International Standard Atmosphere for Aircraft rapid decompression calculations¶
Aircraft rapid decompression calculations require a $\Delta_P$ between cabin and ambient atmosphere as a basic data.
Given a given Cabin pressure $P_{cabin}$, $\Delta_P$ is easilly calculated: $\Delta_P = P_{ambient} - P_{cabin}$
Ambient pressure $P_{ambient}$ is determined by using Standard Atmosphere, also known as ISA (International Standard Atmosphere). ISA defines the atmosphere’s properties (pressure, temperature, density) as a function of altitude.
http://en.wikipedia.org/wiki/International_Standard_Atmosphere
A good reference for a mathematical model of the atmosphere is the NACA report 1235 (http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19930090991.pdf). This report is based on the ICAO standard atmosphere. As stated in SAE AIR5661:
“Consequently, atmospheric properties calculated from NACA
Report 1235 equations will match data provided in more current publications, such as for the U.S. and ISA Standard
Atmospheres.”
Standard atmosphere for the [0km - 11km] range (troposphere)¶
NACA report 1235, eq.18:
$$ \frac{P}{P_0} = \left[\frac{T_0 - a\times H}{T0}\right]^n=\left[\frac{T}{T_0}\right]^n$$
derived from properties at sea level, with $n=5.2561$, and where $H$ is the altitude in $meters$:
$$P = 101325 \times \left ( 1-2.25569\times 10^{-5}\times H\right ) ^{5.25616}\ [Pa]$$
The temperature are varying linearly in the troposphere (NACA1235, eq.13):
$$T=T_0-a\times H$$
where $a=0.0065°C\times m^-1$ is the troposphere lapse rate
Standard atmosphere for the [11km - 20km] range (stratosphere)¶
Once Tropopause (the boundary layer between the troposphere and the stratosphere) is passed, we reach the stratosphere.
NACA report 1235, eq.30:
$$ log{\frac{P}{P_0}}=n\times log{\left[\frac{T_0-aH^*}{T_0}\right]}-B(H-H^*)$$
$$P=0.223356 \times 101325 * e^{-0.000157688 * (H-11000)}$$
The temperatures in the stratosphere are considered constant and equal to Tropopause temperature $T^*$:
$$T=T^*=216.66\ K$$
where $T^*$, $P^*$ and $H^*$ are respectively the Temperature, Pressure and Altitude for Tropopause.
What looks it like? A bit of python¶
Let see now which those equations draw. We will run for that a couple of Python codelines. Let’s write a function isa(altitude)
that returns a tuple (pressure, temperature):