,----~.-

—

NATIONALADVISORYCOMMITTEi-------FORAERONAUTICS

.,. .

TECHNICALNOTE —

-.

.TENTATIVETABLESFORTHEPROPERTIES --

, OF THEUPPERATMOSPHERE. ‘“1 —

.* By CalvinN. Warfield ....

for the ..—..----

NACASpecialSubcommitteeon theUpperAtmosphere“--’”

LamzlevMemorialAeronauticalLaboratory

.- -.

-- .L --

z-

LangleyField, Va..-. ... :.. .——

,.. .—

--—

Washington ““v:.-—.

N A CA lJIRARY-.” .....LANuwYnMmAi.A.m9N.AuikB?k

January,1947,,

J-w LABORATORY.,...,.

LangleyFkkLV8. . ,“

. ..-—— ---

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.

—

—

.._. . -

Two setsof tablesbasedupcntheadoptedtentativestandardspecificationsfortheupperatmospherearepresented.Onesetoftwotablesisbaseduponthesamearbitraryconstantvaluefortheaccelerationofgravityas wasusedin thepreparationoftheexistingstandardtablesforthelowerlevels(NACAReportNo.218).Thissetoftablesfortheupperlevelsof theatnmspheratherefore

.

constitutesa consistentextensionoftheexistingstandardtables.Theothersetof twotablestakesintoconsiderationthedecreasein theaccelerationof gravitywithincreasingaltitudeandthere-foreismoreprecisethanthefirstset. Consequently,thisset

— .—

ispresentedonlyto satisfytheneedforgreateraccuracythatmayexistIn somefieldsofresearch.

EachtableisdividedIntoseparatepartsforbothdayandnightconditionsataltitudesabove&lkilometers.ThenecessityforseparatetablesfordayendnightvaluGsisoccasioned_bythe

&

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,

-T

NavyDepartmentCapt.WalterS.Diehl,USN,BureauofAeronautics,Navy”

—

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

—

InstituteofTechnology.Mr.JeromeTeplitz,NACA,Secretary.

-.

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.

..

—

—

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.

b’

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.

*

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

@%:/m2)$/,80

[-

Ujaaa

m

m

m

____

----

..----

MO*1O 0n2ineerh2 m-m

At pobmble

tempomme

-48.0

225.0

“m

10332.3

1.0132%106

1.5686

1.533

0.15$95

1..wma0-6

N5&x@

9.2twx10-6

W&m

l@.6

5.7&.w-8

5.7W-8

5.W’JO-8

28.9%

1.4

0.20% J

.t zten3m-ammparatmv

15a

288.0

760

10332.3

,.01325xI06

1.2255

1.2018

0.124966

.,fmlwo-c

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14,553x10-6

340.22

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28.966

1.4

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I

.t probable

mmpmatorm

v. o

320.0

763

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1.olwxlo6

l.lm

1.0816 1

0.U2Vf

1.575MI0-61

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l~L 1

8.2CM10-8

8.M3w-8

8.lSUO-8

28.566

l.k

O.mugj

,,

unit

%

% ah.

In.mg at32%h. miterat Uf’2

lb/ft2

lb/ft3

Olw/ft3

lb-n@t2

rt2/m0

[

rt/m

@

kootm

rt

ft.

ft

1---—I

._ —-

1_---,

,,

1. 1

rltlahmumll

At ~okble

t-mpematme

-54.5

405.0

29,9212

W*

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o.0030!37

3.04’2mo-7

,.999kla-4

g%.m

672.69

*.16

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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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..—— *

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

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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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NACATN No. 1200 4(

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NACATN ~0. 1200

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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

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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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-i---l-NATIONAI. kWISORY

COtmll-m FLwAERONAUTIC!

I1

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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@

I I-d -0 & /2 o

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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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——— nay only

.—-— - Night only_/

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(f) Kinematic viscosity, %

Il. II

I

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HATtONM ADVISORYFi&u’e 3.- Concluded. @mHITm FORMRMMITtu

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