ISA Atmosphere Model
International Standard Atmosphere (ISA, or ISA - International Standard Atmosphere).
Description
The ISA Atmosphere Model block realises the mathematical representation of the international standard atmosphere according to [1], generates values of temperature, pressure, density and sound speed for a given geopotential or geometric height .
The ISA Atmosphere Model block works in SI units.
Limitations
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Below an altitude of -2000 m and above an altitude of 1200000 m, temperature and pressure values remain unchanged.
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The density and speed of sound are calculated using the ideal gas equation.
Algorithm
The temperature of each layer up to an altitude of 120 km is calculated using the formula:
where is the thermodynamic temperature gradient along the geopotential height, K/m.
The temperature of each layer above the height of 120 km is calculated by the formula:
where is the thermodynamic temperature gradient along the geometric height, K/m.
Parameter values with the index refer to the lower boundary of the considered layer.
The values of thermodynamic temperature gradients and are given in [1, Table 5] and [1, Table 6], respectively.
The pressure up to the height of 120 km is calculated by the formulas:
for ,
for ,
where
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- free fall acceleration, m/s2;
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- molar temperature gradient along the geopotential height, K/m;
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- specific gas constant, J/kg⋅K;
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- molar temperature, K.
The values of and up to and including the height of 94000 m are equal.
The pressure above the altitude of 120 km is calculated by the formula:
where
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- is the concentration of neutral air particles, m-3;
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- is the universal gas constant, J/K⋅kmol;
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- Avogadro’s number, kmol-1.
The concentration of particles is approximated by a fourth degree polynomial of the form
The coefficients and the exponent of degree are given in [1, Table 7].
Sound velocity is calculated by the formula:
Density of air is calculated using the formula:
where is the molar mass, kg/kmol.
The molar mass up to a height of 94000 m is constant and equal to the molar mass of air at sea level [1, Table 1]. The molar mass up to an altitude of 97000 m decreases according to the expression [1, Section 4]. Further decrease up to the altitude of 97500 m and the altitude interval from 97500 m to 120000 m follows a linear law with gradients , respectively equal to -0.00012 and -0.0001511 kg/m⋅kmol. In the altitude range from 120000 m to 1200000 m, the molar mass is approximated by a third degree polynomial of the form:
Coefficients are given in [1, Table 3].