2.3.1: Hypotheses
- Page ID
- 78094
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Hypothesis 2.1 (Standard atmosphere)
The basic typotheses of ISA are:
- Complies with the perfect gas equation:
\[p = \rho RT, \label{eq2.3.1.1}\]
where \(R\) is the perfect gas constant for air (\(R = 287.053 [J/kg\ K]\)), \(p\) is the pressure, \(\rho\) is the density, and \(T\) the temperature. - In the troposphere the temperature gradient is constant.
\[\begin{array} {c} {\text{Troposphere } (0 \le h < 11000 [m])} \\ {T = T_0 - \alpha h,} \end{array}\]
where \(T_0 = 288.15 [K], \alpha = 6.5 [K/km]\). - In the tropopause and the inferior stratosphere the temperature is constant.
\[\begin{array} {c} {\text{Tropopause and inferior stratosphere } (11000 [m] \le h < 20000 [m])} \\ {T = T_{11}} \end{array}\]
where \(T_{11} = 216.65[K]\). - The air pressure at sea level (\(h = 0\)) is \(p_0 = 101325 [Pa]\). In Equation (\(\ref{eq2.3.1.1}\)), the air density at sea level yields \(\rho_0 = 1.225 [kg/m^3]\).
- The acceleration due to gravity is constant (\(g = 9.80665 [m/s^2]\)).
- The atmosphere is in calm with respect to Earth.