This work is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0) license.
Kamila Zdybał, Science Docs, 2020
Calculator of temperature, pressure and density at a user-specified altitude for the International Standard Atmosphere (ISA).
Credits:
The inspiration for creating this calculator came from the course Introduction to Aeronautical Engineering offered by TU Delft.
This site was created following the tutorial by Professor Tony Saad from the University of Utah.
Enter the desired altitude below:
#HIDDEN
import ipywidgets as widgets
from ipywidgets import interact, interact_manual
from SAC import get_parameters
altitude = widgets.BoundedFloatText(value=55, min=0, max=85, step=0.001, description='Altitude [km]:')
ui_altitude = widgets.HBox([altitude])
out = widgets.interactive_output(get_parameters, {'altitude': altitude})
display(ui_altitude, out)
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mezosphere (2) (71-85)km
mezosphere (1) (51-70.999)km
stratopause (47-50.999)km (isothermal)
stratosphere (2) (32-46.999)km
stratosphere (1) (20-31.999)km
tropopause (11-19.999)km (isothermal)
troposphere (0-10.999)km
----- sea level ----------- (0)km --------------------$T_0 = 288.15K$
$p_0 = 101325.0 Pa$
$\rho_0 = 1.225 kg/m^3$
With the specific gas constant:
$R = 287.058 J/kgK$
and gravitational acceleration:
$g = 9.80665 kgm/s^2$
The values of lapse rates are given in $K/m$.
$T(h) = T_0 -0.0065 h$
$p(h) = p_0 (\frac{T(h)}{T_0})^{\frac{-g}{-0.0065 R}}$
$\rho(h) = \rho_0 (\frac{T(h)}{T_0})^{\frac{-g}{-0.0065 R} - 1}$
$T(h) = T_1$ (isothermal)
$p(h) = p_1 e^{\frac{-g}{R T_1} (h - 11000)}$
$\rho(h) = \rho_1 e^{\frac{-g}{T_1} (h - 11000)}$
where $T_1$, $p_1$, $\rho_1$ are the temperature, pressure and density at the interface between troposphere and tropopause.
$T(h) = T_2 + 0.001 (h - 20000)$
$p(h) = p_2 (\frac{T(h)}{T_2})^{\frac{-g}{0.001 R}}$
$\rho(h) = \rho_2 (\frac{T(h)}{T_2})^{\frac{-g}{0.001 R} - 1}$
where $T_2$, $p_2$, $\rho_2$ are the temperature, pressure and density at the interface between tropopause and stratosphere (1).
$T(h) = T_3 + 0.0028 (h - 32000)$
$p(h) = p_3 (\frac{T(h)}{T_3})^{\frac{-g}{0.0028 R}}$
$\rho(h) = \rho_3 (\frac{T(h)}{T_3})^{\frac{-g}{0.0028 R} - 1}$
where $T_3$, $p_3$, $\rho_3$ are the temperature, pressure and density at the interface between stratosphere (1) and stratosphere (2).
$T(h) = T_4$ (isothermal)
$p(h) = p_4 e^{\frac{-g}{R T_4} (h - 47000)}$
$\rho(h) = \rho_4 e^{\frac{-g}{T_4} (h - 47000)}$
where $T_4$, $p_4$, $\rho_4$ are the temperature, pressure and density at the interface between stratosphere (2) and stratopause.
$T(h) = T_5 -0.0028 (h - 51000)$
$p(h) = p_5 (\frac{T(h)}{T_5})^{\frac{-g}{-0.0028 R}}$
$\rho(h) = \rho_5 (\frac{T(h)}{T_5})^{\frac{-g}{-0.0028 R} - 1}$
where $T_5$, $p_5$, $\rho_5$ are the temperature, pressure and density at the interface between stratopause and mezosphere (1).
$T(h) = T_6 -0.002 (h - 71000)$
$p(h) = p_6 (\frac{T(h)}{T_6})^{\frac{-g}{-0.002 R}}$
$\rho(h) = \rho_6 (\frac{T(h)}{T_6})^{\frac{-g}{-0.002 R} - 1}$
where $T_6$, $p_6$, $\rho_6$ are the temperature, pressure and density at the interface between mezosphere (1) and mezosphere (2).