# U.S. Standard Atmosphere

Comparison of the 1962 US Standard Atmosphere graph of geometric altitude against air density, pressure, the speed of sound and temperature with approximate altitudes of various objects.[1]

The U.S. Standard Atmosphere is a static atmospheric model of how the pressure, temperature, density, and viscosity of the Earth's atmosphere change over a wide range of altitudes or elevations. The model, based on an existing international standard, was first published in 1958 by the U.S. Committee on Extension to the Standard Atmosphere, and was updated in 1962, 1966, and 1976. It is largely consistent in methodology with the International Standard Atmosphere, differing mainly in the assumed temperature distribution at higher altitudes.

Visualization of composition by volume of Earth's atmosphere. Water vapor is not included, as this is highly variable. Each tiny cube (such as the one representing krypton) has one millionth of the volume of the entire block. Data is from NASA Langley.

## Methodology

The USSA mathematical model divides the atmosphere into layers with an assumed linear distribution of absolute temperature T against geopotential altitude h.[2] The other two values (pressure P and density ρ) are computed by simultaneously solving the equations resulting from:

${\displaystyle {\frac {dP}{dh}}=-\rho g}$ , and
${\displaystyle \ P=\rho R_{\rm {specific}}T}$

at each geopotential altitude, where g is the standard acceleration of gravity, and Rspecific is the specific gas constant for dry air.

Air density must be calculated in order to solve for the pressure, and is used in calculating dynamic pressure for moving vehicles. Dynamic viscosity is an empirical function of temperature, and kinematic viscosity is calculated by dividing dynamic viscosity by the density.

Thus the standard consists of a tabulation of values at various altitudes, plus some formulas by which those values were derived.

To allow modeling conditions below mean sea level, the troposphere is actually extended to −2,000 feet (−610 m), where the temperature is 66.1 °F (18.9 °C), pressure is 15.79 pounds per square inch (108,900 Pa), and density is 0.08106 pounds per cubic foot (1.2985 kg/m3).

## 1962 version

The basic assumptions made for the 1962 version were:[3]

• air is a clean, dry, perfect gas mixture (cp/cv = 1.40)
• molecular weight to 90 km of 28.9644 (C-12 scale)
• principal sea-level constituents are assumed to be:
• N2 – 78.084%
• O2 – 20.9476%
• Ar – 0.934%
• CO2 – 0.0314%
• Ne – 0.001818%
• He – 0.000524%
• CH4 – 0.0002%.
• assigned mean conditions at sea level are as follows :
• P = 14.696 psi = 2116.22 psf = 101325 Pa = 29.92 inHg = 0.1013250 MN/m2
• T = 59 °F = 518.67 °R = 15 °C = 288.15 K
• ρ = 0.0764734 lb/(cu ft) = 1.225 0 kg/m3
• g = 32.174 1 ft/s2 = 9.80665 m/s2
• R = 1545.31 ft⋅lb/(lbmol⋅°R) = 8.31432 J/(mol⋅K).

## 1976 version

This is the most recent version and differs from previous versions only above 51 km:

Subscript b Geopotential
height above MSL[4]
Static pressure Standard temperature
(K)
Temperature Lapse Rate
(m) (ft) (pascals) (inHg) (K/m) (K/ft)
0 0 0 101325 29.92126 288.15 -0.0065 -0.001981
1 11,000 36,089 22632.1 6.683245 216.65 0.0 0.0
2 20,000 65,617 5474.89 1.616734 216.65 0.001 0.0003048
3 32,000 104,987 868.019 0.2563258 228.65 0.0028 0.0008534
4 47,000 154,199 110.906 0.0327506 270.65 0.0 0.0
5 51,000 167,323 66.9389 0.01976704 270.65 -0.0028 -0.0008534
6 71,000 232,940 3.95642 0.00116833 214.65 -0.002 -0.0006096

## References

1. ^ Geometric altitude vs. temperature, pressure, density, and the speed of sound derived from the 1962 U.S. Standard Atmosphere.
2. ^ Gyatt, Graham (2006-01-14): "The Standard Atmosphere". A mathematical model of the 1976 U.S. Standard Atmosphere.
3. ^ Tuve, George Lewis; Bolz, Ray E. (1973). CRC handbook of tables for applied engineering science. Boca Raton: CRC Press. ISBN 0-8493-0252-8.
4. ^ U.S. Standard Atmosphere, 1962, U.S. Government Printing Office, Washington, D.C., 1962

## Documents

• U.S. Extension to the ICAO Standard Atmosphere, U.S. Government Printing Office, Washington, D.C., 1958.
• U.S. Standard Atmosphere, 1962, U.S. Government Printing Office, Washington, D.C., 1962.
• U.S. Standard Atmosphere Supplements, 1966, U.S. Government Printing Office, Washington, D.C., 1966.
• U.S. Standard Atmosphere, 1976, U.S. Government Printing Office, Washington, D.C., 1976 (Linked file is 17 MB).