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Air force surveys in geolpysics No. 115
The ARDC model atmosphere, 1959
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Th. Mr~ Forcz Surveys in Geophysics is a publication series the Geophysics Research Directorate, Air Force Cambridgo3 Research Laboratories, Air Force Rassarch DiviAhion, Air R6eearrh and Devrelopment Command. The sole purpose of this i;Ories iz 'Wo satisfy, to the wrAxirnuuc possible extent,prs engineering %r o-Perational piwoblevis of the Depmrtment of and espocially those of the major com~mands of the U")itd Stammt Air Force'
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Air* Porce Surveys in Gophysics No. 115
THE ARDC MODEL ATMOSPHERE,
1959
1
R. A. MizerK. S. W. Champion H. L., Pon'd
August 1959
Photochemititry Laboratory (3EOPHYSICS RESEARCH DIREC TORATE AIR FORCE CAMBPUhGF RESEAR1CH CENTER Alf?, RESEARCH AND DEVELOPMENT COMMAND11UN'ITEL) STATES AIR eOll(2E Bedflord, Mass.
FOREWORD
The 19.q AiDC Model .. rnosphere Is a revision of the 1956 APr.c Model Atmosphere based on new rocket and satellite data.. To an altitude of 53 ilometers the two models are the same. Following the methods developed for the 1956 model, the defining function of the atir I shV7_ Agm'u, LL ku~e en perture.n .1oa-i mosphere is the molecular- scae function for both the 1956 and 1959 models. The quantities tabulated, defining equations, definitions, and conversion factors are those used in i25 the U. L1. Extension to the ICAO Standard Atmosphere. 25 towever, in
41
the present model the tabulation is given only in integral values of the
i
geometric altitude with corresponding values of geopotential altitudegiven in an adjacent column. plotted. average values of the various atmospheric properties are It is realized that density, pressure, temperature, composition,
S1Onlymodel. .... 1e
and related properties are functions of both position on the earth's surface and time. However, the amount of reliable data on these variations at, altitudes above 30 km is so acant that it is not included in the present 1959 model molecular weight curve probably represents the molecular weight at high latitudes, such as Fort Churchill, where the ]experimental data were obtained. At lower latitudes the molecular weight may be nearer the curve given in the 1956 model. Since the present model is strongly dependent. on the 1956 ARDC
Model Amniqphere and the U. S. Extension to the 1CAO Standard Atmos.phere,appropriate to acknowledge the contribution of the many
iselentl_
who helped in the development of these models.
I.
9001000 90 e00
IT
. Mn
... /
---
900
TM T M
MOLECULAR-SCALE TEMPERATURE KINETIC TEMPERATURE MEAN MOLECULAR WEIGHT MO= SEA LEVEL VALUE OF M
i
.
70
J700
Tooo 0 ~600 -
1,59 T. ........ "600w
.
S 5000-------
0 ~0400400zt2 00*
. io/'
I
/I ',K
2! 00
i'
300.0 200-
000'
2000.0:0.'
t1(10OKkm
+/
r
-scal
K'Of +--OK/-Mvs. i/mp., .
0
fMolecular- I .. '.:5 OKI 0 W .',1/k.,I [?1l i. 0,OK/
I
... ' All I , ..O00 0:"
,.
I000 2O 3000 4000 50
iiiFIG..I.
_]
TEMPERAURE IN k
I4
Molecular- scale temperature vs. altitude. (Th~edfnn
property of the model)
0
10u
AB9',TRACT A model 6f, the earth's , tmosphere to 700 kilometers i7. , Below 53 Idlometer:i,- Ae present aodel is the same as The ARDC Moc _. Atmosphere 1956. 10.iove this hei ht, changes have been made l-ased on data deduced from r,'61.ket flights 2nd from the rate of change of the orbL!:alperiod of satellit4S, At appro ;mately 600 ilometers the new mo, !e! gives densities that; a: 20 times .her than the 1956 model. B3elow 600 kilometers the two mr~eies gradu'ily come closer .togcther ,.zd t.1T he ,d.,,"t-r'; dencross at about 150 kIVrmeters. Fetween 90 and 150 1956 , half 'hat ofe Lrab sity for the 1959 mod iLis lowver,;4 In model at 120 kIlomete,':s. At thepresent time, the maximum atcitudl, a.. which density data fronn satelUteii.;Ihas been obtained is just below 700 x, kilometers. For this 1"easor the tables end at 700 kilonete:rs. Dashed lines in the plots pres~int a tentative ,xtrapolation of the data to 1000kilometers.
The value ofthe molecular we1~ht,, like other atmospheric properties, probably diepends on both locatitA and time. Tue 1959 mod curve probably repres:nts the molecular weighat high latitudes, suc , as Fort Churchill, wht..re the experimental data we.'obtaned. At '1 lower latitudes the mo/.ecular weight may be nearer tht-I,-ve the 1956 model.
V
C ONT ENTS Section Page
,Abstract List of Figures
v
ix
List of Tables1. 2. List of Symbols arct Abbreviations Introduction Basic Assumptions and Formulas 2.1 Perfect Gas Law and Hydrostatic Equation 2. 2 Relationship Between Geopotential -ind Geometrc Altitude 2.3 Relationship Between Temperature and Molecular-Scale Temperature 2.4 Altitude Fwaiction of Molecular-Scale Temper*l.ure Determined From Pressur,: and Density Data 2.5 Temperature-Height Profile of the 1959 Mode]. 2.6 Pres.ct......
xixji 1 4 4 5 8
9 11 13
2.7 2.82.9
Density Speed of Sound
14 1415 15 16
Mean Air ;article Speed (Arithmetic Average) 2.10 Geopotential Scale Height and Scale Height 2.11 Specific Weight 2.12 Molecular Weight, The Sea-Level Composition of I~he Atmosphere, and the Altitude Variation of Molecular Weight 2.13 Mole Volume ? 14 Number Density 1b 'Mean Free Path 2. 16 Collision 'e 4uency 2.17 Viscosity
16 20 20 21 22 22
vii
Section 2.- 13 1inematic Viscosity2. 19 Thermal Conductivity 2. 20 Relattonshi.p Between Various Properties 3. Termination of Certain Properties at 90 Standard Geopotentlal Kilometers 3.1 Viscosity, Kinematic Viscosity, and Thermal Conductivity 3.2 Speed of Sound Computations Sea-Level Values of Atmospheric Properties 5.1 5.2 6. 7. 8, Metric Units English Units
Page 2323 24 25 25 26 26 123 123 124 125 125 126
4. 5.
Ice-Point Values of Some Atmospheric Properties Based on P = Po Physical Constants Conversion Factors 8. 1 Metric to English Conversions of Units of
Length, Mass, and Geopotential8. 2 8.3 Metric to English and Absolute to Nonabsolute Conversions of Temperature Units Absolute Systems of Units to Absolute-Force, Gravitational System of Units, Metric -
126126
English
Las129
8.4A ....ZFFVjJ1X
Thermal to Mechanical Units, Metric - English.1.-
Appendix A - References for Rocket and Satellite DatarJ.o-,AA.
. ,. ,--r,,WJA
i,,. f.A%4 the -
thin A~1,tw t, nn 1' 11pAceerto Due-
to Gravity Appendix C References-
131 1,34 135
Systems of Mechanical Units
viii
LIST OF FIGURES OF ATMOSPHERIC PROPERTIES AS A FUNCTION OF ALTITUDE Figure Metric Units 1. 2. 3. 4A. 4B.'I
Page
Molecular-Scale Temperature vs. Altitude Variation of Atmospheri. Density with Altitude Var4tin ifMeau Molecular Weight with Altitude Kinetic Temperature and Molecular-Scale Temperature vs. Altitude Mean Molecular Weight vs. Altitude Pressure vs. Altitude Mass Density vs. Altitude Specific Weight vs. Altitude Acceleration of Gravity vs- Altitude Mole Volume vs. Altitude Mean Particle Speed vs. Altitude Scale Height vs. Altitude Number Density vs. Altitude Mean Free Path vs. Altitude Collision Frequency vs, Altitude Speed of Sound vs. Altitude Coefficient of Thermal Conductivity vs. Altitude Kinematic Viscbsity vs. Altitude Coefficient of Viscosity vs. Altitude English Units
Wii 2 i8 27 27 27 27 28 28 28 28 29 29 29 29 30 30 30 30
4C. 4D. 5A. 5B. 5C. 5D. 6A. 6B. 6C. 6D, 7A. 7B. 7C. 7D.
8A. 85. 8C. 8D. 9A.
Kinetic Temporature and Molecular-Scale Temperature vs. Altitude Mean Molecular Weight vs. Altitude Pressure vs. Altitude Mass Density vs. Altitude Specific Weight vs. Altitude
31 31 31 31 32
Jx
Figurei
Page Acceleration of Gravity vs. Altitude Mole Volume vs. Altitude Mean Particle Speed vs. Altitude Scale Height vs. Altitude Number Density vs. Altitude Miean Free Path vs. Altitude Collision Freqency vs. Altitude Speed of Sound vs. Altitude Coefficient of Thermal Conductivity vs. Altitude Kinematic Viscosity vs. Altitude Coefficient of Viscosity vs. Altitude 32 32 32 33 33 33 33 34 34 34 34
913
9C. 9D. 1OA. 10B. 1C. IOD. I 1A. IIB. 1iC. 1 1D.
7
x
ILIST OF TABLES OF ATMOSPHERIC Tables Atmospheric Properte. as a Function of Altitude, Metric Units* A. Temperature, Pressure, Density and Molecular Weight B. Acceleration of Gravity, Specific Weight, Scale Height, Number Density, Particle Speed, Collision Frequency, aim! Mean Free Path C. II. Sound Speed, Viscosity, Kinematic Viscosity, and Thermal Conductivity PROPERTIES Page
35
51 67
Atmospheric Properties as a Function of Altitude, English Units* A. B. Temperature, Pressure, Density, and Molecular Weight Acceleration of Gravity, Specific Weight, Scale Height, Number Density, Particle Speed, Collision Frequency, and Mean Free Path Sound Speed, Viscosity, Kinematic Viscosity, and Thermal Conductivity 77
95 113
C.
*
Anonrdlng
Tabulation is on integral values of geometric altitude, but the corres(nonintegral) values of Reopotential altitude are included.
xi
LIST OF SYMBOLS AND ABBREVIATIONS
ezacceleration a radins of the earth at the equator b subscript Indicating base or reference levelponvau BTU British Thermal UnitIdegees
H
~
geopotential scale height rn JJuocdicd geopotc-ntiU altitude sbcitidctn c ic international nautical mile degrees, in thermodynamic Kelvin scale thermal conductivity kilogram- calorie kilogram (mass) kilogram (force)
i. i n nit
Cal
OF f fps
inthemodnani~c Celsius scale C seedof sundOK 5 S calorie enimeerkg-cal cm E enrgykg degrees, in thermodynamic Fahcnh~tScale ellipsoid flattening F frcekm foot-pound- second system of untskloer
k
kgf
kg-miol kilogram- mole kilometer kkilostandrgpoeta kwhr Lma kilowatt hour rept molecular- scaletemperature g Iradient
ft'tadrgeotita foot stndr gepootW oo dimensional constant InL, G geometric -geopotentia
relationship9acceleration of gravit, effective valuee
Ilength lb pound (mass) lb 1 pound (force)M
I:
gm
the equator gram
LO
'"
W_
mean moiecular weightof air m ~meter meter mass
i
g-molgrammol Haltitude in geopotental measure H9H8
standard geopotentia.mnillibar
mercuryscale height
mbinks
meter- kilogram- second
N n r. nt o
Avogadro's number number density (positive integer in Eq. (B-i) Loschrild's i_,'u.lber newton subscript indj.catl, level value pA ... sea-
thsd ftt
temperature in nonabsolute thermodynamic scales thousands of feet ice point temperature in nonabsolute thermodynamic scales particle speed (arithmetic average) mole volume of air under existing conditions of T and P altitude in geometric measure constant used in Sutherland's viscosity equation ratio of specific heats
V v
pdl al51 poundal degrees, in thermodynamic OR Ranlne scale universal gas constant R* effective radius of earth r see T second'a temperature in absolute thermodynamic scales Ti ice point temperature in absolute thermodynamic scales molecular- scale temperature in %bsolute thermodynamic scales time
Z
y
coefficient of viscosity mas desity mass density effective collision diameter of a. mean air molecule latitude of the earth specific. weight
p a'
T
M
t
xiv
THE
ARDC MODEL ATMOSPHERE,
1959
I
1.
INTRODUCTION.
New data from rockets and satellites have indicated the need of revising The ARDC Model Atmosphejr_956. 2, 3, 26 The new data consist of density measurements on rockets in the region of 110 to 220 geopotential kilometers (km') and densities inferred from the change in period of orbit of satellites having perigee altitudes of 1710 to 650 kn. The actual data on which the 1959 Model Atmosphere is based are shown In the lower right-hand corner of this figure are listed eight rocket flights from which density data for altitudes above 100 km' was obtained. The data from flights of 7 March 1947, 22 January 1948, and one point at 219 km' from the flight of 7 August 1951, were used in derlvation of the 1956 ARDC Model. The remaining five flights and addition., al data from the 7 August 1951 flight were not available for the 1956 Model. Between 120 and 130 km' the spread of data is within about a factor of two. If the data of the test of 18 October 1955 are neglected because of its unusual variation with altitude, the mean of the data between 120 and 130 kin' is considerably below the 1956 Model. In the region of 200 kn the spread of data is covered by a factor of 20 and the mean of the data is about four or five times higher than that of the 1956 Model. The horizontal arrows in Fig. 2 indicate the possible errors in data based on estimates given in the references listed in Appendix A. Rocket data for lower altitudes is shown by shaded areas in Fig. 2 which nf bOdvidual rocket flights. nmh"br e o of -A larga a t Densities computed from satellite observations are also shown in Fig. 2. The now calculations by Champion" were made using the method and orbital data supplied by the Air Force Camdeveloped by Sterne bridge Research Cenier Project "Space Track," Project "Vanguard," and the Smithsonian Astrophysical Observatory. lates the density to the rate of change of period. Sterne's equation reThe particular satellite n Fig. 2.
is specified by its effective cross- sectional area, mass, and drag coefficient. (Author's manuscript approved 29 July 1959)
____
-
AROC
956
-60
00
(L
-------
\.I_14
S200Z-ze
ATLTEDRIE A1CHAMPION OTI4RS 19TQ O x___ WHITE SANDS 7 MARCH'47 in W IE$N42 JA 8 WHITE SANDS T7AUG5*1
LU;
HAMPtI
6OTHERS}
WHITE MII 10OC
455
STRN HAFIONE 1OINT U CAMIS N 1986 O CHAMPION
O
EAC O0VERLAP SHOWN
CHRCIL CHURHIL
ITOIV
IN
A-I ClMI -10 _1" AN t% ~LG fo
1
-8 -612 PO-2 (DENSITY m_
0
FTERN FOR~heiofIN ONEa~oOit 2AS EACH~t
APltitude.N16
v .I
106a
AD)
U HZ
VRA
2
For a sphere and for other bodies with their orientation varying randomly, the effective cross-sectional area can be taken as one-quarter of the total surface area of the body. A nonstabiized satellite can be considered randomly oriented if its motion is averaged over a sufficiently long time. For a cylinder, such as the Explorer satellites, the effective cross- sectional area could change by as much as a factor of 10 depnding on its orientation. The appropriate range of densities obtained by Champion from .xplnre- T 1195 , .- 41^ l.n-dth-n cAqel of the satellite side-on (lower density) and end-on (higher density) at perigee is indicated by the horizontal dashed arrow in Fig. 2. The range for other Explorer satellites (.1958 b and 1958 6) Is the same, and for Sputnik U and MI (1957 P 1 and 1958 b 2 the range is somewhat smaller. In addition, Champion has also Investigated the possible variatlon in the drag coefficient for different- shaped bodies moving in free molecule flow. The shapes considered were cones, cylinders, and truncated cones. The variation in the drag coefficient from the value of 2 for a sphere was about 25 to 50 percent. There is some doubt about the densities derived from Sputnik I carrier rocket (1957 al) and Sputnik H (1957 p 1), since the values of the ratio of mass to effective cross- sectional area have not been published for these satellites. The densities plotted for these satellites were calculated by using values of the ratio of mass to effective cross- sectional area based, on the estimated size and mass of the satellites. Although there is some spread of the computed densities, all values derived from satellites (extending from 170 to 650 kin') are higher than the corresponding densities of the 1956 ARDC Model. The difference !s small at 170 kin' but increases with altitude. As shown in Fig. 2, the estimated mean values of densities derived from satellite data tend to lie on a smooth curve. At 600 km' the new curve is about twenty times higher than the 1956 model, but the two curves gradually come closer together and finally cross at 153 km'. Between 170 and 200 km' the densities derived from rocket and satellite data are in reasonable ".% c s of the 1959 model Is
p
r3
somewhat lower, being about one-half that of the 1956 model at 123 km'. The present model is limited to 700 kin', since the greatest altitude for w-.1 denrs +y djt w.ere ,av,-lable was 656 km'for Vanguard I (1958 p 2),! (Dashed lines in Figs. 4, 5, and 6, pages 27, 28 and 29 present a tentative extrapolation of the data to 10300 kin.)
2.2.1
BASIC ASSUMPTIONS AN]) FORMULASIPerfect Gas Law and Hydrostatic Equation The atmosphere is assumed to obey the perfect gas law, 14 1 PM P R*T
(1)
where, in inks units, = density in k g m- 3, p P T - atmospheric pressure in newtons m 2(kg m sec = temperature in OK, 1 3 R*L =universal gas constant, 8. 31439 x 10 joules kg (OIC1
M
molecular weight of air (dimensionless).
The air is assumed to be in hydrostatic equilibrium 1 5 and to
satisfy the differential equation,SdP=-g p dZ where = acceleration of gravity In m sec- 2 g Z = geometric altitude in m. Equations (1) and (2) may be combined to obtain the usual differeatial form of the barometric equation, dLnP which contains five variables. dZ For calculating pressures below 30 (3) (2)
k1lometers (100,000 ft), it has been customary to assume g and M to be constayit. Thus the replacement of T by a linear function of Z permitted Eq. (3) be simply Integrated. to For the high altitudes to which these tables are computed, the
4
simplifying assumptions of constant g and M are no longer valid. The replacement of g and M by even very simple functions of Z produces 31--I Ile ,cd,.i adcl -LI conskderabie complexity upon integraLion. .. , ;3.zu.'P1k'eaa of the low-altitude calculations may be retained, however, without the invalid assumptions of constant g and M, through two transformations of variables. These are the combining of g and Z into a single new altitude parameter, "geopotential H," and the combining of T and M into a single new temperature parameter, molecular-scale temperature TM. Defining TM as a series of linear functions of H then permits a simple integration with the resulting equations in exactly the same form used in earlier standards. Values of Z may then be extracted from H by using the known relationship between g and Z, and values of T may be extracted from TM- by assuming a function M of H. 2.2 Relationship Between Geopotential and Geometric Altitude
4!.j
Following the concept originally introduced by Bjerknes, vertical displacement can be expressed in units of geopotential. 7 Geopotential at an altitude Z Is the potential energy of a unit mass at that altitude relative to the potential energy of that same unit mass at sea level. Geopotential R of a point at altitude Z may be rigorously defined as the increase In potential energy of a unit mass lifted from mean sea level to Z against the local force of gravity, Mathematically this definition becomes,
AEG z m-= 1 g(Z)dZwhere AE increase in potential energy in joules,
(4)
ng(Z) H G
= mass Uf the body Ln klograrms,acceleration of gravity in m sec expressed as a function of Z, geopotentlal of a point at altitude Z proportionality factor depending on the units of H.
5
Solving Eq. (4)for H in terms of Z yields: f g(Z)dU (5a)
The differential form of this relationship to be used later is GdH = g(Z) dZ (6)
Geopotential is energy per unit mass. The basic unit of geopotentIal used in this Model Its one standard geopotential meter, m' , which is defined to be 9.80665 m sec 2 If one kilogram is moved through an intervPd of one standard geopotential meter, its potential energy is increased by 9.80665 joules. Geopotential Is essentially proportional to the product of the value of the acceleration due to gravity and the distance moved In the vertical direction. The constant of proportionality has been chosen so that if g = 9.80665 m sec-2, an Interval of one standard geopotential meter corresponds to a distance of one meter/ If g is less than this value, the distance in meters corresponding to one standard geopotential meter is increased. The above definitions of geopotential and the geopotential meter are in accord with international convention. 7 ' 13 However, it Is important to note that several recent reports have used a different definition of geopotential altitude. 2 8 , 32 The defining equation in this case is H* = -
1
Z
og(Z)dZ
.(5)
Here H*
has the dimension of length, but the numerical magnitude is the same as that of H defined by Eq. (5a), provided the same sea-level value of a is used. Thus the tables of geopotential altitude are the same for either definition. For those who prefer the second definition,
#
At sea level at latitude 450 321 33", g has the value 9.80665 m sec withbi tw.o parts in a mnllion.
_____-2
6
It is only necessary to replace H by
H* throughout and define H-* by
To evaluate geopotential as a functiufn vu geom-etric Oltitude fro Eq. (ba), a relationship between g and Z must be established. In an unpublished document, Lambert prepared a refined version ri '& previous equation 2 1 relating g to both altitude and latitude. The following is an evaluation of the refined equation for 45c 32 33" latitude: 1-3 , 2 - 6 g(Z)= 9.8066500 - 3.0864195 x i0 Z + 7.2539455 x 10-
H(Z)-
1.5167771 Y 10 -1 9 z 3 + 2.9724620 x 10-26 z 4 3910-3 5.9596 0 3 3 5. 5905936 X iO Z 1.0219762 x 0 Z6.
(7)
Substituting Eq. (7) Into Eq. (5) and integrating gives Z - 1.5731262 x I0- 7 z 2 + 2,4656553 10 - 14
z3(8)
3.8667054 x I0- 2 1 Z4 + 6.0621354 x9.5013649 x 10 3
I0- 28 z 5
6 Z
.
The followbig relationship, derived from Eq. (8) by use of Maclaurin's series, is used for computing Z for integral values of H: Z(H)= H + 1.57 31262 x 10 + 3.9380519 X i02 1
H2+ 2.4837966 X 10
14
H3
H4 + 6.2746418 x I0 - 2 8 H (9)
+ 1.0054032 x 1O- 34 H6
A much Simpler relation between H and Z, based on the Inversesquare law variaioun Of g, yieldM. iLetioi w-.,, ,if . . . Eq. (7) by only 4 meters at 300 km altitude (see Appendix B) when a suitable value of effective ear-t's radius I for latitude 450 32' 33" /Professor A. Miele of Purdue University has suggested the name "modified geopotential altitude" for H.. He has recommended the use of If* in model atmosphere work, since it measures altitude in units of length and eliminates the use of geopotential meters which have the dimensions of energy per unit mass.
7
Iis used. This relationship is
11where r 321 33" 2.30
S-\G. r + Z
(10)
356, 766 m, the effective earth's radius at latitude 4b =6,
Relationship Between Temperature and Molecular-Scale
IJTemperature
The molecular- scale temperature introduced by Minzner and Ripley 2 2 is the defining atmospheric property of this model. This prop-
4
erty is a composite of temperature and molecular weight, and is defined by the equation:
TM = (-i)where T TM M Mo
Mo
(11)
temperature in the absolute thermodynamic scales, =molecular- scale temperature in the absolute thermodynamic scales, molecular weight (nondimensional), sea-level value of molecular weight
No direct measurements of temperature have been made at altitudes above those which are reached by balloons, instead, the temperature i" derived from values of the velocity of sound, or by substitution of measured pressures or densities into the barometric equation. The i^,r,,. Q rc2 temne rature can be derived in this way without Specilying the molecular weight, whereas the temperature can be derived only if the mollecular weight is known. Since the molecular weight is not well known at altitudes above 90 kin, the molecular- scale temperature is more precisely known than temperature. Thus the introduction of molecular- scale temperature increases the validty of some of the tabulated properties while simultaneously decreasing the complexity of the mathematics relating the basic atmospheric properties. The use of molecular-scale temperature also avoids the necessity for changing Ohe
8
defined atmosphere eacn time new values for the inadequately known moecular-weight distribution may be adopted.The use of TM retdins consistency with ie u...
Ouiuaru
Atmosphere, since over the altitude region of that Standard (as well as to considerably greater altitudes), the ratio of Mo/M is unity, and hence TM = T over the same altitude region. 2.4 Altitude Function of Molecular-Scale Temperature Determined From Pressure and Density Data The combining of Eqs. (3), d InP dH (6), and (11) leads to 0~0
S-M
(12)TM-
R TM
where Q is a constant equal to 0.0341648OK/ml From this equation it is evident that the negative reciprocal of TM Is directly proportional to the slope of the curve, InP vs,, H. entiating Eq. (12) yields d 2 lnp dIl 2 Q TM2 dT M = dHi Differ-
(-3)
from which one sees that the altitude gradient of molecular- scale temperature (dTM/dH) is proportional to the rate of change of slope of the curve, InP vs. H, as well as to TM2. Equations (12) and (13) form the basis for the determination of TM vs. H from pressure-altitude data. Equation (13) may not be explicitly solved for either TM or dTM/dH, but this equation does assist in determining the approximate shape of the related TM vs. H curve. Equation (12), on the other hand, may be solved for TM; but, since TM varies greatly for even small variations in the logarithms of pressure, the values of TM determined from the pres sure data usually have a large scatter, and smoothing of either the initial pressure data o r of the resulting TM data must be _ v. n prui,,e. used to outain a reasonab, 9
For technical reasons, pressure data have not been measured T but density data are now available from above 120 km on rocket fihts, botd rocket instrumentation and satemte uIL ;;]vation to much greaer alt tidonr Consequently, one is forced to use more complicated relaJ tLon.s depending on density in deducing the variaton of TM with v" - '"c to H. If one eliminates T and M from Eq. (1) through the ITtroduction of E.. (11) and then expresses the results in terms of natvur;_).Iogar~thms, the derivative of this expression with respect to H yields dinp dH dinP dH dInTM -dH
(14)
The olirdnation of d .. nP/dH between Eqs. (12) and (14) provides the basic relationships between TM , p , and H, and thus provides the means for deducing TM from density- altitude data., These relationships are d Inp dH and d2) np
Q TM d 2 InTM
dJnTM dH 1 ~2 dT M
1 TMi
dT
M
N
Q
dTM
dTj'
1 d 2 TM
li'\2
lI d
TT diM
d
TM TMd
.(16)
Neither of these equations may be solved for TM or dTM/dH explicitly, and numerical methods must be used to deduce the TM vs. H profile from d,n--, data, The general procedure begins by drawing an average densityaltitude curve through the observed data points and estimating from this curve approximate values of TM and dTM/dH for the various altitude reglons by means of Eqs. (15) and (16). Then, starting at the lowest altitude region under investigation, a range of values of dTM/dH,
10
including the previously estimated values, are selected.
Each of these
TM gradients are then used to operate on the lown or accepted base va-lues of o and TM to determine a segment of the p vs. H curve. The value of dTM/dH yielding a density-altitude curve most closely fitting the data is adopted. The process is then repeated for successively higher altitude regions until a TM vs. H function and a related *density-altitude curve is constructed tj the highest altitude for which data are available. Equation (21) given in Section 2.7 is used for these computations. The deiisLtti hd C -,urve developed in this manner for the 1959 ARDC Model, along with its supporting satellite and rocket density data, is shown in Fig. 2. The related TM vs. H function is defined in the following section. 2.5 Temperature -Height Profile of the 1959 Model In accordance with precedent 5 * 12, 29, 31 and by agreement of the Working Group on FExtension to the Standard Atmosphere, the defining temperature parameter is a continuous function of altitude consisting of a consecutive series of different subfunctions, each linear with respect to altitude and with first derivatives which are discontinuous at the intersections of the linear segments. The use of such a function implied that the atmosphereis made up of a finite number of concentric layers, each layer characterized by a specific constant value of the slope of the temperature parameter with respect to geopotential. This slope will hereinafter be referred to as the gradient, LM ; It is equal but of
opposite sign to 'lapse rate."ature ftuctiont
-
The following is the general form of the molecular- scale temper-
whereH TM = geopotential (altitude) in m' = the molecular- scale temperature in OK at altitude H,
I
TM = (TM)b + LM(H -HO
(17)
11
IiI
LM = dTm/dl = the gradient of the molecular- scale temperature M in K m'-(constant for a particular layer) , Hb = geopotential in m! at the base of a particular layer characterized by a specific value of LM , (TM) b = the value of TM at altitude Hb The molecular- scale temperature functions of both the 1959 and the 1956 models are shown in Fig. 1, page iW. In the following table, the molecular- scale temperature at the extremities of each atmospheric layer and the gradient within each layer are given. Temperature .Height Profile of the 1959 ARDC Model Atmosphere LM (TM)b H
m'
(oK)320.66
(OK/m)-0.0065 -0.0065
I0
-5,000
288,16 i, 000 216.66
25,00047,00053,000 79,000
216.66282.66
0.0000 0.0030 0.0000
282.66 165.66
-0.0046 0.0000
90,000105,000 160,000 170,000 200,000 700,000
105.66225.66
O,00400.0200
1325.66 0.0100 1425.66 1575.60 0.0035 3325.66
0. 0050
12
2.86
Pressure
2.6.1. Standard Pressure at Sea Level The standard pressure at sea level, P , is defined as 101, 325 newtons m- 2 or 1013. 25 millibars. 10.11. 120 This pressure corresponds to the pressure exerted by a column of inercury 760 mm -3 (13. 5951 gm cm -3 ) and subject high having a density of 13, 595.1 kg m to a gravitational acceleration of 9.80665 m sec-2 2.6.2 , Pressure-Altitude Formula S The basic pressure- altitude relationship was given by
Eq. (3) in terms of five variables. The introduction of geopotential through Eq. (6) and the introduction of molecular- scale temperature
I
through Eq. (11) yields: In P
-GM o -GM 0 R*
d(18) TM
In terms of only three variables: P, TM, and H. Replacing TM in Eq. (18) by a function of H (in terms of a constant gradient LM) from Eq. (17) leads to expressions in terms of only two variables which, in turn, permit integrations resulting in the folowing equations for pressure explicitly in terms of geopotential: S P= Pb [(TM) 5 andP=
(TM)b+
b
GM/ R * L M
LM (H-
H )
forI. I3
0
(19a)
Pbexp
-CMo
R*forLm
(H
-
b)
0
(19b)
where P = pressure in the same units used for Pb, and where the subscript b refers to the value of the quantity at the base of the constant-gradient layer.
13
Density The formula for atmospheric density at any specific altitude is obtained by introducing Eq. (11) into Eq. (1) which yields: 2.7
MoPpR* TM where -3.4838395 10- __ TM (20)
3 p = density in kg m- , P = pressure in newvtons m-2
Lw '-n..
,it.U ( _ _J___4- _ _
fIn
an1 onmhinir. '_b_.........
p and Pb with Eq. (19a) yields: (TM)b Pb P =4 (TM) b+
th P Ynrp.qtion for .. .. .. .....
bnth
I + (GM/R*LM)(H -
LM
H
for LM 30. (21a)
When expressions for p and Pb from Eq, (20) are combined with Eq. (19b), P Pb exp R*(TM) for LM = 0 (21b)
in which the exponent is identical to that of Eq. (19b) 2.8 Speed of Sound The speed of sound propagation is defined in this model by the
classical equation,
Cs Li .][/-.oo*TMwhereC y P speed of sound in m sec"
=
2 20.046333 (TM)/
(22)
= the ratio of specific heats of air defined to be 1.4
pressure in newtons mwt density in kg m'-3m
2
For reasons which are discussed In a later section, the concept of the velocity of sound in the atmosphere becomes essentially meaningless at 'very great altitudes except perhaps for very special cases. To point out this limitation, the values of C1 are not tabulated above 90 ki
14
2.9
Mean Air Particle Speed (Arithmetic Average)
The mean particle speed V in this model is definOd as -t ar*thmetic average of the maxwellian distribution of speeds of al1 air particles within a given elemental volume, assuming that al air molecules have the average mass associated with the mean molecular weight. 1 8 The value of V thus determined for a given tcmperature is not exactly equjal to the weighted mean of the separate values of mean particle speed for each pure constituent of the atmosphere. However, this value does not depart greatly from such a weighted mean. The quantity V retains
Iparticles for their velocities to follow a maxwellian distribution,Ithe
its significance provided (a) that the volume considered contains enough and
I
(b) that variations of p and T/M in any direction are negligible within volume element. formula used for the computations is R T / ; TM = 27.035910 (TM)(23)
*The
S=
-
Mi
LM
]
where V =
air particle speed (arithmetic average) In m sec-1
2. 10 Geopotential. Scale Height and Scale Height Rearranging Eq. (18), an expression having the dimensions of "standard geopotential" meters is obtained, 25 -1 HT= ....nP R* TM G- o=
29.269897 TM
(24)
:: dH Vwhere H's = geopotential scale height fn m'. This property is seen to be equal to the negative reciprocal of the slope of the urve, LnP vs. H, and to vary only with TM. It is apparent that dH's/dH Is directly proportional to LM and that H' s is, there-
I--
fore, a linear function of H, Values of this property are not tabulated. Similarly, rearranging Eq. (3) and introducing Eq. (11) yields an expression having the dimensions of geometric neters; this expression
I
15
is given the name of "scale height. ,27 -1 R* T R* TM == I = -nP 9M gd gM o dZ
=
TM 2871.03963-
(25)
g
where Hs = scale heitght in m Scale height is seen to be equal to the negative reciprocal of the slope of the curve, JnP vs. Z, and to vary with TM as well as with g.F
2.11 Specific Weight The specific weight of a body of uniform density at any point in space is the weight per unit volume of the body at that point. The comr the putational equation is thus the mass pur unit volume times g, density times g, thus gMoP 3 gP (28) FL = Rg 3.4838395X 10TM R*TM where co = specific weight in kg, m2
sec- 2
2.12 Molecular Weight The Sea-Level Composition of the Atmosphere, and the Altitude Variation of Molecular Weight In this model, molecular weight is considered dimensionless. Values of molecular weight are given in terms of the chemical mass scale in which the naturally occurring mixture of oxygen isotopes has, by definition, a value of 16. In accordance with the ICAO Standard, 11, 12 the atmosphere defined by this model is assumed to be dry. The sea-level molecular weight M. I as determined by the sea-level atmospheric composition indine-ted in the following table, is 28.966 (dimensionless). In this model, the composition is assumed constant between 0 and 90 standard popotential kilometers altitude; consequently, the sea-level value of molecular weight applies in this altitude interval. To proceed from the molecular- scale temperature curve to a curve of kinetic temperature, it is necessary to know the mean molecular weight as a function of altitude. A mean molecular weight curve may be based on a theoretical description of the atmosphere or on the
16
Sea-Level Atmospheric Composition for a Dry Atmosphere/ Mol. Fraction Percent 78.09 Molecular Weight_(0
Constituent Gas Nitrogen (N 2 )
16,000)28.016
Oxygen (02) Argon (A)Carbon dioxide (C2)
20.95 0.93v3
32.0000 39. 94444 010
Neon (Ne) Helium (He) Krypton (Kr) Hydrogen (H2) Xenon (Xe) Ozone (03) Radon (Rn)
18 X 10- 3-4 5.24 x 10
20.183 4.003 83.7 2.0160 131.3 48.0000 222.0
1.0
X 10 4
5.0 x 10-58.0 X 10 6
1.0 x 10"6 6.0 X 10 "18
dicate the exact condition of the atmosphere. Ozone and Radon particularly are known to vary at sea level and above, but these variations would not appreciably affect the value of Mo.
-/Thesevalues are taken as standard and do net necessarily in-
results of experimental probes. Unfortunately, at the present timeneither basis Is adequate to an altitude of 700 kin', although it is hoped tnat satellite mass spectrometric data will soon remedy this deficiency. The variation of mean molecular weight with altitude above 90 km used in the 1956 Model Atmosphere wa based on theoretical calculations which indicated that oxygen dissociation commences sharply at 90 km and ia nearly complete by 175 kin', where diffusive equilibrium applies. Recent rocket data reported by Townsend 3 0 suggest that the molecular weights of the 1956 ARDC Model are in error, particularly between 90 and 200 km'. The average molecular weights deduced from rocket flights
17
70-
of a. Bennett mass spectrometerare compared with the 1956 model
600
values L Fin.\L. MODEL
. However, mnlec-
w5
ular weights determined from this curve, when combined with the
400 4959 Sature
values of molecular-scale temper..at corresponding altitudes, yielded a kinetic temperature curve with negative gradients (dT/dH < 0) in the region just above 200 km'. Townsend-s
NMODEL 0_-
--
-
0,oo
---
MOLECULAR WEIGHT ROCET OBSERVATIONS ROCKET 6SEVA~ONSurements
values of M are based on measwh lch are probably much.28 29
0
,5
1 17 I ,9
II. J_ I ' ' 2.0 21 22 23 24_ 25 26 27
less reliable than the various density data. Furthermore, the molecular weight data above 180 kin' represent the results of only
MOLECULAR WEIGHT (DIMENSIONLESS)
FIG. 3. Variation of mean molecular weight with altitude,
a single rocket flight while at lower altitudes there were three flihts, Accepting the molecular weight data below 200 kin' and keeping the restriction of dT/dH : 0 then leads to the molecular weight curve for the 1959 model shown in the figure. The equation of this curve is:
TM=
28.966 22 - 5.044.835.74 arctan
,5
km' H H
90 km' 180 kin'
1
.90km'
1.27106
-
7. 935,.697, 10
FH- 180"] 80m': H [Hta -220
vn61dpeqL-_Th
a.t4eo
iconst ant 28A)966 is the defined sea-level value of M.
constanta multiplving the arctangent functions were determined 18
after the other constants had been selected and were used to adjust thedifferent segments at junction and end points.
The meaan molecular v,,eftht ece for the 1959 model results froman attempt to make use of the apparently best avlable experimental data.
I
1lar
It leads to such questions as: Does oxygen dissociation commence at a higher altitude than 90 km, or does it start at 90 km but increase with altitude at a much slower rate thpai was previously believed? The apparent alternative is to reject the mass spectrometer measurements between 100 and 200 kmn. However, mean molecular weight, ilke most properties of the upper atmosphere, is a function of both time and location. Townsend's rocket measurements were made at Fort Churchill, which is near the magnetic north pole. Measurements of temperature made at the same time showed rather high gradients in the upper atmosphere, evidently due to the influence of higher energy particles following the lines of the e arth's magnetic field. This could result in more efficient mixing of the air components and, in particular, a smaller ratio of atomic to molecular oxygen at altitudes of 100 to 200 km than at other parts of the earth. Thus, at lower latitudes, a curve such as that given in the 1956 model (see Fig. 3) may more accurately represent the mean molecular weight as a function of altitude. Since sufficient data are not available at present to adequately discuss variations in atmospheric properties with latitude, It is possible It would be best to consider that the mean molecular weight lies between the values given for the 1956 and 1959 models. The mean molecular weight for the 1959 model is about 10 to 20 ~-c~nt . .ht,, 4.ht ,! tho_1" model. Usi19 the smaller molecu.A weights would decrease the kinetic temperature and mean free, path by ihe same percentage. Similarly, the number density and collision frequency would be increased by 10 to 20 percent. However, it should be noted that the molecular- scale temperature Is not uniquely determined by the density data. The result is that at altitudes above 200 km the effect of the uncertainty in molecular- scale temperature can exceed the efpct of 10 to 20 percent change In molecular weight.
19
2.13 Mole Volume Mole volume of a gas is defined as the upeCiiic voume ofth.e gas which is the reciprocal of the density, when that density is expressed in terms of the mole mass unit:
1V
M (R*
M TM287.03963
MTMp (28)
Ii .
where
v =mole volume in m 3 (kg-mol)I-1 p =density in kg-mo rn- 3 .This property is not tabulated but is plotted in Fig. 5c, page 28 (Fig. 9c, page 32,inEnglish units).
j2.14
Number"DensityThe number density of a gas is defined as the number of molecules per unit volume and is equal to Avogadro's number, the number of mol-
i!II
ecules per mole mass, divided by the mole volume. The value for air at any particular altitude depends among other things upon the degree of dissociation, which is inferred through the value of mean molecular
The.mole is defined as a mass of substance equal to M times the common mass unit of a particular system of units, where M Is the dimensionless molecular weight of the substance. To distingWish between the various kinds of mole masses. when several systems of units are involved, prefixes indicating the related common mass unit are used. Thus, for this document, one requires the following units and conversions,
ikg-moi ilb-mol
= MiA = Mlb
[pkgm
I sug-mo-3
= M slugs.'kg-mol m ]
Applying the first of these mass conversions to density yields:P k gm kg-mol m- 3
ISimilar
relations hold for the other systems of units.
20
weight.
Thus, N v
NM 0 P
P - 2.0985952 x 1024 MTM
(29)
where ahr N
number density in rnAvogadro's number, 6.02380 x 1026 (kg-mol)-i
2.15 Mean Free Path Mean free path is the mean value of the , . s tU ,c ele by each of the molecules -f - gi.v:n volume between successive collisions with other molecules of that volume, provided that the dimensions of the volume are large compared with the mean free path and provided that the density does not vary appreciahly within that volume. For altitudes above 120 kin, the tabulated values of L must be used with caution since the conditions implied by Eq. (30) become increasingly invalid at these altitudes. It is believed that the tabulated values, however, approximate the actual value for molecules moving horizontally even for much greater altitudes. The expression for mean free path adopted for this model follows from kinetic theory assuming a homogeneous maxwellian gas ind elastic collisions between spherical molecules of uniform mass. 19 As in the case of mean particle speed, the values of mean free path calculated for this model are those applicable to an atmosphere consisting of hypothetical average air molecules, sisting of a mixture of gases.SV4--r-"
rather than to an atmosphere conThe expression used and its equivalent
of
n.
1 -909)
J-1
1V2"n o 2 n
= R* M'MAfclr
B.0504605 I0"7 MTM 7P
(30)
y2 NM 0 P
where L = mean free path in meters, a = average effective collision diameter of air molecules assumed to be 3.65 x 10" 10 m. 71 , The value of cr adopted for this i-nodel was rather arbit-r~lv choen to fall within the range of values listed by Hirschfelder. 21
2.16 Collision Frequency The mean collision frequency of the molecules of a given volume Of al -r la -= L where 'the collision frequency in sec 1 v the average particle velocity in m sec" V The limitations and approximations applying to V and L obviously apply also to collision frequency.2.17 Viscosity
the- avcrag,'2NL= 4 (1
velocity of the
Ym-lecules in
that+vUA4n-
"Ivd-vA~r
the mean free path of the molecules within the volume, or
3.3583060 x 10M()P M)1M)1/2
(31)
Viscosity of a fluid or gas is a kind of internal friction which resists relative motion between adjacent regions of the fluid. This internal friction is usually determined by a viscometer from the drag force experienced by one of two parallel plates separated by the fluid, when that plate is moved with, known velocity and constant spacing relative to the fixed plate so as to create, at any instant, a constant normal velocity gradient in the fluid between the plates. The measured drag force per unit of effective area of the plate is proportional to the normal velocity gradient within the fluid. This proportionality factor is defined as the coefficient of viscosity, p . The value of p. has been found to vary with the temperature of
t
I",o ut+~
ham 4r"AwnnAoMn
o~f
+h~ a
-acmen urlthirt
a
1im~tadran
Kinetic theory has been used In attempts to develop theoretical expressions for .1 and Chapman 4 has de:rived cumbersome formulas for accurately representing the dependence of p. on the temperature at least over the range of 1000 to 15000 K. Because of the complexity of these equations, however, the values of p. in this model are computed from the well-known empirical Sutherland's equation with coefficients as used by the National Bureau of Standards. 8 This equation is
/ See Section 4 for limitation of the equation used.22
PT3/ 23 _where i= coefficient of viscosity In kg sec 1 m -(1 kg sec 1 = 1.458 X 10-6 kg sec-Im 1 (K) /2 m1
(32)
T+S
10 poise),
S - 110.4 0 KT = temperature inUK
Values of p. tabulated in this model from -5, 000 m' to 90 ,000 m' are applicable over this range of altitudes when the body dimensions are sufficiently large, but each application should be exar-dned with caution. especially for altitudes above 40 km.
2.18 Kinematic ViscosityKinematic viscosity of air is defined as the ratio of the coefficient of viscosity of air to the density of air. p where=
kinematic viscosity in m. sec -1 coefficient of viscosity in kg sec In-, atmospheric density in kg m3
S=p
2.19 Thermal Conductivity Kinetic theory determinations of thermal conductivity of some 17 For these gases monatomic gases agree well with observations. thermal conductivity is directly proportional to the coefficient of viscosity. M&iftcation of the simple theory has accounted in part for
/The-/-x
same precautions advised in the use of the tabulated values of p. above 40 km are, of course, also applicable to the tabulated values of See Seciioa 4 for "LinrIttons of theqttion 23
differences itroduced by polyatornic molecules, but no valid theoretical equations exist for mixtures of gases. The following empirical equation has been adopted in this model for compdting the coefficient of thermal conductivity for dry air. 6.325 X 10 - 7 T 3 1 2 T + 245.4 x 1 0 - 12/T where T = temperature in OK, k = coefficient of thermal conductivity in kg-cal m-I sec-l(K 2.20 Relationship Between Various Properties An analysis of the equations of the various atmospheric properties presented reveals several very simple relationships. It is seen that-I
(34)
TM
H,o
C0-
V
Pp
0
H
g
TM
-C
2
-- 2o 1-
Po
1 H-0
oAlso v C no
jT o:0-_&-
P(1 n V T F Po(35)
og L
vO
36
vo
n
Lo
V
V
To
P
Each of the segmDnts of Eq. (36), when multipUed by PMo/PM becomes equnal to each of the segments of Eq. (35). Only the coefficient of thermal conductivity derived from an empirical relationship could not be included in these simple relationships. The coefficient. of viscosity, also derived from an empirical equation, Is essentialUy In the same situation; but by virture of the deffnition of kinematic viscosity, the quotient i/ q is equal to density and hence in the ratio both find a place in the above equation, 24
3. 3.1
TERMINATiON OF CERTAIN PROPERTIES AT 00 STANDARD GEOPOTENTIAL MiLOMETERS Viscosity, Kinematic Viscosity, and Thermra Conductivity
Tabulations of the coefficient of viscosity, kinematic viscosity, and thermal conductivity are terminated at 90 km' where the composition of the atmosphere is assumed to change. One of the reasons for this termitation is that these properties are computed from empirical equations which assume sea-level composition of air and which do not account for changes in molecular-weight of the air. Another reason for this termination is that the independence of these properties from variations in pressure or density implied by the empirical equations____
does not continue to be applicable at very low pressures except, perhaps, under special conditions involving extremely large bodies or volumes. Measurements with laboratory- size viscometers show that pL is independent of pressure or denesty oly in the pressure range from approxzimattdy 2.0 domi to 0.1 atmospheres. It is for this pressure region that Sutherland's empirical formula is known to apply. This pressure independence appears to cease at low pressures when the mean free Path of molecules becomes greater than some small fraction of the plate separation of a well-designed viscometer. This relationship sug-
I
gests that for viscometers q times larger than existing mtnenIs, the pressure or density independence of p. might be extended to approximately q times smaller values of pressure. Assuming that viscometer-measured values of L& apply to bodies comparable in size to viscomoter, such an extonsion would be applicable to present-day practeal-size bodies only to altitudes below 90 kin' (if such extension were warranted at all). Thermal conductivity ceases to be pressure independent at low pressures for which the mean free path becomes comparable to the
1the
I
dimensions of the volume under consideration or comparable to the distance Ain which the temperature gradient varies appreciably. However, these latter limitations do not usually apply until pressures lower! than those at 90 km' are reached. 25
3. 2
Speed of SoundThe concept of the speed of sound is related to the attenuation of
sound transmission in that as the intensity approaches zero the concept of speed transmission becomes meaningless. The rate of absorption or attenuation of sound energy per unit length in air is related to frequency of the sound and the air pressure so that the attenuation increases with increasing frequency and also increases with decreasing pressure. Thus,AL
~
~ ~
~
~
-
4 -. -. -- -~* -*----------------a -
zero for very high frequencies at sea-level pressures, it also approaches zero even for very low frequencies at the low pressures of the upper atmosphere, thereby suggesting an upper limit for tabulating sound velocity. Furthermore, while the direct dependence of sound velocity on the variation of molecular weight above 90 km'would be taken care of by the use of molecular-scale temperatures, the variation of y above 90 km' is not accounted for by the use of TM. The value of y increases slowly above 90 km as the percentage dissociation of 0 2 and N 2 n-, creases, and without separately defining this variation of y the tabulation of the speed of sound must be terminated at 90 kin'. 4, COMPUTATIONS
The tables of this model have been machine computed, using the formulas given in the preceding text. The properties have been calculated to eight significant figures, although they appear printed out to fewer figures dependent on altitude. The defined, independent physical constants are assumed exact. A one- or two-digit number (preceded by a pius or minus sign) foiiowing the intiai entry of each block indicate8 the power of 10 by which that entry and each succeeding entry of that block should be multiplied. A change of power occurring within a block is indicated by a similkr notation. The results of the computations are given in Table 1 for metric units and in Table 2 for English units. In addition Figs. 4 through 7 provide plots of the various atmospheric properties in metric units and Figs. 8 thrnmuh 11 thp rOnrreSnndn ri t1inFtns E ish unftR_
26
TEMPERATURE IN C 41000
sooj ? OC
1 1
-01
1
,,v/0
10
....
A---700
------...-.
0g oo
ii0-
__
.-
600
2-
r9
Iu
5Soo
~sw300 TM-..----
-T- I20
-0
too
zo
f-
ITM M h6
_ I
it
IItCULA - CALE TEMP T a KINETIC TEMPERATURE
-
-0
4NJ1Eto
1ANMLCL.EU
6EA L"VEL VALU. Of M
I11000
2000
:15
I
*0I3000 IN *K 4000
0 A.
TEMPiRATURE
I 19 20 21 22 23 24 25 26 2? I7 MEAN MOLECULAR W&IGHT gdlmnalonlIsf)
l
25
29
XIMTIC TEMPERATURE AND MOLECULAR-SCALE
i
0 MAN M& ECULAR WriewT VS ALTITUoE
--
ITEMpRAURE VS. AI iUDE
.*
.;.\ I-1
I
/.. 1 l 1 :,'I
.!.I~ .
.
.
"Sooo
,o
too1
I --
'
.
. ?
00oo
.....---
IGOV i .oo i-iI i00
I
-i-!1"----4001
30
300-
300
FI0UR10 -9 -J .I __l0
40
c.
i -- t -~-:0.~
~
~ -4
-
-2 -I1
4~0
L PUM 0 Z C. G,
-.. FIGrE 4
-
(WIIW.lNSITV
INhO W1
PRESSURE VS.ALTITUE
MASS DENSITY VS. ALTITuDE
27
o9
v,... 4 .I .. ..
-
I-I--..
,_']Ij900 .
-_o
_,o
\l--
I--_0 T-0 00-~a
00
60
-o 600 * 500-0
o,Goo 40
I
0
I
__300t ]-~~~0
~200
10
I-0o . 4
"
-.
-
20.0
00
1
14 w L0OGo2 SooI"13
7 0 -I -I 11 SPECIFIC WEIGHT
IN
45" 4 3 ,it rn-i
0
t/
7.6
&2
6
.
4
I
A(CEILCERAI0N OF GRAVITr IN m I1
o
,*. 40oi
SPECIFIC WEJ/IT VS ALTITUDE
5.
ACCELERATION OP GRAVITY
VS. ALTITUDE'.
00
loo
A.
0
-
I
I
,
- 4-11* _Goo-----
I
II--
FGR_0
o0 ,o41f1-Q
0006
F 11000
-
L0IIj_
I VOLUMle
INd I k.'-mot1 rn
1
"1
M!EAN PARTICLE
-PIS lO IN m II6e
1
EVOLUME
VS. ALTITUDE
0.
MEAN PAJRTICL.E SPEED VS. ALTITUDE
28
900So
a'w
--- 4 -lH-I1
__
70 LK740
---1-A II
III
I
I
___
-400,
w
-30
zoc'10 ,0_0 --
-no4
200
0
4
4
l2q. 96 72 SCALE HEIGHT IN kmR
144 LIS
0
1
I
Is LOG10
I I? I NUMBER DENSITY IN m14
s
-oo
lo
So 0~ 0600
---
I
-.150.
-100Goo-
X
bl 0
H
U----
----
-----
--
~
-5003-
_ ii
0-------
4W
40C
400
-
-
dif
L N, 06
EA PAT W EFRL
H ISNLT T O
. F EQ OWO NO RO UEN CYS
A -UD T
FIGURE 6
29
s
os
j70
-
eo
TO
TOI
p-oK
9-0
0
50
.0 0
540
al!
o30
40-30
0
L
-
-
-
-
-
-
-
z t-0
240
108
-
-
Ti
- -~do
ea 291. BOUND SPEE
30 IN0
i 3166
328
340
.0
3.5
S
D OFSPEED VSm11 SpgrD -A O SOUD VS ~rlrEf*
ALTTD
5,2 4.6 4.4 4.0 COEFFICIENT OF THERMAL CONDUCTIVITY 1 I& (hc.Isrn scC krl 1 0-6 N
6
rC/rZyroi C~ RMAL CONDUIVITY VS. ALTirTWE
40
NO
To~
.7-W
Tto
4
20---* L20-0
20
-5
4
-3
OF~~~~~
-2
KIEATCVIC-IYINw
-1
0 YUE. '
COEFFICIENT
IO 1.0 .5 1.0 10 or VISCOSITY IN 4 rn-1 11*0"
CKINEMATIC
VISCOSITY VS. A LTiro
~
~
'SO'Yk~
TTD
FIGURE7
.
IN TEMPERATUnRE THOUSANDS Of 'r .2 .8 2.4 3.0 3/, 4.2 48 5.4 6.6
7,6
...
.
. _
-T
-,2-
,-
.
-o.\ -- 22800 . .
I.o
=
, 28 0_.ooS24O004 "2 I-00
,O 0.
i --G,
V
04
r- - - - -OO4
-00
goo
TMOLECULAR-SCALF TEMP. * KINETIC TEMPERATURE /T M MTEAN MOLECULAR-WEIGHT ". SEA LEVEL VALUE OFM-
0 00
12 Soo
I0
YOI
I4 23 TEMPERATURE IN THOUSANDS OF * 7
I t.40
.14151617
]
298
_, 400I-"
25qs 222324 1192021 MEAN MOLECULAR WEIGHT (dfiI@IiIOFIInUs)
400-
A xl#Erl
7LEffLAR-SCALE rERR iAN
MtAEAN MOLECULAR WEISr VSALTirumP
I3---6-i100 O 1 --2 3
2000
,OOI'1600--
-23
--
--
,,-,--
--
2 00
I G
40---
--
-
-40
4L409
*11 '10
-
S -7
-1 -S4-3-2 flLO0,0 OF PRE&,SURE
0
1
2
1
4
-17
.5 M16
-4
-3-I
Plft.NUME VS ALTIfUDE
-8 -7 11-10 LOO OF DENS0ITY rS LVnv rvr s.1-1 Trr I 4
-
5 -4
-3
FIGURE 8
31
3t
.!50.
.2400Vi
-
I
-
I--240
"x._
000
1200
law
N
IIwo12400I-u1
4
-
4
S.--LOSto OF
--
43
PECIFIC WEIGHT IN fl bEll r
A
spEciFIC WeII
VS. ALTITUDEB
-.-- J.--
V-
-
3 -
,,-
E IAN
RTI UGRAVITY IN #t 11rOf
1
-
ACCEEMAN
FR SAVITY VS ALT1T
o.t
t
1117-
-
/I
-
0 16-I4-I
I2
III
1-84- ;5 4
151-2
I
!0
2
Is
0
24(
2*
2*
0 3IX0
UOSIO 1
I- I4
~IU
1200:64600
---
-4111g1o a
,.nn...
-~el
it
3
4
6 7 S 01 L0 8 FMOEVO~HE IN
12
3
4 1
16
IT
Is0
low
low
mm "O 0 3000 mm0 4000460 M~-,.Ir ftrn'ICLE 5P IEE IN Oft EAN
~
20
50
MdOLE Mnk
VS At1MFlT FIGURE 9
mci4N PA*'lE spreE
vs AmrwiTU
32
i
00/60 3!52o
-- t-
32000w 240000 200o0" 100 pII =w--
2oo0
3202400
,,o
' --
\
,,oo
i-O--0---
-
--
-
Goo
,,,
2
1
I-
n
xL4
6
.noo
o
-Boo
o
0. 10f
20
30
40
w
0
010
4
1 It 13 1
5 1 1
8 1
02
22
4
I
\
I_ . . .
ot Boo
Io
-i
,~
20
\-
200 =
-_-sooo
-I--
80
I
rVS.AWD r/ A3LNI-4
NUBRDN1" SAr~~}--
0
4OO--I14Ifl~
1102400 ECLO HoFJ
'A I"GHTAT IN-
t)OPflIUA EP ALTITUDE 0
LG. OFNUOLISEO NULMBERO DRENY 1 2
FRD ENY
-
-12400
A00
SMAAE FREIHATH VS. -00 00300 -000 400
VS. ALTITUDE 1920212223 4 0 02 0
00
7004
hJJ-7 -1 0 -5 1 -4 3 3 5 7 .4 3 4 * 7~ a -
0o
IF IGURE 10
33
V
VT
f-
[300.;
i-
1-
0 o300- 20LI LI'
,o,250w' 200
"" ..
Ioo[--oo --
=I
---
I-I
200-.---
oo-
ro
-
----
-
--
--
io
o50
0--------040 Boo 920 960 1000"
0
0
1040
I080
1120I:
2.54i10
- 11
-
3.011 0
6
&51
10
-
6
4.0 x 10t -
SPEED
IN It slac
..
COEFFICIENT OF THERMAL CONDUCTIVITY
IN STU 119' see-'
(*R) '
A.
SOUND SPEED VS. ALMIW'E
COEFFICIENT or THERMAL CONDUCIVITrY VS. ALTITDE
0z-
-D
I IIt se1
I0I -t -
-50.
0 u
L300 KN loO
MTCS
- IN COSI-
ft
e
-300 I0
300
-?
II-CO
FII 1
T O
T.FI0
-7
A
CONDUCTIVITY
l,IN I0 9 9'
-?
1
,
VO
-
tATSOSEED VS ALTITUDE
COEFFItCIENT
HRMALCODCITY O
V.ATTD
-
z660 92 91 40 1010 112 0 2.8I II 10 0
S
-
U.~ 00
5
I.w
.0
I008
in1( 50-
.15
IslaI f-i
a [-4 -3 2
I.I
II0 IN II 1 VISCOSITY
-~I
GURE
q50-K CD(T x 0-5 7 (z I.7 xICY' 8 xI0' 2.1 x to9 x O 02.5 K 10-7 . 0-5Y 1.1 x 103.31 IT 7
2 s1 -
130-5 3.7x 101
LOGIO OF KINEMATIC
2.9 m 0-
C. KINEMATIC VISCOSITY VS. ALTIT~uDE .FIGURE 11
COEFFICIENT OF VISCOSITY
IV
.- VCFI~NTo A,'TI~
34
TABLE IA ATMOSPHERIC PROPERTIES AS A FUNCTION OF ALTITUDE, METIC UNITS Temperature, Pressuro, Density, and Molecular Weight
II
V1
NOTE: A one- or two-digit number (preceded by a plus or minus sign) following the Initial entry of each block indicates the power of 10 by which that entry and each succeeding entry of that block should be multiplied. A change of power occurring within a block Is indicated by a similar notation,3
35
ALTITUDE lirn' Z,m ,-
TEMPER TURE TM, 0 K T, -K 320.69 19.38 i 318.T5 318.OB 317.4.3 316.78 316.13 315.48 314.83 314.18 313. 5 312.87 12.22 320.69 319,38 318.73 315.0U 17.43 316.78 316.13 315.48 314.83 314.18 313.53 312.87
P, nb 1.7761 + 3 1.7400 172-15 1,7031 1.6848 1.6667 1.6488 1.6311 1.6134 1.5960 + 3 1.5787 1.5613 1. 5445 1W77 1.4945 1.4781
PRESSURE - 2 likg] m 1.8112 + 4 1.7743 1.7554 i.13566 1.7180 1.6996 1.6813 1.6632 1.6455 1.6275 + 4 1.6098 1.5923 1.5750 I, 1.5239 1.5072
DENSITY - 3 p,kg n nm Hg P, 1.33.2 1.3051 1.2912 i.2-(4 1.2637 1.2502 1.2367 1.223 1.2102 + 3 1,9296 + 0
MOLECULAR WEIGHT M 28.966 28.966 28.966 .. 28.966 28.966 28.966
-Og904-
48004700 4600 4500 4400 43oo
ISOc
1.898o1.8816 ., 1.8491 1.8330 1.8171 1.8012 1.7854 1.7698 + 0 1.7542 1.7388 1.6780
1>0 410040o0 3900 3800 3
4703 - 1503 - 4503 - 41 03 - M.0 - 120 - 4103 - 4005 - 3902 - 38W
-
28.96628.966
3700 3600.3300-
00
-"3702 - 362-
311.57
12.22 311.57
1.1971 + 3 1.1841 1.1713 1.."744P7-
28.966 28.96628.966 28.966 28.966
3 10.27
310.27
1.1209 1.1o86
3200100
33e - 32(2 - 3102-3001 - 2901 -2801
309.62 3C8.97 308.32307.67 307.2 306.-37
309.62 3C6.97 308.3 307.67307. O 306-37
1.46181.14457 1. 297 + 3 1.4139 1.3982 1.3827
1.49061.4742 1.479 + 4 1.18 1.1258 1,4100
1.0964i.0814 1.024 + 3 1.0605 1.01"8 I.071
1.6631 1.64831.6336 1.6189 + 0 1.60.4 1.5900 1.5757
28.966 28.966 28.96628.96 28.966 28.96 28,966
- 3000 -2900 -2800 - 2700
-26oo-
2701 -26oi-
30.72 3
305.72 303.17 305.10300
- 00 "01 2200 4,2100 -2000-
3041. . .11
a05.(t 1.3673 1.3521
1.39431.139
1.02561.0141
1.56151.5473
28.96d98.966
1-7
.2401 2300
-
- 2201 -2101
2301
503.77 303.12
1.3369 1.39201.307
1.3633 1.3480
1.0028 +2 9,918
1.W3 1,51941.5059996 1.2998 114781+0
28.966 28.9668.66
-2001
3M2.46 301.81 301.16
301.81 301.16
1.3179 1.294 1.2778,+ 1.300+.4
9.6938 9. m5 +,
28.96 28.966 .08.06 28.966 28.966 28.966 28.966
1900 - 1800 - 1700 - 1600 . 1500 - 14.00 - 1300-1200
1901 - 1801 1700 - 1600 -1 00 1%-1300 -1200
-
1100.
-
1100
300.71 299.86 099.21 9856 9791 297.26 296.61 295.96295.31 294.66
300.51 99.86 99.01 298%96 097.91 297.26 29661 291.9d295.31 29.66
1.2631. 1.0191 1.2349 1.220 1.2070 1,19N2 11795 1.1661.1526 1.1393 +
.29I 11.737 .293 1.149 1 2308 1.2167 1,298 1.18901.1753 1.3618+4
9.3689 9*9Q6 9.157 9. 30 8.;96 8.84.71 8.71578.51 8.5456 2
1.4.5 1:4379 t.e16 i.W411 1:.,184 1.3854 1.37251.397 14 70 + 0
28.966
28.66 28.966
-1000-800
- 1000-
900 700 o60 o-
-
900 e00700
294.01 293.36292.71
2.01 293.36292.1
-
600 5040 300 200 !On 0 100 200
292.06 o. 21. l41290.176 290.11 289.46
29..0 29 41290.76 290.11 289.1.6 288.81 288.16 87.51 286.86 286.21 285.56 284.91
1.192, 1.1131 002 1::087 .1.0=.9
1.84 1.131 11219 1.1089 1.08961.7711.7
S 8.3492 8.,521 8.1565 8.o65 7 87437,782O 7.6906 7.6000 + 2 7.51o5 7.101 7. 3 36 7.2146 7.1602
1. 33448. 1:32191.,3095
1.2972 1.28497
28.966 8.966 28,.966 g8.966No:=
-
400-300
-
1,04981.0375
1.07051.050 1.0155 1.0332 + 4 1.0210 1.0090 9.9700 + 3 9.8516 9434
1:2607
20.628.966
200 C0 0 100 9 00 ZO0 500
-
PRA.Al
1.C2531.o125+ 3 1.0013 9,8945 + 2 9.7773 9.6611 9. 461
1.2487 1.23W8 1.2250 1.233 1.2017 1.1901 1.1787 1.1673 0
26.966289 " 28.966 28.966 28.966 28.966 28.960
288.16
6o0 700800900
287.51 286.86 286.21 -6 -wZ140 500 2 9. 9 1
6oo
284.e6
284.2628t3".6i 28e.96 282.31
9.143e29., 1.Jo 9.2077 9,0971
9.61829.3893 9.2765
7.07486.9064 6.8234
1.1 50
28.96628.966 28.966
7u800 900
!83.61 28.96 282.31
!. 1.1537 1.1Ii6
36
ALTITUDE Zrm 1000 1100 1200 1300 1500 1500 1600 1700 1800 1900 2000 H in' 1000 1100 1200 1300100
TEMPERATURE T, K TM, K P, mb 8.9876 + 2 8.879.2 8.7718 b,6655 8.5602 8.560 8.3527 8.2506 8.1494 8.0493 7.9501 + 2
PRESSURE P, kgf' m- 2 9.1648 + 3 9.052 8.c417 8.856) 8.7290 8.6227 8.5174 8.4132 8.3101 8.2080 8.1069 + 3 P, mm Hg 6.7413 + 2 6.6599 6.5794 6.4996 6.4207 6.425 6.2651 6.1884 6.1126 6.0374 5.9631 + 2
MOLECULAR WEIGHT DENSITY p, kg m" 3 1.1117 + 0 1.1008 1 .0900 i. 07(9. 1.0687 1.0581 1.0476 1.0373 1 .o269 1.o167 M 28.966 28.966 28.966 28.966 28.966 28.966 28.966 28.966 28.966 28.966 28.966e8.966
1500 1600 1700 1799 1899 1999
281.66 281.01 280.36 279,71 279.o6 279.1 277.76 277.11 276.46 275.81 275.16
281.66 281.01 280.36 279.71 279.06 278h0 277.76 277.41 276.46 275.81 275.16
2100 2200 2 00 24002500
2099 2199 2299 23992499
*714.51 273.86 27.92 22.=5?271.92
274,51 273.86 27.22 27207271.92
7.8520 7.7540 7.6-56 7.56347.4692
8. oo68 7.9077 7.8096 7:71257.6161,
5.889 5.8166
5.745.
5.673o5.6C23 5.1631
a.9649 9.8649 9.7657 9.6673 9.4727
1.0066 + o i =
28.96620
28.96628.966
.yu
9.5696 9.3765
2600 28002900 3000
25969 9
271.272700 270.6-
271.27270.62
7.3Z59 7.1921
7.137.4271
28.96626.966
7.2 35 7.1016 7.0191 + 2
27992899 2999
969.97269.32 268.67
269.97269.52 266.67
7.3397.2416 7.103 + 3
5.39455.3267 5.2595 + 2
9.28119.1865 9.0926 - 1
28.96628.966 28.966
71
3100
oo
26.3198 268.02309B m 3598 96 2,77 262.83 263:26,18 267.63
2Q . M 6.9235 167-37 6.035 6.7489 6. 6,4 +
7.0600 6.97
5022
5.1930
8.90708.9994
028.96
28.966 28.966 2o.966 g8.966 go.966 28.966 28.567
-4
Roo
00
266.72 398 266.72 j@ 6.66o 26Z.87
6.[94
6.8820 6.7077 6.6219 6.39 0 6,V71069876 + . 6,906
:9977.0621 .93.0 1.870B
8.74
8.8153 8 .61 8928.61 8.828,966 8.3676 8.7028.1935 - 1 70059
3500 3600
3798 3800 390 3898ho00 4700 .97 1.097
262.83 6.2.6 9 86376.382.18 260.53 69 + 5.0627
4.8W4 4746514.69 + 2 4.5165
370D76
28,966 28.966
.800 51Oo
4197
250.98
26.88 28.9 26.23 258.29 25.7. 95956
6.0 5.71 5.19773 5.6995 5.620 5.8178+
6025 5.38%1 6.0859 38119 5.7356 5.96 1
44.8
5
7. 5W2
2.966 98.966 28.966 e8.966 28.966 28.966
1.900 4600 ,700 500
k2096 459
98.93 26.33 28.29 257,6 97 96 58
4472 4.27560 3.81, .4.03W+
7.2751 7o93762 7.6878 7.628 7.14 85
1
MO
qIQ S 5 5065 589 519559914
256*98
256.98
5:1506
5:660 5.153 5:.0343 538O943 1..114.81148 + 3
6
3.12 .7907 4.739 + 4.0004 3.8943 .63963.5.116 + 2
7.0217 6.977 .84-7 6.8281 7.6186 6.72866.6011
28.966 28.966 28.966 0%096 28.966 ,28.966 1 28.966 28.966 28.96628.966
9500 5600 5700 I900 woo6000
-33 226.1 251 249.8 2,0o.q 2219.20
5. 3 4 5.0539 +2 25.74 49188 25.14 2453 144867 .8621 2:0.g249.20 1.7217 + 2
-
6100 66006600
-091 67936593
2-n.90 21.492-040
2-M.95 250.092145.30
5. 1675 4.271.058
S. .415.15 14,254
.. 3.63963.260
05
1 6.74866.1733
67006900
66936193
21.67243.36
21'.g 243.36
4.2867.1686
3.2153 :W,7135,1267
6.10415.9676
28.96628.966
37
ALTITUDE Z, m H,m'7000 6992
TEMPERATURE T,oK TM, K2L0-7l
P, mb4,.1105 + 2
PRESSURE P, kg' n '1.1915 + 3
DENSITY P, mn Hg3.0851 + 2
MOLECULAR WEIG-T M28.966
p,kg m 5.8334 5.7015 5.6364 5.5719 5.5080 5.4446 5.3818 5.31955.7u7.
3
71nn7200
709127192
242.06241.41
2412.71 242.06241.41
5.9002 - 1
40531 3.9402 3.8848 3.8299 3.7757 3.7222 3.6692 3.6169 3.5651 3.51140 3.4635 3.4135 3.3642 3.315.4 2,1.9963
4.13304.o751
* *
7300 71400 7500 7600 7700 7800 7900 8000 8100 8200 8300 81400 8500
7292 7391 7491 7591 7691 7790 7890 7990 8090 8189 8289 8389 8489
24o0,76 2110.12 239.47 238.82 238.17 237,52 236.87 236.23 235.58 234.93 234.28 233.'63 232.98
2p0.o76 214o.12 239-.47 238.82 238.17 237.52 236.87 236.23 235.58 234.93 234.28 233.63 232.98
4.0179 3.9614 3.9054 3.8502 3.7956 3.7416 3.6882 3.6354 + 3 3.5833 ).5.ijo 3.488 3.4305 3.3W
3.0401 2.9975 2.9554 2.9138 2.8727 2.8320 2.7919 2.7521 2.7129
28.966 28.966 28.906 28.966 28.966 28.966 28.966 28.966 28.966 28.966 28.966 28.966 28.966 28.966
2.6357
2.6741 + 2
2.5976 2.56o4 2.5233 2.4867
5.2578 - 1 5.1967 5.136 5.0760 5,0165 4.9575
86oo 8700 880 8900 9000 9100 00 93009400
858 6688 8788 8888 8987 9087 9187 928696
232.34 231.69 231.o4 230.39 229.74 229.09 228.45 227.80227.15
-32.34 231.69 231.04 230o.9 229.74 229.09 228.45 227.80227.15
3.2672 3.2196 3.1725 3.1260 3.0800 + 2 3.0346 2.9898 .9452.9017
3.3316 3-2830 3.2350 3.1876 3.1408 3.09* 3.0487 3.00352.9589
2.4506 2.41149 .3796 2.3447 3 2.3102 + 2 2.2762 . 2.2425 2.20932.1764
4.81412 4.7838 4.7269 4.6706 - 1 .618 4.5595 1.01474.4W4
24.89 8.966 28.966 28.9 28.966 28.966 8.96 20.966 28..56M28.966
9509600
94869586
226.50225.85
226.50225.85
2.85842.8157
e.91482.8712
2.14402.1120
4.39664.3
28.96628,966
96859900
97859885
225.21223.91
2.56223.26
22.21 224 56223.91
2.7r,35 2.7318
2.8282
2.6906 2.6500 + 2 2.69 2.570 2 09 2.
2.78572.7437
2.0803 2.04902.0181
4.2905 4.23w4.1351
28.966
4.1864-
28.96628.966
10oo 10100 102001=
9984
223.26222.61 221.97 221.32 220.67
2.70222.6612 2.6e 2.5808 2.5414
3
1.98761.9575 1,9277 1.8983 1.8693
1
28.966 28.966
10084 10184
10 1050010600 10700
10283 10 3
222.61 221.97
101
1058)2 10682
1 220.02219.37 218.73
221.32 220.67
4.0w1 . 5!m2.6 3. 9346
28.966966
220.02219.37 218.73
245W2.4163 2.3790
2.5m42.63 2.4259
1.780 1.81231.7844
3,75 3.83723.78W2
28.966 28.96628.966
11000 11100
10981 11081
216.78 216.66
216.78 216.66
2.2700 +2 2.2346
2.3147 + 3?.2786
1.7061.6761
2
3.6180 - 13.592
28.966 28.966
1m20 1110011500 100 11600
1180 i138011479 11579 11T8
216.66 16.66216.66 Wi6.66 216.66
216.66 216.66216.66 216.66 216.66
2.1997 2.1317 2.0985 2:3.5.2.0018
2:2431 2.17372.1398
1.&%"~ 1.5959 1.57401.529 1.5914
3.W71 3.4 e.966 '27 3.37143 3:6993.2189
28.966 28.966 28.96620.966
2.07162.03
11900 1200O12100 122'0 12300 i24oo 12500 1260o12700 12800 12900
11878ii9'7 12077 12177 1-76 12376 12415 1257512675 12774 128714
216.66216.66 216.66 216.66 216.66 216.66 216.66 216.66216.66 216.66 216.66
216.66216.66 216.66 216,66 216.66 216.66 216.66 216.66216.66 216.66 16.66
1.97o61.9399 +2 i.9097 1.8799 1.8506 1.8218 1.793. 1.76541.'(5-2( 1.1379 1.7108 1.6842
2.00951.9782 + 3 1.9473 1.9170 1.8871 1.8577 147 1.80031.7446 1.7174
1.47811.4551 +2 1.4324 1.4101 !.3881 1.3664 1.3452 1.324*21.3036 1.2832 1.2632
3.16873.1194 - 1 3.07-07 3.0229 2.975$8 2.9294 2.87 2.83882,A,-,96, 2.7510 2.7081
28.96628.96 28.905 28.966 28.966 28.966 28.966 28.96628.966 28.966
38
ALTITUDE ,Inv i Z, r 13000 13100 13200 133W00 13400 13500 13600 13700 1380 13900 14000 11100 11i400 143M0 I14400 12973 13073 13173 13272 13372 13471 13571 13671 13770 13870 13969 14069 11168
TEMPERATURE T,OK 216.66 216.66 216.66 216.66 216.66 216.66 216.66 216.66 216.66 216.66 216.66 216.66 216.66 216.66 216.66 216.66 216.66 216.66 216.66 216.66 TM, OK 216.66 216.66 216=66 216.66 216.66 21b.66 216.66 216.66 216.66 216.66 216.66 216.66 216.66 216.66 216.66 216.66 216.66 216.66 216.66 216.66 216.66 216.66 216.66 216.66 216.66 216.66 216.66 216.66 Pmb 1.6579 + 2 1.6321 1.6067 1.5816 1.5570 1.5327 1.5089 1.14854 1.14622 1.14394 1.4170 + 2 1.3950 1.3732 1.3518 1.3308 1.3101 1.2896 1.2696 1.2498 1.2303 1.2112 + 2 1.1923 1.1737 1.1555 1.1575 1.1198 1.1023 1.0852
PRESSURE in"-2 P,kg;fm 1.6906 +3 1.6643 1.6384 1.6128 1.5877 1.563 1.5386 1.5146 1.4911 1.4678 1.41450 + 3 1.4225 1.14 03 1.3785 1.3570 1.3359 1.3151 1.2946 1.2744 1.2546 1.2350 + 3 1.2158 1.1969 1.1782 1.1599 1.I18 1.121i 1.1066 P, mm Hg 1.24 6 + 2 1.2242 1.2051 1.1863 1.1679 .1.49-( 1.1317 1.1141 1.0968 1.0797
DENSITY MOLECULAR p kg m- 3 .662 -1 2.6244 2.585 2.5433 2.5036 2.4646 2.4262 2.3884 2.3512 2.3146 2.2785 - 1 2.2430 2.2081 2.1737 2.1399 2.1065 2.07W7 i 2.0414 9-0096 1.9783 1.9475 - 1 1.9172 1.88 1.8 .90 1.8006 1.7725 1.7449 IGHT 28.966 ,28.966 28.966 28.966 28.966 28.966 98.966 28.966 28.966 28.966 28.966 28.966 28.966 28.966 28.966 28.9o0 28.966 28.966 28.966 28.966 28.966 28.966 28.966 28.966 28.966 28.966 28.966 28.966
1.0629 + 21.0463 1.0300 1.0140 9.9817 . I 9.8262 9.6732 9.5225 9w47142 9.2282 9.0845 + 1 8.9431 8.8038 8.6667 8.p1a 8.3989 8.2682 8.1394
14268I1467 14467 14567
14500 160I4700 148* 11i4900
1466614766 865
1500015100 15200 15300 1500 1 15500 156o0 15700
1965
216.66 15064 216.66 2i6.66 15164 216.66 15263 216.6 15363 16.66 1 216.66 15562 216.66 15661
1580015900 I60 16100 1620 16
1576115860 15960 16059 16159 16258 16358 16457 16557 166% 16756 16855 16955 17054 17154
216.66216.66 216.66 216.66 216.66 216.66216.66
216.66216.66 216.66 216.66 216.66 216.66216.66
I.O6831.016 1.0353 +2 1.0192 1.0033 9.8767 + 1 9.723 9.5717 9. 4M27 9.2760 9.1317 8.9895 8.8496 8.7119 8 6 1
1.08931.07241 1.0557 + 3 Y.0392 1.0231 1.0071 9.9147 + 2 9.7604 9.6085 9.459 9.3117 9.1668 9.0241 + 2 8.8837 8.71
8.01277.8880 7.7652 + 1 7.6443 7.5253 7.4o82 7.2929 7.1793 7.0676 6.9576 6.8493 6.71427 6.6378 + I 6.3345 6.4328
1.71781.6910 1.6647 - 1 1.6388 1.6133 1.58821.5634
28.96628.966 28.966 28.966 28.966 28.966 28.966 28.966 28.966 28.966 28,966 P8,966 28.966 28.966 98.966
11650 166o0 16700 16800 16900 17000 17100 17200
216.66 216.66 216.66 216.66 216.66 216.66 216.66 216.66
216.66 216.6 216.66 216.66 216.66 216.66 216.66 216.66
1,5391 1.5151
.19161.,4683 1.455 .1230 1.4009 1. 37911
1730 171s0 17500174Mlf
17. 17353 1745217q1
216.66 6.66 216.66lqr
01
216.66 216.66 216.66
81.1M; 8-31.5
A.IrA6A S.of51&o
8.10227.- 99
860 8.4754 8.34,57.9601 7.8362
R.9-1 7
6.3327 6.2341 6.1371
6.01416
1.3576 1.3365 1.31571.2952
28.966 28.966 28.96628.966
g17900 18000
176511775o 17850 17949
216.6216.66 216.66
216.66216.66 216.66 216.66
8.-086
5.911765.8551 5.764o+
1.27511.2552 1.2357i
28.96628.966 28.966 7 28.966 -8.966 28.966 28.966
7.8062 7.6847
181oo18200 1=
18o4918148 18247
216.66 216.66216.66 216.66
216,66216.66 216.66
7.5652 +1 7.144757.3316 7.2175
7.7143 7.59437.4762 7.3599
2
5.6y41 3
1.+165 -
5,58615.4992 5.4.136
1.19751.1789 1.1606
0 i 4 18 185m i856 186c:18700 160 18900 18615 18745 188114
216.66 216.66 216.66216.6 216.66 216.66
216.66 216.66 216.66216.66 216.66 216.66
7.1053 6.9947 6,88596.,r8 6.6734 6.5696
7.2454 7.1327 7,02176.9125 6.8050 6.6991
5.3294 5.2465 5.16495.0845 5.0055 4.9276
1.1425 1.1247 1,10721.0900 1.0731 1,0564
28.966 28.966 28.96628.966 28.966 28.966
39
ALTITUDE Z,rm 19000 19100 19200 19500 19400 19500 19600 19700 19800 19900 20000 20200 201400 -, r' 18943 1945 19142 19242 19341 19140 19540 19639 19739 19838 19937 20136 20335
TEMPERATURE T, K 216.66 216.66 216,66 T ,K P,mb 6I.4674 + 1 6.3668 6.2678 6.1703 6.0744 5.9799 5.8869 5.7954 5.7053 5.6166 5.5293 + 1 5.3587 5.1933
PRESSURE P, lg/ m2
DENSITY P, mm Hg 4.8510 + 1 4.7755 4-7013 4,,6281 45562 I4.4853 4.4156 4.A469 4.2793 4.2128 4.11473 + 1 4.0193 3.6953 p,kg m-3
MOLECULAR WEIGHT M 28.966 28.966 28.966 28.966 2u.966 28.966 28.966 28.966 28.966 28.966 28.966 28.966 28.966
216.66 216.66 216.66
26.66216.66 216.66 216.66 216.66 216.66 216.66 216.66 216.6f 216.66
216.66216.66 216.66 216.66 216.66 216.66 216.66 216.66 216.66 216.66
6.5949 + 2 6.-49214 6,39014 6.PQ9!0 42 6.19 I 6.0978 6.0030 5.9097 5.8178 5.7273 5.6383 + 2 5.14643 5.2957
1.0399 - 1 1.0r238 1.0079 9.9218 - 2 9.7675 9.6156 9.4661 9.3189 9.1740 9.0313 8.8909 - 2 8.6166 8.3508
20200 2080021000 21200 214oo 21600 21800 21oo 22r=0 22o00 22600
2o533 2073220931 21130 21328 21 -;7 21725
916.66 216.66216.66 216.66 216.66 216.66 216.66
26.6 216.66216.66 216.66 216.66 1216.66 216.66
5.0331 4.8779
5.0300 9740 4.4.8206 4.6719 4.5278 4.3882 4.2529
38.75 3.6587
851 3575 7 28.9667.6015 7.3671 7.1399 6.9197 6.7063
28.96628.966 28.966 28.966 28.966 28.966
4.7274 4,5816 I 4.4403 4t.3034 4.1706
11
3.5458 3.4365 3.3305 3.2278 3.1282
22123 2192422321 22520
216.66 216.66216.66 216.66
216.66 216.66216.66 216.66
3.914 4,.04203.7966 3.6796
3A,!98 2 4 .1217 + 23.8715 3.7521
.2283 3a03518 + 12.877 2.7599
6.91 6*4 995)6.',9 5.9167
2
28.966 28.96628.966 28.966
22800 9300093200
2719 2291723116
216.66 216.66216.66
216.66 216.66216.66
3.Z661 3..5623.3497
3.6364 3.521433.4157
2.6748 2.59242.5125
5.7343 5.55755.3862
28.966 28.96628.966
23400 236oo 2380024000 21900
23311 23513 2371123910 214108
216.66 216.66 216.66216.66 216.66
216.66 216.66 216.66216.66 216.66
3.214614 ).1464 3.04942.9554 + 1 2.8644
3.104 3.2c04 3.10953.0157 + 2 2.920
2.14350 2.3600 2.2872.2167 + 1 21084
.22oe 5.059 Z4.9034.75M2 4.6058 2
28.966 28.966 28.966 2.96628.966
21440024600
214307245 05
216.66216.66
216.66216.66
2.77612.6906
2.83082.7436
2.08222.0181
4,46394.326)
8.966 28.966
200oo 25000 200 25140025600
e4704 249oe 251 00 2529925497
216.66 216.66 216.96 217.56218.15
216.66 216.66 216.96 217.56218.15
2.6077 2.5 73 249 2.37-422.3015
2.6591 2572478 2.42112.31469
1.9559 1.8957 1.8373 1.78081.7265
4.1951 4.0639 3.9333 3.8ao3o61$5
28.96628.966 98.9"6 28.966 98.966
25800 2600026200
25696 25891426092
218.75 219.34219.94
218.75 219.34219.94
2.251i 2.1632 + 12.0975
2.P752
1.6735 1.6225 + 11,5"3
3-.55353.43593L,225
18.9662 28.96628.966
2.2059 + 22.1388
2640026600
2629126489
220.53221.13
220 53
2.03391.9725
2.07o402.0114
.p56I3475
3.2131.1076
221.13
98.966 28.966
26800 2700027200 271400
26687 26886270814 27262
221.72 2M2.32222.91 224.51
221.72 222.32222.91
1.9130 1.8555i.7999 1.7461
1.950I 1.8921. 1.780
.4 1.3918,1.3097
300059 2.90771f2.7217
28:9"
28.96698:o66 28.96
223.51
*
200 97800
271481 27679
02.1224.10) 2214.70 224.70
1.69140 1.6437
1.7P714 1.6761
1.2706 1.2328 1.1609 1.12671.0935 1.0614
2 6M 2:5484 2.3871 2.31062.2367 2.1654
a.6 28 28.966
2800028200 28140028600 28800
2787728075 2827428472 28670
225.29225.89 226.48227.08 227.67
225.29225.89 226.48227.08 227.67
1.5949 + 11.5477 1.5.I1.4579 1.14151
1.62614 + 21.5783 1.53171.4866 1.14430
1.1963 + 1 2.14663 - 2
28.96628,966 28.96628,966 28.966
29000 29200291o00 29600 29800
28868 2906629265 29465 29661
228.26 228.86229.45 23o.05 20.614
228.26 228.86n29.45 230.0230,64
1.3737 1.33361.2948 1.257 1.2C8
1.14008 1.35991.5203 ,2en 1.21M1
1.0304 1.00039.7116 + 0 ).14296 9.1565
2.0966 2.03011.9659 1.939 1.840
28.966 28.966 28.966 28.96628.966
40
ALTITUDE Z,i 3'0JO0 301200 30600 30500 Hm' 2965930V17
TEMPERATURE T, K TM,oK P,mb 1.1855 + 1
PRESSURE P,kg/m- 2
P. mm ig
MOLECULAR WEIGHT DENSITY M p,kg m- 3 1.7861 -21.7302
231.24 231.24 231.8313
1.2089 + 2
1
1154
1.17411.1076 1.0760 1.0156 9.8674 + 1
8.6921 + 0 8.63598.14D 7.9144
28.966
28.96628.966 26.96
3015. 50651
233. 2 235.61 234.80 235.40
233.02 233.61
1.062 1,0592 9.9592 +0 9.6766
1.6240 15T35
31000 31600 31800
31200 311400
30850 3114144 31614251840
30o1* 12146
21.21
2534.21
25.80 235.40
1.0251
1.0453
7.68877.1.700 7.581
.2481. 4777 1.:421
28.96628.966 28.966
2355.99 236.59237,18
2-35.99 256.59237.18
9.14(2 9.13718.8802 + 0
9.58EP 9.31769.0552 + 1
7.0527 6,85M66.667 0
1.3881 1.314551.3041 - 2
28.966 28.96628.966
32000
52200 32600
35400800 3000
32058
3ir256 3545439632 32850
237.77
208.37258.96239.55 2.40.15
237.77
208.37238.96239.55 240.15
8.6508
8.157.9273 7.7069
8.840 8.,.. .. 8.100.06 7.88
6.14736
1.264161.1889 1.1529 1.1180
6.11655.9460 5.780
28.966 28.9 2889 ^)2'e328.966 28.966 28 .966
3390051400 55600
35(283225551105
2140.714241.34 A1393
2140.714
7.149527.28 9 089
7.61097.4996 7.,2245
5.62a15.4649 5:3141
i.014141.0518 1.0m-
28.966
2141-34241
e8.966 p96966
3380?361
41..52
24o. 523 2943.19 243.71 2g.4.309144.90
6.9 6.7007 + 0 6.5171 6.35916.1663
7,C257 6.8328 6.61456 6.1464o6.879
5.1678 1 5.(259 + 0 4.8882 4:751474.6251
9.8972 9.6(20 963162 9.05968.7720
3 3
28.966 28.966 2B,966 28.96628.966
534000 311006
55819 9.3.12 214).71 5101 5105 3W,40 2141.3031414 244.90
55000 3520035400
;t.00 5161 0 350065204
2115. c 2 09 216.68 94787 2148.1:6 949.05
2417.97
2145.149 210 24.6.68
217.27
5.99W6 9 58 5.6705.52.48
6,4169 .9510 579005.6537
4.4W9
4.3
4,294.11139
8.5128 8.o60 8,01917.7839
98.966 28.966 98.96628.966
5580
35600
34
35600 35797
,
W.4 99.0 949.67
87
53795 -1
, Z.0530.78 4.660 4 4: .79 .9185
4 09":
0
7.55577. ii
7357
28.966 296-
36000 *Aboo5
s59
21.9.6
495534:8123
.0114 + 0 94.9.
5.1918 +1
3.818M + 0
3.7168
6.91 ' 16.711
3
28.96628.966
8.,966
3660037,.0
0
36195
36590
050.2 9
5a800 37000 57100 37600"014
3658836 3)7181
20.85 251.1.2 952:02 9.61 W81 22.9
955.20
250.8 251.21 252 02 252.61,
50.2
36177
11.5704.2176
25590
4 4493 4.3318,
4.5o00
3.X14 3.1.080 3.5572 3.21913:16"
6. Xo0 6.3398 6,1506 5:74 5.6373
O.800
8.966 98.966 98.966 98,966 28.966g8.966-
8.966
.7"7357
so
20.80 954.98255.58
L: 186o
"4.0779 9,9995
5.4767
771 57912 3~0 8169 300 58367 380 38365 3a760 39000 58960 39200 3W00ISq40 5900 59157
3800
254.96255.58
3.84 +03.7928
5.9712 + 13,8673
2.9211 + 02.8418
5.210 I.C238
3
98.966
5. 17018.0
956.76
056.17
957.55 257.95 25".5129.13 259.72 260.91 261. iC
956.17 .56.76 257.55 257.95 258.514259.13 259.7
3.69140
3.59803.501.8 3.4141 5.52613.20 3.1T1
3.7668 .6690 3A15 3s4815 5.5916
269: &7.
2.7707 26 2:191
59800o000 4m00
59355 352397 3
3 14.5566 3 3.2195
2.11305 2.3681
1.7o48.961S 9.28 1611 2a.95 28.966 4.48194.235O 28,966 28.966
o
28.966
28.966
260.329260.39260.91 961.50
3.0642.9977 + 0 2.9213
3.1370.0%,68 + 1 2,9789
2.30759.285 + 2.1911
1.1171.oc28 5.8919
28.9662.966 2.966
26.09 e 6.69 5Wow 4054o 26528 100 40757 g6 a87 40935 961.146 41200 32r.65.0600.5050 4C4005 o0600 5.18o(: 4152
401415
262.09
62.69
2.814702.77417
2.9051
2:1)542.0812
2.8291
3.7&13
3.6799
28.966
28.966
263,98 26.87 .416
2.7114 2:6561 2.569
2.757 2.6880 2,62o32
2.02838.96 1.97m72c 1.92741.0.10 1.7859
3.58503M5
28.966 28.966O.
41600266 41o330 956266:2z") 266 .2I4
.02,418372.3810
0
322
8966
2.,27039
3.1156
28.966
41
ALTITUDE Z,m H,m' J49-LO 417234 422oo 4192 . .4o ,119 2 42-316 4_600 12800 .42514 412711 43o0o
TEMPERATURE T, K TM,K 166.83 67.43 68.c2 268.6! P69.2O 269.79 266.65 267.
