 14,andofunpublisheddataresultingfraasimilarindirectmeasurements,recommendationsconcerningtemperature-heightandcomposition-heightrelationshipsweremadeby theSubcommitteeonJune24,1946.Therecommendationsregardingtemyorature-heightrelationshipscoverthreearbitrarysetsoftemperature:(1)tents-tivestandardtemperatures,(2)probableminimumtemperatures,and(3)probablemaximumtemperatures.
—.Also,recczmnendationwasmade
thatat thistimeno tablesbe preparedforaltitudesin excess”of l.EOkilometersbecauseoftheuncertaintyregardingthevalidityof thedatainthisregion. -—— -.
At e meetingoftheexecutivecon.mitteeoftheNationalAdvisoryCoumitteefGrAeromuticsheldonAugust15,1946,thepreviouslymentionedreconwendationsof theSubcommitteewereadopted.As a resultoftheadoptionoftherecommendationsoftheSubcommittee,twosetsof tablesfortheupperatmosphere,baseduponthetentativestandardtemperatures,havebeenpre~aredat theLangleyLaboratoryof thelVACA.
Thefirstsetoftablesprovidesa consistentextensloriof -.thepresentstandardtablesforthelowerlevelsoftheatmosphere
4 NACATN No.1200
(reference1)becausethesamesimplifyingassumptionofanaTbi-traryconstantvaluefortheaccelerationof gravityIsmadeinbothcases.Becauseofthisccm.sj.etencywltihthepresentstandardatmospheretables,andinconeideraitlon~f:the.fa.g.t.tBa!.t~~presentstand,md.tablee(reference1)are~dely u~~d-ineval”titingperformancecharacteristicsofaficraftandfordesignpurposee,itappearsthatthisfir~tsetoftableaMy alsobe foludusefulInthoeesamefteldsofaeronauticalen@n+ering.In”additlon,Inordertobe consistent~th presentpracticeintheUS6ot thoterms“pressurealtitude’’.and“densityaltitude”(reference15)itappearsthatitmaybeyropertousetheterm“tentativeyrK3S-su.re altitude”to d.esi~ta that altitude ~n thisftists~toftableswhichcorrespor~dstoa specifiedamlient-airyressure.Likewise,theterm“tentativedensityaltitude”canconsistentlybe usedwiththissetoftgblasfn connectionwith&mblant-airdensities.
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Thesecondsetoft~blemis more precisethanthefirstbecauseittakesintoconsiderationthedoeroaseinthaaccelera- —.
tionof gravitywithfncr~asingaltitude.;Thisset“isintendedprimarilyforusein co~ectiontithresear~hon thepropertlos 4
oftheupperatmosphere.ValuesofstillgreatercomputationalprecisionthanthoseJiste&inthiseecon~setmeybe obtainedbymeansof “latitudocorrectionfactcrs”whl:chhavubeencomyuted randtabulatedin anothertable. —
Thesetwosetsoftableefortheupperatmosphereconsistoftwotableseach,OriOinthemetricsys&rn Of units endtheotherin theBritishsystemof units.Thealtituderange.covered.isfrom20 kilometersand&j,000feet,respectlvaly,to 120kilo- —
m~tersand.itsBritishequivalentof about393,700feet.In addl.-tlontothosequantitiesreportedinrofe~tincesLto ~, thereisincludedtheMan freepethof theairmcleculo6.Thisquantityhasbeenaddedbecaueeof itssignificanceat”highaltitudeswherethemolecularmeanfreepathemaybe com~&ableto orlergerthmcer%indimensionsoftheaticraftor missiles that maybe f-lowntherti.
AcknowledgementISgrawfullygiven~or.the,contrlbutionsmadebyDr.R. G, Stone,oftheA&?WeatherService,whcsuppliedvaluabledataconcerningmaxim~andminmumtemperaturesovortheentireworldtoaltitudesof 12kilofiater$,andfcrthethorough .tuchrulcalreviewandexcellentsuggestionsofferudbyMr.L.Z’.HarrisonoftheU. S.WeatherBureau.
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4
ii
NACATN No.1200
SYMBOLS
8
h
K
L
M
m
N
P
R
r
T
t
v
w
7
speedof sound
mostprobablemolecular
averagemolecularspeed
accelerationof gravity
altitude
speed
()ATvolumegradientof oxygendissociationG
5
-- z- --.---—
a
/&temperaturegradient
()z
molecularweight
massof a molecule
numberofmoleculesperunitvolume
pressure
universalgasconstant
radiusof theearth
absolutetemperature , ..
temperature —
volumeofmolecuhroxygeninan initialunitvolullleof .-normalair,at thesametemperature“andpressure
specificweight (@)
ratioofspecificheats
,..
-.---— -. —--
NACATN No.12006
h meanfr9epathofm51eculea
P coefficientofviec~8it~
U kinematicvi8ccsfty(v/p)
P density(massperunitvol.um9)
o moleculariiiameter;elsodensityratio (/)P P(-J
z averagemoleculardiameter
Thefollowin~subscriptsareusedtoreferto theindicatedcoali-tions:
o
1
a
A
B
c
D
6
m
n
N
G
air
~
sealevel
lowerlevel
topofregicmcfdlaeociatlon,wheroG~gen isallatanlc
baseofrep~onwtthcmnstarlttemperfitureandconetentccmpoaition ,’ .-
b~seofregionwithconstanttemperaturegradientandcormtantcomposition
baseofragj.onwithconst~nttemperatureandconstuntvolumegradientofdissociation
b~seofregionwithconetanttempei?atu.ro‘@adlentandconstantvolumegradientofdtstiociation
accelerationof gravityvariable:
baseofregionof dissociaticm,whereo~~enisallmoleculm
nitrogenmolecules
non-cxlygen(i.e.,allconstituenttiotherthanoxygen)
oxygen
mixtureofmoleculesinatmosphere-
latitude
. ---~.
.+.-
.-
EC—.
-5
.—
,
—.—.
b.-.
t
I’iACATN No.l&OO 7
ADOPFEDSPECIFICATIONSFoRTEEWIPER
TentativeTemperatures
mMosm3.RE
Threesetsoftentativeteqerature.heightrelationshipshave%eenadopted.Onesetgivestentatiw13tsmdardtenrperaturesandtheothertwolistvalues of thepro’bahleminimumaidthe .
Probablemaximumtemperaturesfortheentireworld.Thesethreesetsof temperatureswhichwereoriginallyreco~nded%y theSubcommitteeontheUpperAtmospherearegivenbylinearv&ria-tionswithaltitudebetweenthepointsspecifiedinthefollcmd~tabulationof temye~tures. -
-—
TEMmRhllYsm!s—.
AltitutleI
minimum(km) (%)
o
172025. -.
g50556070?7me3120
225
180
200
300
170
300
Tentativestandard(%)
%?8b218
’218
218
3W
3Y240
240375
320
250
255
380
3&)
300
600
%e valuesofambientairtemperaturelistedInthesetwocolummsarenotintendedtorepresmtextremevaluesfortheentireworld,andforilltime,butmthervaluesthatbracketthetemperaturesovernearlyalltheearthmostallthetime.
bThesevaluesarestandard,andhavebeenusedpreviouslyinreferences1,3,4,~d 5; . — .
Thesete~erature-altituderehtionshi~sarealsoshowninfigure1.. .. ___ __
8 NACATN No.1200
TentativeComposition
Thetentativecompositionusedin computingthetableswasarrfvodatby takingintoco~siderztionthefactthat-,at altf.tudesbelow@ kilometersinthedaytimeandbelow105kilometersatnight,thegenerally.acaeptedvari~-uionoinche?dcd.oomposltiollaretooSDXLU.toaffectappreciablythe.c~utedQressuresanddensities.However,itisbelievedthatat levelsabove-thosejustspecifiedsignificantcham~esin compcmitlonresul%fromthediseociatlonofoxygenmoleculee%y-solarradiaticm.It-isfurther-moreknownthatthepresenceofwatervaporin theatmospheredoesnotappreciab~vaffectpreesuresandderisities.As a resultofsuchconsiderations,andintheinterestiofsimplicity,thefollowi~tentativespecificationsforcompositionof theupperatmoeyherewererecommendedby theEhlcommitt.eandhavebeenadoptedforthepurposesof computingthevaluesinthesetables:
(1)Fordaytime,thedissoclatioriof’oxygenis suchas toproducea linearvolume~dient fromall-molecularoxygenat&) kilometerstoall-atomicoxy~enat 100kilometers.Fxceptforoxygendissociation,+;hecompositionis the&uneas thatat scalevel.
(?)Yornighhtime,thedissociation“ofo~~en is suchas toproducea ldnearvolumegradientfromall-molecularoxygenat10~kilometerstoall-atomicoxygenet 120k$lometere.%cceptiforoxygendissociationthecompositionis thesameas thatat sealevel.
(3) A*altitudes ‘belowtheregionsof oxygendissociationthecompositionisthesme as thatat sealevel.
(4)At altitudesabovetheregionsInwhich%othmolecularendatomicoxygenexist, as stipulated i,II(1) and (2), andup toat least12CJkilometers,thecompositionisthesameas thatatsealevel,exceptforoxygenwhichis in the atomic ratherthanhthemolecularform.
Thevariationwithaltitudeofthespecifiedmolecularoxygencontent---u?theatmospheresi,sgraphicallyportrayedinfigure2.
PBYSICALKEIATIONSHIPSBasfcEquations
Inadditiontothespecfficatiorflfortemperatureandcom-positionalreadylisted,certainotherassumptions”aremadeand.
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w
H.- .
‘4
“d
NACATN_NQ. 120Q.
serveas thebasisforderivingcomputingthepropertiesof’theassumptionsare:
(a)Theairisdry
.9 _.
thevariousequationsusedinuyper
(b)Theairbehavesas a yerfectgeneralgaslawwhichmay
m
—atmospheret Theseailditional
gasand.heacebe written
PP’OM—=—— —00 2+)T q)
obeysthe
(1)
(c)Theairisat restwithrespectto theearthandhenceobeysthebasiclawforfluidstatics
dp..gpa,, (2)
,.By meansof equations(1)and(2)andequationsrepreeentl_n~ -
theadoptedspecificationsfarte.myere.tureandc@upositfoA,relationshipsmy be-deducedbetween.p%mureandhel@t. The __equationsrepresentingtheadoptd~p~clfi~tionsare .. “. ._ ___.. ,
‘T=Tl+L(h - hl) i31-”-”-- -
where L isthetempefiture‘gradientAT/Ah,and
(4)
where K isthevolume~dient ofoxygendissociationAv/Ah.Thederivationofequation(4) is given inappendixAs
Inadditiontothethreeassumptionsjust listed, it isnecessa~tomakeanassumptionconcerni~’thevalueof theacceler&-tionof gravity.Forthepurposeof furnishfn~tabl~sfortheupperatmospherethatwillbe consistentwithtli6presents&iidardtiblesfortheioweratmosphere(reference1),it isnecessa~tomake’thesaneassumptionconcerningtheaccelerationof gravityas wasusedinpreparingthestandardtal?les.Thisassumptionis
(d)Forthetablesbasedona constantvalueof g the—
accelerationof gravityat allaltitudesisthe —standardsea-levelvalue;that is,
.-
10 NACATN No.12Q0
Forthoseinstk.ncesinwhichcloserconformitytoactualconditionsisreauiredthanisinherentinthesetablesitisnecessarytomakeanotherassuqtion concerningthevalueoftheacceleratio~ofgravity.Thisassumptionis
(e)Fortablesbasedona varlallsvalueof g theaccelera-tionofgravityvariesinverselyas thesquare5fthedistancefrom thecenteroftheearth;that1s,
2
()6=%* (6)
Pressure-HeightI?elationshlps
Ry useoftheforegoingbasicequationsandassumpt$c@s,otherequationsarederivedwhichrelatepreswretoaltitude.“-$wosetsofequationsareused,onesetbasedon’sconstantvalueof g asspecifiedInassumption(d),theotherset%asedonthevariationof g thatisspecifiedinassumption(e). Thedeductionsfortheflrs~setareln~icatedinappend~xB ~d”forthesecondsetinappendixC. Theequationsthatarebasedona constantvalueofareas-follows:
Forcombination(constanttemperatureanaconstantco~ositlon)
where
where
-3, ($)= cA(h- ~A)
CA=@PO To M
-%-~”%
Forcombination(constanttemperaturegradientcomposition):
()log ~’ =
m ‘?9~g (~-
‘%POTOM%=-—– ~L %
6
:
(7)
(8)
andc&siEint
(9)
(10)
P-
.
w
NACATN MO.1200 11
ForcombinationC (constanttemperatureandconstantvolumegradientofdissociation):
(PIlog : ()=cc log -;
(11)
~rhere
ForcombinationD (constanttemperaturegradientendconstantvolumegradientofdissociation):
where
(14)
TheequationsderivedinappendixC,basedcna va~ia%levalueof ~,aremorecomplexthanthoselistedintheforegoingendconsequent~theyarenotreproducedhere.
Speed-ofSound
Thespeedof soundatanyaltituderelativetoth?.tat sealevelis computedly theequation
wheretheratioofthespecificheats 7’,as
Y I!X?K(h- ha~=1- 21Mo
(15)
derivedinapyendixA, is
(3.6)-
~p I?ACATN NO.UOO
Thevariationtikhaltltudecftheratioofspecificheats 7for thespecifiedatmosphereis shownin,?fgure3(a).
CoefficientofViscosity
Sutherland’sequationfor thevariationofthecoefficientofviscositywithtemperatureIsused. 1% in
inwhich,accordingtoreferenoa16,
s = ~120
whenthe T’s arein%, and
6 =916 ‘
whenthe Tre arein% absoluto.
A cautionconcerrdngtheuaeofvalueso%ta.inodfromequation(17)fortheuppers,ixnoapherois givenin tiesecticnentitled“DiscusEIionofTables.”
MolecularMean
Theratioofthemolecularmeanthecorrespond.ingvalueat sealevel
(17)
.
Freel?ath‘
freepathatanyaltitudetoiecomputedby
Thisequationis justifiedina,ppendixD.
(18)
—
...
.—
-.
In theprecedingsectionequationsaregiventymeansofwhichseveralpropertiesoftheupperatmosphereareccmqn,ztcd.Themcomputationsinvolvenumkricalvaluesoftheseveralpro~ertlesat aealevel.ApTendixE discussestheohogensea-levelvaluesfor
NJ-CATN NO.1.200 13
eachofseveralpropertiesoftheatmosphereandtheyareliste~in--
tableI inbothmetricandBritishengineeringsystemofuriits..-
Yaluesarelistedforeachofthethreespecifiedatmospheresand ‘-””in someinstancesthequantityisexpressedinmorethanoneunitin eitherthemetricorBritishsystem.
ThevalueslistedintableI forthestandardatmosphereatsealevelareidenticalwiththoseusedinreferences2 and5exceptina fewinstances.Theexceptiurmareinappendi.xE.
I)ISCVSSION@ TABY~S
notedandexplained
[
Thea~propriateequationequation(7),(9],(11)or (23)fortheconstantvalueof g, cm C3)j(c6),(C1O)or (c13)forthevaria%levaluesof g) isusedto computetheratioofthepressurey atanyheigl>ttothepressureat thebaseofthe”
-.
regiontowhichthatpartlcul.arequationap~liqe.Tkesepressureratiosforeachofof thepressurepP/P~ aregivenin
By useof the
theregionsarethenusedto computetheratio----
tothepressureyO at sealevel.These5atio6-tables?Z to V.
computedvalue&ofthepressureratiosp/pOandof theeea-levelvalueofpressureTo as givenfntableI,thevalueofthepressurep iscomputedandthengivenintablegII toV. ThepressuresgivenintablesIV andV arealsoplottedagainstaltitudeinfigure3(b).
Theremainingquantitiesgivenin tahleaZI to V aresimilarlycomyutedbymeansof theappropriateequatlanandthecorrespondingsea-levelvalue givenintableI. ThevaluesYgrthesere~iningquantitiesgivenintables.ZVandT arealsoshownplotteda~instaltltudeinfigures3(c)to~(h).
Attentionisdirectedtothefactthatallt%blesinthisreportarebassdcmtheengineeringsystem(sometimesreferredtoas thegravitationalsystem)inwhichthefvadamentalquantitiesarelength,force,endtime.Thestandardunitsforforceusedhereinare,therefore,poundsfortheXritishsystemendkilogramsforthemetricsystem.
14 NACATN No.L200
ACCUraCyofC2mputedTa~e8II toV
In tablesII toV allquantitiesexceptthemeaxifreepathsof themoleculesaretabulatedtofoursignificant-figures,andthemeanfree pathsoftheuoleculesartitabul~tedtothraeel@ifl- “cantfigures.Allcomputationsfcmtable11 werecarriedthroughtosixsigniftiantfi~uresandconseque~tlythevaluesgiveninthistablearebelievedtobeexact.
Mostof’tinevaluesfortableIVwereobteinedfrcmtableII byuseof suitableconversionfactorsevaluatedby a graphicalmethoddescribedinappendixC. Theerrorsreetiltingfromthemethod,andthereforetheerrorsinthevaluestabulattidintableIV arebelievefi-notto exceed0s01of1 psrcent.
A methodof graphicalintarpol.ation.wasappliedto@bt~infr%tablesIIandIV thevaluesforuseat theintermediat~levelstabulatedintables111andV. Theaccuracyofthismothcdiesuchae tointroducean errorofnotoverone-twentiethof1 percent”inthevalueelisted.intablesIII&l~dV. Consequently,wlwncveradiscrepancyexistsbetweenthemtric andBritishvalues,themetricvaluesshouldgovern.
.&:
v.—
*—
—
.
ValidityofTabulated.Valucmat theHigherAltitude8
Pressure,density,specificweight,andmaanfrea@th ofmolect.ales.-Aa waspreviouslymentioned,”ttiecomputationsfortablesI1and IIIarebasedon a constantvaluofortheaccelera-tionof gravityg sothatthevalueslistedwouldbe consistentwiththoseappearinginthepresentstandardtableaforthelowerlevelsoftheatmosphere(reference1). Theerrorsin thecemputedvaluesofpressure,density,6pecifi-cweightandmeenfreopathinherentintheassumptionofa ccnstan&~aIueforthaaccelerationof gravitybecomeprogressivelygreaterwithincreasingaltitude,beingabcut30perccmtat 120kilomotere;Ecwever,a variationof 30percentinpressureat ~iC)kfloutarscorrespondstoavariationof lessthan4 percentinaltitudeat thisiovel,snd.at lowerlevelsthechangein altitudsctirrespohdlngtotheerrorinpressurerspidlyapproacheszero.It Isapparmtthert.forethatin at leastHomeapplicationsthevaluesin tablesII md IIIwillbe adequateendthereforeuseful.Furthermore,theyrepresentan extemsimcfthepresentstandardtables(reference1).
In orderto satisfytheneedthatm“yexistforvalu@ thatarenotaffectedby theuseofa constan~valuofortheeccelora-tl.onof’gravityg, thblesIV andV areZresented.In thesutablesg isassumedto veryinverselyas thesquareofthe
.-
NACATN No.1200 15
dtstancefromthecenterofthe‘earth.This assumptionthereforetakesintoconsiderationthevariationdueto-gravitational_attrac;tion,butitdoesnotallowfor.tfieeffectof-centrifugali?orc”eoThecentrifugalforceduetotherotationoftheearthiskm.owntobe onlya smallfractionof 1 percentof the~avitationalforceat an altitudeof120kilometer,andconsequentlythis”omissiondoesnotresultina aigniflca~terror. ..-
.. ,, . Thestandardvalueusedfortheaccelerationof gravityatsealevel(andatallal%itudesfortables.11and111)is9.&1665metersperseccndpersecond.Thisvaluecorrespondsrathercloselytothetrueaccelerationof gravityat sealevelat latitude450.,(MoreSpecifically,it correspondstothetheo-reticalaccelerationofgrevityat sealevelandet latitude45°!24’accordingto theInterna~ionelformula,Seereference17.) Ifstillgreateraccuracythenis inherentIntables~ gndV isrequiredat latitudesfardisplacedfromlatitude45°, an estimat~of thelatitude effect uponpressureanddensitymaybe obteinodby useoftheequation
logP#—P.
logF_Po
(>9)
whore“p~
Isthepressureataltitudoh andat la_’titl@eg,and @
distheaccelerationof’gravityat sealevelendat lati-
tude $. A similarequation(replacingp’s with p’s) appliesto densities.
By meansof eqmtion (l$J)it can bs shownthata latitude”‘_correctionfactor(L.C.F.jdefinedby
2.L.C.F.= (20)P
canbe computedby
(21)
—
()L.C.F.= ~ ~Po
16 NACATN No,1200
“If v&lUe8of ~ fromreference17areused,thefollowing,,,“~ (%#-Q)/~~reobt..ine&:valuesfor,theexponent
. . .
v -I,“, ,!
Latitude &q-%. Letlt~&e @# -%’(deg) (dgg)
-. .~ ,“
%“
0’ -$2’.66758x 1.0”3 ,%. o.ki2Y?yx 10”3‘M ; ‘“-2.50922“’ ‘“ 1..28372“Eo: “’~;;
-2>,05299 70 1:*98732-1.3533*{ 83 2;44701’. . . “;-0.4.9405 30 ‘“ 2.60670. +
Theforegoingexpcnentswhenappliedtothe”valuesofprekeure” -ratio p~po tabulatedintablesIVandVgivathe valuesofthe .
latitude’ correction factor desoyihed by &quatii:;ns(&O) and (’21).For.latitudes at increments of 10!and f~r altitudes at incrementsof 10 kilometers the latitude corr.ecti.onfactors that are applicable
●
to thepressuresgivenin tablesIVandV havebeencomputzedtindarepresentedintableVI. By meansoftableVI itis therefore
—
possibletoobtain(XXEpu@dvaluesofpressgewhichtakt3intO ,considerationthevariationwit~hti”tudeof’thu“sea’-le”vel“vilue’
—
of..theacceleration.ofgravity&j,o“’Th3.8”ccraputfitionhaybq.qadeby useofequation(LO)whichmqybe writtenp@ =,(LcC.F.)p.,.,’ - ,.. -, —
Coefficientof viscosityandkinematicviscosity.-TheSutherland.fmmula(equation(l~))~sstrlctlyepplicableonly toa gasof constantcompositionandtopre~suras,wh$chwe nottoosmall,andconsequentlythotab~ateflvaluesforthecoefficientofviscosityandforthekino~ticviscosi$yapeobviouslynotentirelyreliableat thehi~er altitudes.Hcwave~,thelackcf---dataontheviscosityof o~gen,in,th~atcmicformdoesnut permitat thistimean estmtion ofthb correctionthatisneededtoallowforthospecifieddissociation.Furthermore,bocatiaeof thofactthattheeffectivevalueof’thcjviscosity~fa gasat verylowpressureflowingovera bodydependsonthesizeand&hap<‘ofthebody,it ISnetpractical to @VG a correction that will beapplicabletomorethanon~specificsize,andshapeofa body.Thevaluesforviec~sityat thefiigh~raltitudesshouldthereforebeusedwithcaution, .!. — --
.
Smod of sound.-The tabulated wluee forthespeedof soundarebalievedtobe“correctforalla.ltitudeacovaredby thethb.hse
N.ACATN No.1200 17
Cautionshouldbe exercised,however,inuelngthetabulatedvaluesfortheupperaltitudesin con.mctionvithMachnumbersbecauseathi@ altitudesu%erethemeanfreepathsof theair-molecdesarelargein comparison’wfthtinedimensionsofthebodymov~g thoughthem,thelawsoffluiddyrmnicsdonotapplyandthelaws-of“--particledynamicsmustbe used.Whenaerodynamicforces,forexamyle,arecomputedfortheseconditfon8by useofthelawsofparticledynamicsthem~stprobablespeedof theairmolecules~sfoundtobe thebasicquantityratherthanthespeedof sound.
—
As inthecaseofvisco~ity,thealtituderangein whichthemostprobablespeedOf tJ-Ieair molecules replaces the speed ofsound as the basic quantity depends upon the size of the bcdy
under consideration.It j.sconsequentlynotpossibleto syeclfyasinglelevelat whichthemolectiarspeedbecomessignificantinaerodynamics.Forthisreasonvaluesforthespeedof soundarelistedto120kilometers.
In anyeaseinwhichthemostprobablespeedoftheairmoleculesc isneededratherthanthevelocityofsound a itispossibleto obtainthevalueof c fromthevalueof a listedin thetablesby useoftheappropriatefactorobtainedfromthefollowingtabulation:
Altitude,h
(m)
83,000?5,000go,00095,000
100,WO105,,0001-10,0001.15,000
~
Ratioof themostprobablemolecularc
isp+ to the speed of sound, -. ~
a
(ft) I I,Day Night
262,1J67278,87~255,2753u,679328,083344,487360,,@%377,z96393,700
1.1951*18$31.1831.~761@1701.1701.1701.1701.170
I*195l,lq1.1791.170
CONCLUIENGREMARKS
Thefactshouldbe emphasizedthatthevaluesgiven in thetablesfortheupp~ atmosphereareonlytentativeandas suchmaybecomeobsoleteaftera sufficientnumberofreliabledirect
18 NACATN No.&OO
measurementsofcertainquantitieshavebeenmadeavaila%le.Inthemeaiitimethesetentativetablesshouldl)eusefulnotonlyinservtngaae.haslafo~comyaringperformancecharacterlatic~andestimati~limitingvaluesof.performance,butalsoinsecuringtheadditionaldataneededforrevieingthesetentatiwtablesfortheupperatmosphere.
LangleyMemorialAeronauticalLaboratoryNationalAdvfso@CommitteeforAeronautics
LangleyField,Vs.,Deceniber6, 1946
*
NACATN No.1200
-AIPENDTXA ‘
19
VARIATIONWITHALTIZCUDEOFWTMX3LARWEIGHT
ANDRATIOOFSPECIFICHEATS
MolecularWeightintheRe@.onofOxygenDissociation
Consifieran initialunitvolume02norml airoomposedonlyofmoleculargases,consistingof oxygenandotherconstituents.Letallthenon-oxygenconstituentsbe t.ia%omicofavemgemolecular -———
weight~, and.letthemolecularweigh-tof crgygenin themolecularfozmbe ~, andin theatcmtoform ~. TherL
(Al)
Let theinitialconditions he as follows:
‘o volumeofall-molecularoxygenathei@t ‘~
1 - vo volumeofnon-oxygen.componentsat height~
‘o avefigeniolecularweight of theinitialairmixtureatheight&
Then
‘o = VA ‘>(1- VO)MN
.
(A2)
At heighth, between~ and ~ (where~ isheightat%aseofregioninwhichdissociationoccurs,and ha isheightattopoftheregion,andwhersalltheoxygenis intheatomicf&’m)thevolumeofmolecularo~gen v. perunitinitialvolumeofnormalairis
andthevolumenormalairis
AJA—
ofatonico~gen va perunitinitialvolumeof ---—
4
(A4).
La.-. NACAT?iNo,ti”~
ThereforetheavaragemolecularweightM ofthe“atqmphereat heighth canbe showntobe
,,._._2Q._– (A5)l- K(h-~)
-.
V.~.. kliq (A6)
—where
thevolumegradient of.molecularoxygen,Av/Ah.
RatioofSpecificHeatsintheRegion
@ OxygenDissociaticIn
Therat~oofapeciflclicatay fordtatomtc.@sea18 t.akrntohe 7/5andform.onetotic~aaek3,,5/3.~P theratioof thespecificheats Y fortheatmosphereisasmxned*.ohe,eivcnbya weightedavemqe,accor~ngtorelativemaeees,ofthevalueeof Y fordi~totic~d ~9~tomiC~SOSJ itcan’beshcwn,by uainqeq-uations(Al),(A2),(A3),end(A4)thatforthoseregionsoftheahosphcnwh .which&issocjati.onof’.oxy~tenoccurs
(A7)
Thestmndardvaluefor ?’.,Is7/5,andfor ~ thestamkr~
y_ =1-Y~
Tortheatmosphereat sealevel,valuefs 32. Therefore
2?&(h - h~— 2wi (A8)
It isestimatedthatinthetentativestx..ndafiatmospherethovarfa.tionof y duetopressureandtemperatureeffectsi~onlyabout0.6of I percent.Forthisreasontheeffectofpreesure~mdtelnperatumupon ? isi-red incomputingthesetcnte.tiveti%lee.
—.
n
.
NACA‘TNNo.12.00 “k1
VARIATIONOFTRES6UREWITHALTITUJX3(AS~ THE
ACCELERATIONOFGRAVITYISA CONS~NT @)
Theequationsrelatinga~xnosphericl?ress~etohel@t fo?.all .....altituderangesinallthraeatmospheres(minimum,standard,end.maximumtemperatures)areonlyfourinnuniber.Thesefourequationsrepresentallpossiblecombinationsof thetwotypes‘ofk&mpetiture-heightwlationshiyandthetwotypesof composition-height
.-
rola+ionship.Thedeductionsof theequationsarelaseduponthe -famillarh@rostaticrelation
dp. - q-j) dh
anduponthegeneralgasequation
P pMTO— = —-- —Po PO h% T
(Bl)
(B2)
Thesetwoequations,whencomki%d,give .—.—
(B3)
Thedifferentialequation(B3)isthenusedforderivinga~eb~icequationsforpressureasa functionofaltitude,foreachofthefourcombinationsoftemperature-heightandcompod.tion-heightrelationshipspreviouslydiscussed.Thederivationsareindicated“inthefollowingparagraphsandtheresultingequationsareusedinthepreparationoftablesII andIII.
— —.——. .
ConibinationA (constanttemperatureandconstantcomposition).-Thetypeofatmosphereinwhichboththetemperatureandcompositionareconstantmayhe representedalgebraicallyby
.
T= constant —
and
M = CCmetant
L&2 NACA‘TNNo.IX)(I
l?cjue.tion(B.3)wheninte~rated%et>ventheUzdtsofheighthA andhei@t h then?mcoms,, -
(R4)
where hA isthebaseof theregionin_whtchtypeA conditionsprevd.1●
Conibination23(constant+&mperaLure’Peli.en%andconst43.n+composition).-Yorthetypeofatmoayhe~hav??g~constanttempora-tlu?egradientandconst~tCO~O@ition,letthete?qperntu~egrsdientbe roprosentciiky
L = cons-ten-ta ~ (B5)
andthetemperatureby
where~ md h~ are the respective~lues at thebasoof theregiontowhichcombi~tlc)~ B conditionsprevail.AIEIIYM = cons-tent.Mquattm(B3)then%ecomes
(337)
andwhenintegratedbetweenthelimitsof ~ and h t.hisequation%ecomee
(B8)
CombinationC (constmtt~eratureandconstantvolu-.—gradientofdissociation).-In thetypeofatmospherewhere%oththeteznpomtureandvolzuuegradientofdissociationareconstant
.
.—.
.-
—
WICATN No.3.200 23
andan erpreseionfor M asa functionof.h isderivedinappe~dixA, enditisfoundto%e .
(B9)
whereK isthevolumegradientofmolecularoxygemdefinedby
K
Usingtheserelationehlpa
~=P
w%thequmtton(B3)gives
lStegratingequation(Bll)betweenthelimitsof ~ and k,x’here‘e is theheightat thebaseoftheregioninwhichtyyeCconditfoneprevail,gives
.24 NACATN No.MOO “w
Integratingthevariablepart of the right-handmember,betweenthelimitsof ~ and h, gives 2
1 I~+ L(h-@)’hlog
(1+ Khm)L-I-(TD- LhD)K l- K(h-~)-k
Therefore
—
(B14)
u
NAC!ATN NO..~~
..
.
.
VARIATIONOFPRESSUREWITHAWITIJDE(ASSTMR3TEEACCEIJZRATION
OFGRAVITYVARIESINVERSELY”AS T& SQUAREOFTHE,,
DJXWiNCEFROMTHECENTEROFTHEEM/T@
Theequationsrelatingpressureandaltitudederivedhereinare%aseduponthegeneraldifferentialeqyatfcmderivedfromequation(B2)ofappendix33,fromthehydrostaticrelation
dp=-~dl, (cl)
emdfromtheequationrepre6entingtheinversesquare=riati~ of ___theaccelerationof gravity
, ‘“(CA)
Thisgenemldifferentialequationf.e “
As inappendixB fourequationsarededucedforuseineachofthefourpossiblecombinationsof specitied tempera-@re-altftMe endcomposition-altituderelationships.Theremltingalgebralcequationsareusedinthepreparationof ta’ble~Z9aadV- ThedeductionsforeachconbinatfcmareIndicated,j-nthefollowingpam~pha.
CcmibinatlonA(constanttemperaturemd constantcompOsitlm)●-Forcor&inationA (constanttemperatureandconstantpressure)thealgebmicequationrelatingpressureandaltitudeis obtainedbylntegrathgequation(~3) betweenthelimitsofaltitudehA and h.Theresult3s
(C4)
26 NACA~ NOa 3,206
(NotethatinthisequationandsucceedingequationsthesubscriptgisueedtoIndicate-valuescomputedwiththevariationintheaccelerationofgravitythatisspecifiedby equation(C2).)
CombinationB (constanttemperaturegradientandqonetantcompositionJ.-ForcomM.nationB(constanttemperaturegradientconstantcomposition)thedifferentialequationisobtaine~bysubstituting@ equation(C3]the valuefor T gtvenby
T=ff~+L(h-~)
Thedifferentialequationisthen
g. .-g@oT&lr2dh
.- 9
ThealgebraicequationobtainedtheappropriatelimitsIS
() [.22 r(h- hB)low
~g=%g[r+h)(r+l#
where
.-
and
L(~- ~)l(r+ h)-
by integratingequation(c6)between
rL 1(r+ h)TB— (C7)‘rZ+~L-’l3 10% (r + ~)ll?
(m
CombinationC (constanttemperatureandconstant volume~adientofdissociation).-ForconibinatkoaC (constanttemperatureandconstantVOlume gradientofAssociation)thediff~~ntfalequatiOnisoba~nedby substitutingIn equation(C3)thevalueof M gi.venby
.
● �✎
NACATN No.liOO
Thedifferentialequationisthen
&=P
-t@oTor2m
[YOTl- K(h”- ~~(r+h)2
27
(Clo)
Thealgebmicequationobtainedby integratingeqya.tlon(CI.0)betweenappropriateW% IS
*
.
. .
where
(m?)
‘-dorn&atl.o~D(constanttemperaturegradientandconstmt,voliinegradientofdissociation).-ForcombhationD(constanttemperature~d:e~t - Gcms~~~:.Yo,I.unegraii~entofdisfiociation)tiedifferentialequationis’obiainedby &u%stitutinginequation(C3)thevaluesof T end M givenby a slightlymodifiedformof equation(C5)andby equation(C9),respectively,,Theresultingdifferentialequationisthen - J .-.... 1 ----,--------.— ,-. --*, -—
(I-J=.: :3?
..
Thealgebraic
-qPoToT?dh(C13)
‘or% ~ ‘(h “-~~~ - K(h-“~~(r +.h)2 “l.-..
equationobtainedbetweena~propr@te.3i~t.s-is... ,.”.:.,--
~y integqtinge~~tio~(C13).=.......“..-.-+_ *-. ; -,-.~c..zA.,. ...:,---:.... .;-T.-:-----...=.-,, ~.
.-
.+,
.
()l+xh++1% ~
.-_.-.:(j;loge+-&& (Clk)~.. .,-. .
..—
— —
..-.
.—
_>
._. . .. . . . . ...=
,
Y=
--NACATNNo.lZOO
-@PJo
XJo(m - LhD)(l+ ~)
O’1)-LLhD)
X2(X*+ yz -yx‘- 2X)(z- x)*(y-X)2
b_=x(2yz-xy-x%~x (z- x)2(y.- X)2-_ ,
-$” ““”-” ‘~“=(y- X)2(Z- y) .
(cl?)
~z
(z -’x)% - y)
w
.
Equations(Ck),(C7),(Cll)~and(C14)wereusedto computetheTressureratiosat thetransitionIaveleonlyinthetentativestandardatmosphere.By dividi~thesep%wure ratioshy,thepressu~eratiosat thesametransitionIsr7el.aobtainedby useof .theequationsInaypendixB based.on‘ac~taxt &lue fortheaccelerationof~vity, a conversionfactorwasobtainedforeachoftheseveraltransitionaltitude~,Sinceitwaeimpnctical .tousethesecomplexequationsfordfrectlyccmputingthepressure
, .=
—
.,
NACATN No.l.EOO
ratiosatallthelevelsrecordedintableaTV end7, thevaluesat thesenumerousintermediatelevelswerearrivedatfollows:
(1)Foreachaltitudea valuefortheconversionfactorwascomputedby algebn%lcsummationfromtheequation
as
(c16)
where ??gisthepressuz%basedonthevaria%leva3ueof g,and p isthepressurebasedona constantvaluefortfieaccel&k-
— --—
tionof gravity.In equetion(cI.6)thepropervalueof g, T,andof M wassubstitutedforeachre@on of theatmospheresaccordingto equation(C2),(C~)jand(C9),respectively.
(2)Thevaluesof pg/p so computedwereplottedagainst ~~._altitudetodefinetheshapeof thecurverelatingpressure ratiosto altitude.
(3)Theaccu~tevaluosforthepressurera.ttocomputedbyequations(CA) (C7),(Cll),and(Clh)and%y equations(B4),(B8),(B12)$ti(B14\werealsoplottedandanothercurvewasdrawnthroughthesepointsrepresentingtheaccurate~computedmtlosandfairedaccordingtothecurvedrawnthroughthepointsobtaineriby useofequation(C16).
(4)Thecurvearrivedat fromstep(3) was then usedto obtainconversionfactorsforeachof thealtitudesrecordedfnta%lesIV andV.
NACATN No.WOO
APPENDIXD
MOIE2UIARM%3NFRE?3PATHS
RatiooftheMeanFreePathsofMoleoulos
Theconventional equation for the mexm fre.opath of themoleculesX ofa gas(reference10 is
x 1=—x !’zFNF (Dl)
Thereforetheratioofthemeanf~e pathat anyaltitudetothevalueat sealevelis
1+)L)(J5 2&c- (D2)
But
and
(D~)Nrn=P
(Dk)
Therefore
(D5) ‘
x ‘O T q ‘O’()2—=—— —..ho PTO~ a .
(D6)
.
N.RCATN No.MOO 31
Forallconstituentsoftheatmosphereexceptoxygenintheregionofdissociation,
u = co
In theabsenceofava~~b~ data011theMater of atorile of oxygenrelativetothatofmolecularo~gen,andin cmslderatim of thefactthatthesmalldifferenceinthesetwodismetersofoxygenhasan evensmallereffectupontheaveragediameterofall.atmosphericconstituents,andforreasonsof sfmplic~tyit ishereinas-d .foroxygenalsothat u = UC. Fortiepurposeof computingthesetablesthereforeequation(D6)is@mpllfiedto
L PO*T g—=—— —Xo PTO@
(D?).——
Furthermore,inthosecomputationsthatarebasedona constantvaluefortheaccelerationof gravity
-.
G = &-J
whenceequation(D7)isfurthersimplifiedto
(D8)
MeanFreePathsofMoleculesat SeaLevel
Thevaluesof themeanfreepathof themoleculesat sealevel.giventnt@ble.I_are_fornl.t.rogenen~o~gen mlgcqleg..ina 90Z’DELatmosphericmfxtureofnitrogenandoxygen.ThesemeanfreepathsaredesignatedXn ad ho, respective=.A weightedaverageoftheforegoingmEanfreepaths,%asedupontherelativevolumesof~mogenand oxygeninairisalsoincludedand isdesignatedXair.
Themeanfreepathof thenitrogenmolecules in theatmosphereat sealevelwascomputedby thefollowingformula(p.99ofreference18): -—
—
32 NACATN No.I&XXI
where
Nn numberd’ nltmogmmleoulee Qerunit wM3Mof air
l’?~ numberof oxygenIMLeculesper unit voluxoeof atr
u~ diameterofaitrogenmolecu3es
60 diameterofoxygenmolecules
T a$remgeMameterofnitrogenandoxyw molmw.leff
% avexagespeed.
?50 avexqjespeed
S@U1.arly,themeanwa8mmputetlby
oftitro~nmolemles
of OXYp mdeculaci
free pathof the cmyp B@eou!l.esat sealevel
(W)
Thevalueafor the &vemtgespeedq~ and ?JOwereolta$nedfrom
@thefoxmulaT = . Thevaluesfor u were* from
thenwdberof moleculesof nitrogenandcmygan,respectimSy,perunitvolumewerecalouf.atedfromthe LcwOmidtmmberandthe
rel.atiwwhlme 0? thenitrogenand=*II inalrat ma level.
.
NACATNNo.1200
APPENDIXE
33
VAIUESOFCERTAINCOI?S7UWI!S-.. —
TentativeStandardAtmosphcmeatSeaLevel
Thestandardsea-levelvaluesforvariouspropertiesof theatmospherehavebeenlistedinreference17andsea-levelvaluesforcertainotherpropertiesareltstedinreference5. Mostofthesepreviouslylistedvaluesareadoptedforuseincapputingthetablesherein,buta fewchangeshavebeen=de. Thechangesareas follows:
Speedofsound.-Thevaluesforthespeedof soundhavebeenalteredslightlytoavoidthediscrepancywhichexistedbetweenthevaluespreviouslylistedandthevaluescomputedby theconventionalequation .._
(El)
Thevaluesfor ~ listedintableI arecomputedaccordingtoequation(El)by usingtheappropr5.atevaluesfey_7., Po) and Pothatarealsolfstedintable1.
‘-”- ThevaluesfordensityintheBritishengineeringsystemhas een.changedfrom0.002378.to0.Q023779slugspercubicfoottoavgiddiscrepanciesresultingwhencomputationsarebasedeitheronthestandardizedvalueforspecificweight,1.2255kilo-gramspercubicmeter(reference1),oron thederivedvaluefordensity.
Molecularmeanfreepathsandmolecularweight.-In additionto thevariousquantitiespreviouslygivenj.nreferences1 and5, thepresentpaperlistsmolecularmeanfreepathsand.theaveragemolecularweightofnormalsea-levelair. Molecularmeanfreepaths
.—
forthenitrogenmoleculesandoxygegmolecu~sin thenorml airnrlxturehavebeencomputedanda weightedaverageforairhasteentaken,as describedinappendixD. Theaveragemolecularweight- ofnormalsea-levelairistakenas 28.966inaccordancewithreference19,
.
L
34 NACATNN~.l.ZOO w
,.
wg~ewme.- Thevalueforpressure in the Britishengineering
system-en changedfrom407.1or@7.2 Inchesof waterat 15°Cas usedinreference~.$mdreference2P,respectively,to 407.15inchesofwaterat 15°C. ThisvalueOf407;15iEIthecomputedvaluecorrespondingto 760mill.imetere of mercurybasedontheauxiklaryconstantsandconversionfactorslistedInthelastsectionofthieappendixE.
TableofSea-LevelValues
Thevaluesforthevariouspropertiesof theatmosphereatsealevelcorresponding~.otheafioptedvaluesforprobableminimum
,
andprobablemaxinmmt~eraturewarecomputedfromthevaluescorrespondhgto standatisea-leveltempemtures,Allthreesetsofvtdueaunits amlistedinsyi3tem.
uo~dinbothmetricandBritishengineeringsystemsoftabulatedinta%leI. In someinstancesa q’zantityismorethanone unit; ineitherthemetrfcorBritish
AuxiliaryConstantsandConversionFactors,
Inadditiontotheatmosphericpropertiesat sealevelgivenIntableI certainotherbasicconstantsandconversionfactorsareusedincomputingtablesII to V. Theyare
Auxiliaryconstants:
Dengityofmercuryat@0 C, gm/cm3. . 13.5931“i; : : ; :Standardaccelerationof gravity,~, cmjsec “ 9&o.665
DensityofwateYat-15°C, @/ml . . . . . . . . 9 . ●“”0.?9?~~Radiusoftheearthat.45°Iatltude”and.at sealevel,n 6,367,623
Conversionfactor~:
l-lb= 453.5%4w
1 meter= 3.2ti3833ft “ . ‘
‘Fa%s= % + 459.4
1 ml= 1.000027CR13
I’7ACATN NO.1.200 ““35
REFERENCES,.
1.Diehl,WalterS.: StandardAtmosphere- TablesandData. NACARep.No.218,1925.(rReprint1940.) ——
2.Gregg,WillisRay: StandardAtmsphere.NACARep.No.247, 1922.,,3. Brombacher,W. G.: Ta%lesforC@ibratingAltimetersandCom-
putingAltitudesBasedontheStandardAtmosphere.NACARep.No.246,1926.
..4.Brom-cher,W. G.: Altitn~de-I’ressureT8hle8Basedon theUhlited
StatesStandardAtmosphere.NACARey.No.538,1935. -
5. Aiken,Williams.,Jr.: Stanfl.ardl?oqenclatureforAirspeedswithTa%lesandChartsforUseirn”CalculattonofAirspeed.NACATNNO. 1120,1946.~fi~flk’@~F~~@*P37
6.Anon.’:MeteorologloalAspectsofEigh-Altltude3?light.Rep.No.847,WeatherDiv., HeadquarterdAAl?,Dec.1944. (Now “-distributedhy Headquarters,AirWeatherSetice,AirTransportC!onmand.) “, .,
7. Ratner,Ben@lin: TemperatureFrequenciesintheUpperAir.WeatherBur.,U. S.Dept.Commerce,Jan.20~.
8.MUIIWI,D. F.jamd.Pulley,0.O.~ TheTemperatureandConsti-tuentsofthe‘@perAtmosphere.I&cc.Rby.Sot.(Lordon),ser.A, vol.154,no.882,April1, 1936,pp.453-486.
9.Pekeris,C. %,: AtmosphericOscillations.X’roc.Roy.Sot.(London),ser.A, vol.158,no.895,Feb.3,1937,pp.65&671.
10.Martyn}D. 1’.: TheUpperAtmosphere.C - GeneralDiscussion.QuarterlyJour.Roy.Meteorol.Sot.,vol.65,r.o. 28131939,pP.328-330.
11.Pennflorf,R.: DieTemperaturederhohenAtmos@re. Meteorol.Zelt~chr,,Bd.58,Heft1,Jan.1941,pp.1-10, (Ti~~iationinEu.Z1.AmericenMetecmol.Sot.,vol.27,no.6,June194.6,pP.331-342.)
1.2.Whipnle,FredL.: MeteorsandtheEarthtsUpyerAt~sphere.Rey.ModernPhys.,VOZ.”15,no.h,Oct.1943,pp.246-264.
13. Gutenbere$B.: PhysicalPropertiesofIOom. Jour.Meteorology, vol. 3,
theAtmosphereUp toJune1945,pp.27-30.
36 NACATN NO.MOO
14.Wulf,OliverR.,endDerning,LolaS.: OrJtheProductionoftheIoncspherlcRe@onsE andF andtheLowor-AltltudeIonizat-ion CausingRadioFade-Outs.Terr.Mag.$vol.43,nG.3,Septo1938,pp. 283-298,
15, Anon.: Nomenclaturefor Aeronautics.NACARep,No.474,1941.
16, BirCLUDEJhEIW,L. L., and S$ott, VaughanH~: Vlsc@aityof Gat3eBaInternationalCritical.Table8,firstcd.,vol.V. McGrav-HillBookCo.,Inc.,1929,p. 1.
17cAnon,: ThmrettmlGravityatSeaLevelforBachMinuteofLatitudeby theInternationalFormula.U.S, Dept.ofConnzerce?CoastandGeodeticSurvey,1942.
18.Loeb,LeonardB.: TheKineticTheoryof@ses. Secondcd.,McGraw-HillBookCo.,Inc.,1934.
19. ~ildt, Rupert: l!heGeochemistryoftheAt.muaphereandtheConstitutionoftheTerrestrialPlanet8.Rev.ModernPhys.,vol.14,nos. 2-3, April-July lglt2,p, 152.
20. BeiJ,K.Hilding:AircraftSpeedInstruments”.‘NAC”ARep.No.420,1932.
1
.
qurmtitj
Tem?xmmtu-e
Absolute~~
Pre8Bwe
Spolric weight
Ilemity
Coeffloiemt of tiaOOBiQ
Kinamatfovlsconltr
sped or mvnA
Hem mm path ofnltromn smleoulm
man *Ba pm or
O.vmn Ib31eaulma
Ralativa volume ormen
II
. . ,
..
unit
‘c
%
[eEm E2 d 0°0
oymO/am2j-WA\@ne./.m3k2-B002b4rhA-ama/m2
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[-
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m
m
m
____
----
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MO*1O 0n2ineerh2 m-m
At pobmble
tempomme
-48.0
225.0
“m
10332.3
1.0132%106
1.5686
1.533
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1.4
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unit
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lb/ft2
lb/ft3
Olw/ft3
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[
rt/m
@
kootm
rt
ft.
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._ —-
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t-mpematme
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672.69
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NACATN ISJO. 1200
TABLESII AND III
38
PROPERTIESOF THE UPPERATMOSPHEREFORTENTATIVESTANDARDTEMPERATURESBASEDONANARBITRARYCONSTANTVALUE
OF GRAVITATIONALFORCE
The followhg set of two tables (tables D and~) constitutesaconsistentextensionof the standardtables for the lower atmosphere(NACARep. No. 218). Consequently,altitudes in this set of tables. whichcorrespondto specified ambient-airpressures maybe referredto as “tentativepressure altitudes,” andthosewhichcorrespondto aspecified ambient-air densitymaybe referred to as “tentativedensity. altitudes” (NACARep. No. 474).
NATIONALADVISORYCOMMITTEEFORAERONAUTICS.
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—
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NACATN NO. 1200 40
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..—— *
NATIONALAOVISORYcOHWT7EEF~ AERONAUTICS
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41
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NACATN No. 1200 42
.
.
1
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COS9~ VALUEOF OSAVTTATIOKALFOROE— 2ECT19Hmlcmsmm s29= — Otinttiued -—
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NACATN NO. 1200.
‘TAsmIIL-PRO~~S OF~ O’F- A’IMOS~ FOR TSRT.ATIVSSl!ARllAFDTSMF2RATORSSSASSD OH AR ASBITfUSY
00SSMRT VALO’SOF GRAV77!MZOML FOROS- SRITISEEilt31sE2RImSYW2H. Omoluded
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are baredon the conventiorwlSuWerland fomuln for norml Plr and, oomequentlr,m allowancehas been nude for the efreatof dlssoolatedoxygenh the ata!c.smere at thehigherleveln.
RATIOHAI,Am-mxiY00KWI!TESFOR AESOSAGTICS
NACATN No. 1200 44
TABLESIV ANDV
PROPERTIESOF TEE UPPERATMOSPHEREFORTENTATIVESTANDARDTEMPERATURESBASEDONAN INVERSESQUAREVARIATION .—
OF GRAVITATIONALFORCE
Thefollowingset of twotables (tablesIV andV) does notconstitutea consistent extensionof the standardtables for thelower atmosphere(NACARep. No. 218) but takes into accounttheinverse squarelawofgravitational‘attractionand, consequently,the values in these tablesare more accuratethanthosein tables II andIH.
NATIONALADVISORYCOMMITTEEFORAERONAUTICS.
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NACATN No. 1200 46
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RATIOHAL ADVISORY.
COM41T5?SEFORAEROKAUTIOS
NACATN No. 1200
TABIS~.-
IRV2RSB
?
49
PROPERTIES OF TBS UPPER ATMsFIERS FoR-ATTVS STAHOARD TKKF2RATQms BAssn ox As
S- VARIA~ON OF ORJYITATIOEAL FOROE– BRITISE~IK2ElI~ SYST2N– Conoluded
Absolutaltftude, taqMrR- Fre.mure, Fresaure Deylty, D=wt;r
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Furthmmore, the values 11s ted
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.-
YATIOK4L ADVISORYCO19UTT=SFORA2ROSAOTICS
I● ●
TABLEVT.- LAT’ITWX3 CWtFOlC~OHFA2TCRS ~ V- OF FR2SS021 IN MEl,&9 NA2D V
Altltude, b’ 40 ,50 60 70 80 w
(i-m)
mEi%262,467
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1.02781.0312
1.0260
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NACATN NO. 1200
Y
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I I/m /?@ J@ 49 5@ m- ”-”
Absolutetemperature,T, ‘KNATIONAL ADVISORY
COMMITTEEFORAERONAUTICS
Figurel.- Variationof ambienttemperaturewithaltitude.
●
— Day and n~@t
= — rny only
‘“— Eight only
II./ .2
\\
I ‘“ “,‘“\
h\\
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Night OIi@
-i---l-NATIONAI. kWISORY
COtmll-m FLwAERONAUTIC!
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—
—
—
(.9) Relative volume of molecular oxygen, Vm. (b) Average molecular weight, M.
Figure L.- Variation Or cornpoel~lonof the tentative standard atmosphere withaltitude. (The dissociation of oxygen iS the only chenge In mmpo8itionoccurring in the tentative etandard at~sphere. )
,“ A . .
,,, ,,,,
—
—
—
—
—)
. .
rNATIONAL ADVLSORY
Cowtll-iff m AERONAUTICS
(a) Ratio Orspecificheats,y.
I* .
log p, lbirtz
4 L u z 4
log p, l@U2(b) Pre8sura, p.
Figure3. Varlatlon with altitude of the physica~ properties of the tentative.gtandarrl atmosphere.
i,, 1.
F-+ J-
?,
\.
- Day and night\
——— Day only
——-—- Night only
I/0 d 0’ 4 L
h(9
log p, kg-aec2/~
(c) Density, p,
F@.me 3.- Cmtlnued. NATIONAL AOVISORYCLWIITTEE FOl AEROMAUTK.S
log-, lb@
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I I.4 6 JW-’
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1 2 J
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,F@re 5.- Conttiued. NATIONAL ADVISORY
, CMml-rm Fol MRCNAUTKS.
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.—-— - Night only_/
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log v, m2/8ec
(f) Kinematic viscosity, %
Il. II
I
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HATtONM ADVISORYFi&u’e 3.- Concluded. @mHITm FORMRMMITtu
%$’
1/ 0$’“5
—-— night only
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