Barometric formula
The barometric formula, sometimes called the exponential atmosphere or isothermal atmosphere, is a formula used to model how the pressure (or density) of the air changes with altitude. The pressure drops approximately by 11.3 Pa per meter in first 1000 meters above seal level.
There are two different equations for computing pressure at various height regimes below 86 km (or 278,400 feet). The first equation is used when the value of standard temperature lapse rate is not equal to zero; the second equation is used when standard temperature lapse rate equals zero.
Equation 1:
Equation 2:
where
Or converted to imperial units:
where
The value of subscript b ranges from 0 to 6 in accordance with each of seven successive layers of the atmosphere shown in the table below. In these equations, g0, M and R* are each single-valued constants, while P, L, T, and h are multivalued constants in accordance with the table below. The values used for M, g0, and R* are in accordance with the U.S. Standard Atmosphere, 1976, and the value for R* in particular does not agree with standard values for this constant. The reference value for Pb for b = 0 is the defined sea level value, P0 = 101 325 Pa or 29.92126 inHg. Values of Pb of b = 1 through b = 6 are obtained from the application of the appropriate member of the pair equations 1 and 2 for the case when h = hb+1.
The expressions for calculating density are nearly identical to calculating pressure. The only difference is the exponent in Equation 1.
There are two different equations for computing density at various height regimes below 86 geometric km (84 852 geopotential meters or 278,385.8 geopotential feet). The first equation is used when the value of standard temperature lapse rate is not equal to zero; the second equation is used when standard temperature lapse rate equals zero.
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