.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/aerodynamics/compressible/plot_07_meyer_oblique_shock.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_compressible_plot_07_meyer_oblique_shock.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_compressible_plot_07_meyer_oblique_shock.py:


Meyer's oblique shock and the theta-beta-M relation (1908)
==========================================================

Theodor Meyer's 1908 Göttingen thesis showed that a supersonic stream turned
into itself by a wedge passes through a straight *oblique* shock. Its wave
angle :math:`\beta` follows from the deflection :math:`\theta` and the Mach
number through the :math:`\theta`-:math:`\beta`-:math:`M` relation
(:func:`~engineeringkit.aerodynamics.oblique_shock_deflection`). The jump
itself is a normal shock in the velocity component normal to the wave
(:func:`~engineeringkit.aerodynamics.oblique_shock`). This example draws
the chart, finds the weak and strong solutions for a 20° wedge at Mach 2,
and shows the shock detaching once the wedge is steeper than
:math:`\theta_{\max}`.

.. GENERATED FROM PYTHON SOURCE LINES 18-29

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from engineeringkit.aerodynamics import (
        normal_shock_mach2,
        oblique_shock,
        oblique_shock_deflection,
        oblique_shock_max_deflection,
    )
    from engineeringkit.aerodynamics.visualizers import plot_theta_beta_mach








.. GENERATED FROM PYTHON SOURCE LINES 30-32

Weak and strong solutions on a 20° wedge
----------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 32-49

.. code-block:: Python


    theta = np.radians(20.0)
    weak, strong = oblique_shock(2.0, theta), oblique_shock(2.0, theta, strong=True)
    for name, shock in [("weak", weak), ("strong", strong)]:
        print(
            f"{name:6s}: beta = {np.degrees(shock.beta):5.2f} deg, M2 = {shock.mach2:.3f}, "
            f"p2/p1 = {shock.pressure_ratio:.3f}, p02/p01 = {shock.stagnation_pressure_ratio:.3f}"
        )
    theta_max, beta_max = oblique_shock_max_deflection(2.0)
    print(f"maximum deflection at M = 2: {np.degrees(theta_max):.2f} deg (beta = {np.degrees(beta_max):.2f} deg)")

    # Both waves turn the flow by exactly 20°, and the normal component obeys the normal-shock law.
    for shock in (weak, strong):
        assert np.isclose(oblique_shock_deflection(2.0, shock.beta), theta)
        assert np.isclose(shock.mach2 * np.sin(shock.beta - theta), normal_shock_mach2(2.0 * np.sin(shock.beta)))
    assert weak.mach2 > 1 > strong.mach2





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

 .. code-block:: none

    weak  : beta = 53.42 deg, M2 = 1.210, p2/p1 = 2.843, p02/p01 = 0.893
    strong: beta = 74.27 deg, M2 = 0.728, p2/p1 = 4.157, p02/p01 = 0.756
    maximum deflection at M = 2: 22.97 deg (beta = 64.67 deg)




.. GENERATED FROM PYTHON SOURCE LINES 50-56

The theta-beta-M chart
----------------------

Solid curves are the weak branch seen on wedges and ramps; dashed curves
the strong branch. To the right of the dotted line of maximum deflection
no attached shock exists and a curved bow shock stands off the nose.

.. GENERATED FROM PYTHON SOURCE LINES 56-65

.. code-block:: Python


    fig, ax = plt.subplots(figsize=(7, 5))
    plot_theta_beta_mach([1.5, 2.0, 3.0, 5.0, 10.0], ax=ax)
    ax.plot(np.degrees(theta), np.degrees(weak.beta), "ko")
    ax.plot(np.degrees(theta), np.degrees(strong.beta), "ks", mfc="none")
    ax.set(xlim=(0, 45), ylim=(0, 90), title="Oblique shocks: wave angle against deflection")
    fig.tight_layout()

    plt.show()



.. image-sg:: /api/gallery/aerodynamics/compressible/images/sphx_glr_plot_07_meyer_oblique_shock_001.png
   :alt: Oblique shocks: wave angle against deflection
   :srcset: /api/gallery/aerodynamics/compressible/images/sphx_glr_plot_07_meyer_oblique_shock_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.146 seconds)


.. _sphx_glr_download_api_gallery_aerodynamics_compressible_plot_07_meyer_oblique_shock.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/compressible/plot_07_meyer_oblique_shock.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_07_meyer_oblique_shock.ipynb <plot_07_meyer_oblique_shock.ipynb>`

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

      :download:`Download Python source code: plot_07_meyer_oblique_shock.py <plot_07_meyer_oblique_shock.py>`

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

      :download:`Download zipped: plot_07_meyer_oblique_shock.zip <plot_07_meyer_oblique_shock.zip>`


.. only:: html

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

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