Section: 14 | U.S. Standard Atmosphere (1976) |

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U.S. STANDARD ATMOSPHERE (1976)

A Standard Atmosphere is a hypothetical vertical distribution of atmospheric temperature, pressure, and density that is roughly representative of year-round, midlatitude conditions. Typical uses are to serve as a basis for pressure altimeter calibrations, aircraft performance calculations, aircraft and rocket design, ballistic tables, meteorological diagrams, and various types of atmospheric modeling. The air is assumed to be dry and to obey the perfect gas law and the hydrostatic equation which, taken together, relate temperature, pressure, and density with vertical position. The atmosphere is considered to rotate with the Earth and to be an average over the diurnal cycle, the semiannual variation, and the range from active to quiet geomagnetic and sunspot conditions.

The U.S. Standard Atmosphere (1976) is an idealized, steady-state representation of mean annual conditions of the Earth’s atmosphere from the surface to 1000 km at latitude 45° N, as it is assumed to exist during a period with moderate solar activity. The defining meteorological elements are sea-level temperature and pressure and a temperature-height profile to 1000 km. The 1976 Standard Atmosphere uses the following sea-level values that have been standard for many decades:

Temperature — 288.15 K (15 °C)
Pressure — 101325 Pa (1013.25 mbar, 760 mmHg, or 29.92 in Hg)
Density — 1225 g/m³ (1.225 g/L)
Mean molar mass — 28.964 g/mol

The parameters included in this condensed version of the U.S. Standard Atmosphere are given in Table 2. Column definitions for Table 2 are as follows.

Column heading	Definition
Z	Height (geometric) above mean sea level, in meters
T	Temperature, in K
P	Pressure, in Pa (1 Pa = 0.01 millibars)
ρ	Density, in kg m^-3, (1 kg m^-3 = 1 g L^-1)
n	Number density, in molecules m^-3
ν	Mean collision frequency, in collisions s^-1
l	Mean free path, in m
η	Absolute viscosity, in Pa s (1 Pa s = 1000 cP)
k	Thermal conductivity, in W m^-1 K^-1
v_s	Speed of sound, m s^-1
g	Acceleration of gravity, in m s^-2

The sea-level composition (percent by volume) is taken to be:

N₂—78.084%
O₂—20.9476
Ar — 0.934
CO₂ — 0.0314
Ne — 0.001818
He — 0.000524
Kr — 0.000114
Xe — 0.0000087
CH₄ — 0.0002
H₂ — 0.00005

The T and P columns for the troposphere and lower stratosphere were generated from the following formulas as given in Table 1.

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TABLE 1. Formulas for Calculating Temperature and Pressure for the U.S. Standard Atmosphere at Different Heights

Height	T/K	P/Pa
H ≤ 11000 m	288.15 – 0.0065 H	101325(288.15/T)^–5.25577
11000 m < H ≤ 20000 m	216.65	22632 e^{–0.00015768832(H–11000)}
20000 m < H < 32000 m	216.65 + 0.0010(H–20000)	5474.87(216.65/T)^34.16319

In Table 1, H = rZ/(r + Z) is the geopotential height in meters and r is the mean Earth radius at 45° N latitude, taken as 6356766 m. For altitudes up to 32 km, ρ = 0.003483677(P/T) in the units used here. Formulas for the other quantities may be found in the references.

References

COESA, U.S. Standard Atmosphere, 1976, U.S. Government Printing Office, Washington, DC, 1976.
Jursa, A. S., Ed., Handbook of Geophysics and the Space Environment, Air Force Geophysics Laboratory, 1985.

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TABLE 2. Properties of the U.S. Standard Atmosphere as a Function of Altitude

Z/m	T/K	P/Pa	ρ/kg m^–3	n/m^–3	ν/s^–1	l/m	η/Pa s	k/W m^–1 K^–1	v_s/m s^–1	g/m s^–2
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–5000	320.68	1.778E+05	1.931	4.015E+25	1.151E+10	4.208E–08	1.942E–05	0.02788	359.0	9.822
–4500	317.42	1.685E+05	1.849	3.845E+25	1.096E+10	4.395E–08	1.927E–05	0.02763	357.2	9.830
–4000	314.17	1.596E+05	1.770	3.680E+25	1.044E+10	4.592E–08	1.912E–05	0.02738	355.3	9.819
–3500	310.91	1.511E+05	1.693	3.520E+25	9.933E+09	4.800E–08	1.897E–05	0.02713	353.5	9.818
–3000	307.66	1.430E+05	1.619	3.366E+25	9.448E+09	5.019E–08	1.882E–05	0.02688	351.6	9.816
–2500	304.41	1.352E+05	1.547	3.217E+25	8.982E+09	5.252E–08	1.867E–05	0.02663	349.8	9.814
–2000	301.15	1.278E+05	1.478	3.102E+25	8.623E+09	5.447E–08	1.852E–05	0.02638	347.9	9.813
–1500	297.90	1.207E+05	1.411	2.935E+25	8.106E+09	5.757E–08	1.836E–05	0.02613	346.0	9.811
–1000	294.65	1.139E+05	1.347	2.801E+25	7.693E+09	6.032E–08	1.821E–05	0.02587	344.1	9.810
–500	291.40	1.075E+05	1.285	2.672E+25	7.298E+09	6.324E–08	1.805E–05	0.02562	342.2	9.808
0	288.15	1.013E+05	1.225	2.547E+25	6.919E+09	6.633E–08	1.789E–05	0.02533	340.3	9.807
500	284.90	9.546E+04	1.167	2.427E+25	6.556E+09	6.961E–08	1.774E–05	0.02511	338.4	9.805
1000	281.65	8.988E+04	1.112	2.311E+25	6.208E+09	7.310E–08	1.758E–05	0.02485	336.4	9.804
1500	278.40	8.456E+04	1.058	2.200E+25	5.874E+09	7.680E–08	1.742E–05	0.02459	334.5	9.802
2000	275.15	7.950E+04	1.007	2.093E+25	5.555E+09	8.073E–08	1.726E–05	0.02433	332.5	9.801
2500	271.91	7.469E+04	0.957	1.990E+25	5.250E+09	8.491E–08	1.710E–05	0.02407	330.6	9.799
3000	268.66	7.012E+04	0.909	1.891E+25	4.959E+09	8.937E–08	1.694E–05	0.02381	328.6	9.797
3500	265.41	6.579E+04	0.863	1.795E+25	4.680E+09	9.411E–08	1.678E–05	0.02355	326.6	9.796
4000	262.17	6.166E+04	0.819	1.704E+25	4.414E+09	9.917E–08	1.661E–05	0.02329	324.6	9.794

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