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ISO 2533:1975(en)

	International Standard ISO 2533
Standard Atmosphere Atmosphère Type Reference number ISO 2533:1975(en)	First edition 1975-05 © International Organization for Standarzation 1975

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ISO 2533:1975(en)

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ISO 2533:1975(en)

ContentsPage

FOREWORD

ISO (the International Organization for Standardization) is a worldwide federation of national standards institutes (ISO Member Bodies). The work of developing International Standards is carried out through ISO Technical Committees. Every Member Body interested in a subject for which a Technical Committee has been set up has the right to be represented on that Committee. International organizations, governmental and non-governmental, in liaison with ISO, also take part in the work.

Draft International Standards adopted by the Technical Committees are circulated to the Member Bodies for approval before their acceptance as International Standards by the ISO Council.

International Standard ISO 2533 was drawn up by Technical Committee ISO/TC 20, Aircraft and space vehicles, and circulated to the Member Bodies in April 1972. [The tables of the ISO Interim Standard Atmosphere (see page iii) were circulated separately to the Member Bodies in August 1972 as Addendum 1 and have now been incorporated in the present document.]

It has been approved by the Member Bodies of the following countries :

Austria*	India*	South Africa, Rep. of*
Belgium*	Ireland*	Thailand*
Brazil	Japan	Turkey*
Czechoslovakia*	Netherlands*	United Kingdom*
Egypt, Arab Rep. of*	New Zealand*	U.S.A.*
France*	Portugal	U.S.S.R.*
Germany*	Romania*

*Also approved Addendum 1.

No Member Body has expressed disapproval of the document.

NOTE —The following International Organizations took part in the discussion of this International Standard at all stages of its development :

International Civil Aviation Organization (ICAO).

World Meteorological Organization (WMO).

The characteristics of the ISO Standard Atmosphere have been calculated as functions of geometric and geopotential altitudes for altitudes from - 2 000 to 50 000 m based on the standard atmospheres of ICAO 1964 and USA 1962, which for these altitudes were recognized as the most representative when comparing the current national and international standards and recommendations on the atmosphere [1-4], [6-7] with the results of recent research.

Data from this recent research have been used for calculation of the atmospheric characteristics for altitudes from 50 000 to 80 000 m, representing the ISO Interim Standard Atmosphere.

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ISO 2533:1975(en)

International StandardISO 2533:1975(en)

Standard Atmosphere

1SCOPE AND FIELD OF A PPLICATION

This International Standard specifies the characteristics of an ISO Standard Atmosphere and is intended for use in calculations and design of flying vehicles, to present the test results of flying vehicles and their components under identical conditions, and to allow unification in the field of development and calibration of instruments. Its use is also recommended in the processing of data from geophysical and meteorological observations.

2BASIC PRINCIPLES AND CALCULATION FOR MULAE

2.1Primary constants and characteristics

The tables of the ISO Standard Atmosphere have been calculated assuming the air to be a perfect gas free from moisture and dust and based on conventional initial values of temperature, pressure and density of the air for mean sea level. The following constants and characteristics are used for calculations and their numerical values are given in table 1 :

gn	—	standard acceleration of free fall. It conforms with latitude φ =45° 32′ 33″ using Lambert's equation of the acceleration of free fall as a function of latitude φ [5] : $\begin{matrix} g_{φ} = 9,806 16 (1 - 0,002 637 3 \cos 2 φ \\ + 0,000 005 9 \cos^{2} 2 φ) \end{matrix}$
M	—	air molar mass at sea level, as obtained from the perfect gas law (2) when introducing the adopted values ρn, ρn, Tn, R* (see table 1);
NA	—	Avogadro constant, based on the value of the nuclide 12C, atomic mass = 12,000, as adopted in 1961 by the Conference of the International Union of Pure and Applied Chemistry as the basic atomic mass unity;
ρn	—	standard air pressure;
R*	—	universal gas constant;
R	—	specific gas constant;
S and βs	—	Sutherland's empirical coefficients in the equation for dynamic viscosity;
To	—	thermodynamic ice-point temperature, at mean sea level;
Tn	—	standard thermodynamic air temperature at mean sea level;
to	—	Celsius ice-point temperature at mean sea level;
tn	—	standard Celsius air temperature at mean sea level;
$κ = \frac{c_{p}}{c_{v}}$	—	adiabatic index, the ratio of the specific heat of air at constant pressure to its specific heat at constant volume;
ρn	—	standard air density;
σ	—	effective collision diameter of an air molecule; taken as constant with altitude.

TABLE 1 — Main constants and characteristics adopted for the calculation of the ISO Standard Atmosphere

Symbol	Value	Unit of measurement
gn	9,806 65	m · s−2
M	28,964 420	kg · kmol−1
NA	602,257 × 1024	kmol−1
ρn	101,325 × 103	Pa
	1,013250 × 103	mbar
	760	mmHg
R*	8 314,32	J · K−1 · kmol−1
		or
		kg · m2 · s−2 · K−1 · kmol−1
R	287,052 87	J · K−1 · kg−1
		or
		m2 · K−1 · s−2
S	110,4	K
To	273,15	K
Tn	288,15	K
to	0,00	°C
tn	15,00	°C
βs	1,458 × 10−6	kg · m−1 · s−1 · K −1/2
κ	1,4	dimensionless
ρn	1,225	kg · m−3
σ	0,365 × 10−9	m

2.2The equation of the static atmosphere and the perfect gas law

Being static with respect to the earth, the atmosphere is subject to gravity. The conditions of air static equilibrium are determined by the equation of the static atmosphere which relates air pressure p, density ρ, acceleration of free fall g and altitude h as follows :

- d p = ρ g d h

...(1)

The perfect gas law relates air pressure to density and temperature as follows :

p = \frac{ρ R^{*} T}{M}

...(2)

At the altitudes considered in this International Standard,

\frac{R^{*}}{M} = constant = R, then

p = ρ R T

...(3)

2.3Geopotential and geometric altitudes; acceleration of free fall

In considering pressure distribution in the atmosphere it is convenient to introduce the gravity potential or geopotential Φ, which characterizes the potential energy of an air particle at a given point.

Any point with x, y, z co-ordinates may be characterized by a single value of gravity potential Φ (x, y, z) in it. The surface defined by the equation

Φ (x, y, z) = constant

is of the same potential in all points and is called an isopotential or geopotential surface. When moving along an external normal from any point on the surface Φ1, to the infinitely close point where the value of the potential is

Φ_{2} = Φ_{1} + d Φ

the work performed for shifting a unit mass from the first surface to the second one will be

d Φ = g (h) d h

...(4)

hence

Φ = \int_{0}^{h} g (h) d h

...(5)

By dividing the geopotential Φ by the standard acceleration of free fall gn, one obtains the value of a length dimension which, symbolized as H, will be :

H = \frac{Φ}{g_{n}} = {\frac{1}{g_{n}} \int}_{0}^{h} g (h) d h

...(6)

Expressed in metres, the value H is numerically equal to the geopotential altitude, which in meteorology is measured in so-called standard geopotential metres1); hence, this value will be called geopotential altitude. The mean sea level is taken as a reference for readings for both geopotential and geometrical altitudes.

From equation (6) it can be seen that, in order to relate geopotential and geometric altitudes, it is necessary first to find a relation between acceleration of free fall g and geometric altitude h.

It is known that gravity is a vectorial summation of the gravitational attraction and the centrifugal force induced by the earth's rotation; it is therefore a complex function of a latitude and a radial distance from the earth's centre and the expression for acceleration of free fall is generally awkward and unpractical for use. However, the acceleration g may be obtained with sufficient accuracy for the purpose of this standard atmosphere by formally neglecting centrifugal acceleration and using only Newton's gravitation law. In this case :

g = g_{n} {(\frac{r}{r + h})}^{2}

...(7)

where r = 6 356 766 m is the nominal earth's radius [5], for which acceleration of free fall and the vertical gradient of acceleration at mean sea level are very close to true values at the latitude 45° 32′ 33″.

The values of g as calculated using the simplified equation (7) with gn = 9,806 65m·s−2 for the altitude of 60 000 m does not differ by more than 0,001 % from the values calculated using the more accurate equation of [6].

Integration of equation (6), substituting for g with its function from (7), gives the following relationship between geopotential and geometric altitudes :

H = \frac{r h}{r + h}

...(8)

h = \frac{rH}{r - H}

...(9)

2.4Atmospheric composition and air molar mass

The earth's atmosphere is a mixture of gas, water vapour and a certain quantity of aerosol. Under certain conditions the quantity of water vapour, carbon dioxide, ozone and some other ingredients the contents of which in the atmosphere is not significant, may vary. The water vapour content undergoes the greatest variations; its concentration at the earth's surface may reach 4 % under high temperature conditions and abruptly diminishes when altitude increases and temperature decreases. Dry clean air composition up to altitudes of 90 to 95 km remains practically constant and corresponds to that given in table 2 [6].

The air molar mass is determined from the perfect gas law (2) using the adopted standard values of pressure ρn, density ρn and temperature Tn for mean sea level, as well as the universal gas constant R*.

TABLE 2 — Dry clean air composition near sea level

Gas	Content of volume %	Molar mass M, kg·kmol-1
Nitrogen (N2)	78,084	28,013 4
Oxygen (O2)	20,947 6	31,998 8
Argon (Ar)	0,934	39,948
Carbon dioxide (CO2)	0,031 4 *	44,009 95
Neon (Ne)	1,818 × 10−3	20,183
Helium (He)	524,0 × 10−6	4,002 6
Krypton (Kr)	114,0 × 10−6	83,80
Xenon (Xe)	8,7 × 10−6	131,30
Hydrogen (H2)	50,0 × 10−6	2,015 94
Nitrogen monoxide (N2O)	50,0 × 10−6*	44,012 8
Methane (CH4)	0,2 × 10−3	16,043 03
Ozone (O3) in summer	up to 7,0 × 10−6*	47,998 2
in winter	up to 2,0 × 10−6*	47,998 2
Sulphur dioxide (SO2)	up to 0,1 × 10−3*	64,062 8
Nitrogen dioxide (NO2)	up to 2,0 × 10−6*	46,005 5
Iodine (l2)	up to 1,0 × 10 −6*	253,808 8
Air	100	28,964 420**
The content of the gas may undergo significant variations from time to time or from place to place. *This value is obtained from the perfect gas law (2).

2.5Physical characteristics of the atmosphere at mean sea level

For the calculation of the ISO Standard Atmosphere the mean sea level is defined as zero altitude for which the initial characteristics gn, pn, ρn and Tn given in table 1 apply. The remaining characteristics have been calculated using the initial ones as a basis and are presented in table 3 :

an	—	speed of sound;
Hpn	—	pressure scale height;
ln	—	mean free path of air particles;
nn	—	air number density;
${\overline{v}}_{n}$	—	mean air-particle speed;
γn	—	specific weight;
νn	—	kinematic viscosity;
λn	—	hermal conductivity;
μn	—	dynamic viscosity;
ωn	—	air-particle collision frequency.

TABLE 3 — Physical characteristics of the atmosphere at mean sea level

Symbol	Value	Unit of measurement
an	340,294	m · s−1
Hρn	8 434,5	m
ln	66,328 × 10−9	m
nn	25,471 × 1024	m−3
${\overline{v}}_{n}$	458,94	m · s−1
γn	12,013	N · m−3
νn	14,607 × 10−6	W · m−1 ·K−1
λn	25,343 × 10−3	W · m−1 · K−1
μn	17,894 × 10−6	Pa · s
ωn	6,919 3 × 109	s−1

2.6Temperature and vertical temperature gradient

Thermodynamic temperature for the melting point of ice under a pressure of 101 325,0 Pa is taken as To=273,15 K. Thermodynamic temperature T (in kelvins, K) is :

T = T_{o} + t

...(10)

where t is the Celsius temperature.

According to the temperature variations with altitude, the atmosphere is divided into several layers.

The transitional zones between these layers are called tropopause, stratopause and mesopause respectively.

For calculating a standard atmosphere, the temperature of each layer is taken as a linear function of geopotential altitude, so that

T = T_{b} + β (H - H_{b})

...(11)

where Tb and Hb are respectively the temperature and the geopotential altitude of the lower limit of the layer concerned and β is the vertical temperature gradient,

\frac{d T}{d H}

The values of temperature and its vertical gradients adopted for the ISO Standard Atmosphere are given in table 4.

TABLE 4 — Temperatures and vertical temperature gradients

Geopotential altitude H, km	Temperature T, K	Temperature gradient β, K · km−1
− 2,00	301,15	− 6,50
0,00	288,15	− 6,50
11,00	216,65	0,00
20,00	216,65	+ 1,00
32,00	228,65	+ 2,80
47,00	270,65	0,00
51,00	270,65	− 2,80
71,00	214,65	− 2,00
80,00	196,65

2.7Pressure

Assuming a linear variation of the temperature with geopotential altitude, the simultaneous solution of the equation of static atmosphere (1) and the perfect gas law (2) yields the following expression for pressure :

\ln p = \ln p_{b} - \frac{g_{n}}{β R} \ln \frac{T_{b} + β (H - H_{b})}{T_{b}}

\begin{matrix} or p = p_{b} {[1 + \frac{β}{T_{b}} (H - H_{b})]}^{- g_{n} / β R} & for β \neq 0 \end{matrix}

...(12)

and

\ln p = \ln p_{b} - \frac{g_{n}}{R T} (H - H_{b})

\begin{matrix} or p = p_{b} \exp [- \frac{g_{n}}{R T} (H - H_{b})] & for β = 0 \end{matrix}

...(13)

Here subscript "b" refers the values of the pertinent characteristics to the lower limit of the layer concerned.

2.8Density and specific weight

The density ρ is calculated from the pressure and the temperature using the perfect gas law :

ρ = \frac{p}{R T}

...(14)

The specific weight γ is the weight per unit volume of air, that is :

γ = ρ g

...(15)

2.9Pressure scale height

Pressure scale height Hp is determined by the equation

H_{p} = \frac{R^{*}}{M} . \frac{T}{g} = \frac{R T}{g}

...(16)

2.10Air number density

The air number density n, i.e. the number of neutral air particles per unit volume, is given by the equation

n = \frac{N_{A} p}{R^{*} T}

...(17)

2.11Mean air-particle speed

The mean air-particle speed

\overline{v}

is defined as the arithmetic average of air-particle speeds obtained from Maxwell's distribution of molecular speeds in the monatomic perfect gas under thermodynamical equilibrium conditions disregarding any exterior force, hence

\overline{v} = {(\frac{8}{π} R T)}^{1 / 2} = 1,595 769 \sqrt{RT}

...(18)

2.12Mean free path of air particles

An air particle between two successive collisions moves uniformly along a straight line, passing a certain average distance / called a mean free path of air particles. Taking into account the distribution of relative speeds of colliding particles, the mean free path of air particles is defined by the expression

I = \frac{R^{*}}{\sqrt{2} π N_{A} σ^{2}} \cdot \frac{T}{p} = \frac{1}{\sqrt{2} π σ^{2} n}

...(19)

2.13Air-particle collision frequency

The air-particle collision frequency ω is the mean air-particle speed divided by the mean free path of air v particles at the same altitude, i.e.

ω = \frac{\overline{v}}{I}

; hence, taking into

account equations (18) and (19)

ω = 4 σ^{2} N_{A} {(\frac{π}{R^{*} M})}^{1 / 2} \cdot \frac{p}{T^{1 / 2}} = 0,994 541 \times 10^{- 18} n \sqrt{R T}

...(20)

2.14Speed of sound

The speed of sound a is given by the expression

a = {(κ R T)}^{1 / 2} = 20,046 796 \sqrt{T}

...(21)

where

κ = \frac{c_{p}}{c_{v}} = 1,4

This expression (21) presents the speed of propagation of an infinitesimal perturbation in a gas. That is why this formula may not be used for calculation, for example, of the speed of propagation of shock waves induced by blast, detonation, body motion in the air at supersonic speed, etc.

The concept of speed of sound loses its meaning with very intensive attenuation of sound pulses which occurs above the altitude limits considered for the ISO Standard Atmosphere.

2.15Dynamic viscosity

The dynamic viscosity μ is defined as the value of internal friction between two neighbouring layers of air moving at different speeds. The tables are established using the following equation based on the kinetic theory with, however, constants derived from experiments :

μ = \frac{β_{s} T^{3 / 2}}{T + S}

...(22)

In this equation βs and S are Sutherland's empirical coefficients (see table 1).

Equation (22) is invalid for very high or very low temperatures and under conditions occurring at altitudes above 90 km.

2.16Kinematic viscosity

The kinematic viscosity v is defined as the ratio of the air dynamic viscosity to the air density, i.e. :

v = \frac{μ}{ρ}

...(23)

The limits for the use of this equation are similar to those of the dynamic viscosity.

2.17Thermal conductivity

The thermal conductivity λ is calculated from the following empirical formula :

λ = \frac{2,648 151 \times 10^{- 3} \cdot T^{3 / 2}}{T + [245,4 \times 10^{- (12 / T)}]}

...(24)

where λ is expressed W·m−1·K−1 and T in kelvins.

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REFERENCES

[1]		COSPAR Working Group IV. C0SPAR International Reference Atmosphere, 1965 (CIRA 1965). North Holland Pub.Co. (Amsterdam1) 1965.
[2]		Comitet Standartov USSR: G0ST 4401.64 "Tablitsa standartnoy atmosfery". Izdatelstvo Standartov, Moskva, 1964.
[3]		Deutscher Normenausschuss: DIN 5450 "Norm Atmosphère", 1968.
[4]		Doc- 7486/2. Manual of the ICA0 Standard Atmosphere extended to 32 kilometres (105 000 feet), sec. edition, 1964. International Civil Aviation 0rganization, Montreal, 1964.
[5]		List R.J., ed.: Smithsonian Meteorological Tables, Sixth Revised Edition, Washington, D.C., 1963.
[6]		U.S. Committee on Extension to the Standard Atmosphere: U.S. Standard Atmosphere, 1962- U-S- Government Printing 0ffice, Washington, D.C., 1962.
[7]		U.S. Committee on Extension to the Standard Atmosphere: U.S. Standard Atmosphere Supplements, 1966. U.S. Government Printing 0ffice, Washington, D.C., 1966.

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ICS 49.020; 17.020; 19.020; 07.060 Price based on 108 pages © International Organization for Standarzation 1975	iso.org

1)The standard geopotential metre (m') which is equal to 9,806 65 m2·s−2 has been adopted by the World Meteorological Organization (see Technical Regulations, WMO , No. 49, vol. l, ed. 1971-Appendix C) and from the 1st July 1972 replaces the geopotential metre formerly in use. Its value was 1 gpm = 9,8 m2·s−2.