The US Standard Atmosphere 1976

MJ Mahoney

The US Standard Atmosphere 1976 is an average, piece-wise continuous, mid-latitude temperature profile of the earth's atmosphere. It is defined as having a temperature of 288.15 K at mean sea level (0 km geopotential height = 1013.25 hPa) with various lapse rates which change at seven specified geopotential heights. It also assumes that the relative humidity is zero throughout the atmosphere. The Table below summarizes the value of several parameters at each of the defined levels.

Geopotential Height
Temperature
Lapse Rate
Pressure
Density
(km)
(K)
(K/km)
(hPa)
(kg/m3 )
0
288.15
-6.5
1013.25 00
1.225
11
216.65
0.0
226.3206
0.364
20
216.65
+1.0
54.7489
8.803E-02
32
228.65
+2.8
8.6802
1.322E-02
47
270.65
0.0
1.1091
1.428E-03
51
270.65
-2.8
0.6694
8.616E-04
71
214.65
-2.0
0.0396
6.421E-05
84.852
186.95

0.0037
6.958E-06

Using this definition of the US Standard Atmosphere, the hydrostatic equation (HE1 ) can be used to derive expressions for converting between pressure and pressure altitude. First we use the Ideal Gas Law (IGL ) to eliminate the density; this results in: HE2 . On rearrangement, this becomes: HE3 , which can be converted to the following integral equation: Int1 . In this equation, we use the letter "s" to denote standard atmosphere values, and the subscript i denotes the level from which the integration is being initiated . Zsi, Psi, Ts i, and LRs i denote the pressure altitude (km), pressure (hPa), temperature (K), and lapse rate (K/km), respectively, at level i as given in the above table; Rd is the gas constant for dry air (287.05307 J /kg K), and gamma 45 is the acceleration of gravity at a latitude of 45.542 degrees (= 9.80665 m/s2). Integration of this equation to solve for the pressure (P) as a function of the pressure altitude (Z) has two cases depending on whether the lapse rate (LRsi) in the expression ( Ts ) for the standard atmosphere temperature profile is zero or not. (It is zero from 11 to 20 km, and from 47 to 51 km.) The resulting expressions for P(z) are given below, and these are easily inverted to obtain expressions for Z(p). The factor of 1000 in the equations converts the lapse rate from K/km to K/m to be consistent with the other units.

Convert from Pressure Altitude to Pressure

Lapse Rate is Not Zero

z1 where Ts

Lapse Rate is Zero

p2

Convert from Pressure to Pressure Altitude

Lapse Rate is Not Zero

p1

Lapse Rate is Zero

p2




[Back to Home Page]