.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/aerodynamics/atmosphere/plot_01_international_standard_atmosphere.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_api_gallery_aerodynamics_atmosphere_plot_01_international_standard_atmosphere.py>`
        to download the full example code or to run this example in your browser via JupyterLite.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_api_gallery_aerodynamics_atmosphere_plot_01_international_standard_atmosphere.py:


The International Standard Atmosphere
=====================================

Aircraft performance depends on air density, which changes with weather.
Albert Toussaint proposed a reference atmosphere in 1919, and ICAO adopted
the International Standard Atmosphere in 1952: a 6.5 K/km linear lapse to the
tropopause at 11 km, then an isothermal layer. Hydrostatic balance and the
ideal-gas law give closed-form pressure and density
(:func:`~engineeringkit.aerodynamics.isa_atmosphere`). This example checks
hydrostatic balance numerically and shows how thin air raises the stall speed.

.. GENERATED FROM PYTHON SOURCE LINES 15-20

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from engineeringkit.aerodynamics import isa_atmosphere, stall_speed








.. GENERATED FROM PYTHON SOURCE LINES 21-23

Profiles and the hydrostatic check
----------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 23-35

.. code-block:: Python


    h = np.linspace(0, 20000, 401)
    state = isa_atmosphere(h)
    residual = np.gradient(state.pressure, h) + state.density * 9.80665
    print(f"max |dp/dh + rho g| / (rho g) = {np.max(np.abs(residual[1:-1] / (state.density[1:-1] * 9.80665))):.1e}")
    for km in [0, 5, 11, 20]:
        s = isa_atmosphere(km * 1e3)
        print(f"{km:2d} km: T = {float(s.temperature):6.2f} K, p = {float(s.pressure):8.0f} Pa, rho = {float(s.density):.4f} kg/m^3")
    fig, axes = state.plot()
    fig.suptitle("International Standard Atmosphere")
    fig.tight_layout()




.. image-sg:: /api/gallery/aerodynamics/atmosphere/images/sphx_glr_plot_01_international_standard_atmosphere_001.png
   :alt: International Standard Atmosphere
   :srcset: /api/gallery/aerodynamics/atmosphere/images/sphx_glr_plot_01_international_standard_atmosphere_001.png
   :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    max |dp/dh + rho g| / (rho g) = 3.7e-04
     0 km: T = 288.15 K, p =   101325 Pa, rho = 1.2250 kg/m^3
     5 km: T = 255.65 K, p =    54020 Pa, rho = 0.7361 kg/m^3
    11 km: T = 216.65 K, p =    22632 Pa, rho = 0.3639 kg/m^3
    20 km: T = 216.65 K, p =     5475 Pa, rho = 0.0880 kg/m^3




.. GENERATED FROM PYTHON SOURCE LINES 36-38

True stall speed rises with altitude
------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 38-45

.. code-block:: Python


    fig, ax = plt.subplots(figsize=(5, 3.6))
    ax.plot(stall_speed(10_000.0, state.density, 16.0, 1.6), h / 1e3)
    ax.set(xlabel="stall true airspeed [m/s]", ylabel="altitude [km]", title="W = 10 kN, S = 16 m², $C_{L,max}$ = 1.6")
    fig.tight_layout()

    plt.show()



.. image-sg:: /api/gallery/aerodynamics/atmosphere/images/sphx_glr_plot_01_international_standard_atmosphere_002.png
   :alt: W = 10 kN, S = 16 m², $C_{L,max}$ = 1.6
   :srcset: /api/gallery/aerodynamics/atmosphere/images/sphx_glr_plot_01_international_standard_atmosphere_002.png
   :class: sphx-glr-single-img






.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.288 seconds)


.. _sphx_glr_download_api_gallery_aerodynamics_atmosphere_plot_01_international_standard_atmosphere.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: lite-badge

      .. image:: images/jupyterlite_badge_logo.svg
        :target: ../../../../lite/lab/index.html?path=api/gallery/aerodynamics/atmosphere/plot_01_international_standard_atmosphere.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_01_international_standard_atmosphere.ipynb <plot_01_international_standard_atmosphere.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_01_international_standard_atmosphere.py <plot_01_international_standard_atmosphere.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_01_international_standard_atmosphere.zip <plot_01_international_standard_atmosphere.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_