.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/aerodynamics/airfoils/plot_02_thin_airfoil_theory.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_airfoils_plot_02_thin_airfoil_theory.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_airfoils_plot_02_thin_airfoil_theory.py:


Thin-airfoil theory: lift slope 2π and the camber shift
=======================================================

Max Munk (1922) and Hermann Glauert (1926) replaced a thin section by a vortex
sheet on its camber line. Satisfying flow tangency gives a lift slope of
exactly :math:`2\pi` per radian for *every* thin section, while camber only
shifts the curve by a zero-lift angle given by an integral of the camber
slope. :func:`~engineeringkit.aerodynamics.naca4_zero_lift_angle` evaluates
that integral for NACA four-digit camber lines, and
:func:`~engineeringkit.aerodynamics.thin_airfoil_cl` gives the lift line.

.. GENERATED FROM PYTHON SOURCE LINES 15-20

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from engineeringkit.aerodynamics import naca4_zero_lift_angle, thin_airfoil_cl








.. GENERATED FROM PYTHON SOURCE LINES 21-26

Zero-lift angle versus camber
-----------------------------

The integral is linear in the maximum camber ``m``; moving the camber
aft (larger ``p``) makes it more negative.

.. GENERATED FROM PYTHON SOURCE LINES 26-33

.. code-block:: Python


    for designation in ["0012", "2412", "4412", "4612"]:
        m, p = int(designation[0]) / 100, int(designation[1]) / 10 or 0.4
        a0 = float(naca4_zero_lift_angle(m, p))
        print(f"NACA {designation}: alpha_L=0 = {np.degrees(a0):+.2f} deg")
    assert np.isclose(naca4_zero_lift_angle(0.04, 0.4), 2 * naca4_zero_lift_angle(0.02, 0.4))





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

 .. code-block:: none

    NACA 0012: alpha_L=0 = -0.00 deg
    NACA 2412: alpha_L=0 = -2.08 deg
    NACA 4412: alpha_L=0 = -4.15 deg
    NACA 4612: alpha_L=0 = -5.18 deg




.. GENERATED FROM PYTHON SOURCE LINES 34-36

Parallel lift lines
-------------------

.. GENERATED FROM PYTHON SOURCE LINES 36-55

.. code-block:: Python


    alpha = np.radians(np.linspace(-6, 12, 100))
    fig, axes = plt.subplots(1, 2, figsize=(9, 3.6))
    for designation in ["0012", "2412", "4412"]:
        m = int(designation[0]) / 100
        a0 = naca4_zero_lift_angle(m, 0.4)
        axes[0].plot(np.degrees(alpha), thin_airfoil_cl(alpha, a0), label=f"NACA {designation}")
    axes[0].axhline(0, color="gray", lw=0.5)
    axes[0].set(xlabel="angle of attack [deg]", ylabel="$c_l$", title="Slope 2π, shifted by camber")
    axes[0].legend()

    m_values = np.linspace(0, 0.09, 10)
    for p in [0.2, 0.4, 0.6]:
        axes[1].plot(m_values * 100, [np.degrees(naca4_zero_lift_angle(m, p)) for m in m_values], label=f"p = {p}")
    axes[1].set(xlabel="maximum camber [% chord]", ylabel="zero-lift angle [deg]", title="Glauert's camber integral")
    axes[1].legend()
    fig.tight_layout()

    plt.show()



.. image-sg:: /api/gallery/aerodynamics/airfoils/images/sphx_glr_plot_02_thin_airfoil_theory_001.png
   :alt: Slope 2π, shifted by camber, Glauert's camber integral
   :srcset: /api/gallery/aerodynamics/airfoils/images/sphx_glr_plot_02_thin_airfoil_theory_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.228 seconds)


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.. only:: html

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

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