.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/aerodynamics/forces/plot_04_wright_smeaton_stall_speed.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_forces_plot_04_wright_smeaton_stall_speed.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_forces_plot_04_wright_smeaton_stall_speed.py:


The Wright brothers, Smeaton's coefficient and the stall speed
==============================================================

The nineteenth-century lift equation was :math:`L = k V^2 S C_L` with
Smeaton's coefficient :math:`k = 0.005` lb/(ft² mph²). After their 1901
glider lifted far less than predicted, Wilbur and Orville Wright measured
:math:`k \approx 0.0033` in their own wind tunnel; the modern value,
:math:`\tfrac12\rho` at sea level, is 0.00256. Since the minimum flying speed
:math:`V_s = \sqrt{2W/(\rho S C_{L,\max})}`
(:func:`~engineeringkit.aerodynamics.stall_speed`) scales as
:math:`1/\sqrt{k}`, Smeaton's value under-predicts the take-off speed of the
1903 Flyer by about 30%.

.. GENERATED FROM PYTHON SOURCE LINES 17-23

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from engineeringkit.aerodynamics import stall_speed
    from engineeringkit.units import convert








.. GENERATED FROM PYTHON SOURCE LINES 24-28

Smeaton's coefficient as an implied air density
-----------------------------------------------

:math:`k = \tfrac12\rho`, so each historical value implies a density.

.. GENERATED FROM PYTHON SOURCE LINES 28-35

.. code-block:: Python


    lbf_per_ft2 = convert(1.0, "psi", "Pa") / 144
    mph = 0.44704
    for label, k in [("Smeaton (1759)", 0.005), ("Wright tunnel (1901)", 0.0033), ("modern", 0.00256)]:
        rho_implied = 2 * k * lbf_per_ft2 / mph**2
        print(f"{label:22s} k = {k:.5f} -> rho = {rho_implied:.3f} kg/m^3")





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

 .. code-block:: none

    Smeaton (1759)         k = 0.00500 -> rho = 2.396 kg/m^3
    Wright tunnel (1901)   k = 0.00330 -> rho = 1.581 kg/m^3
    modern                 k = 0.00256 -> rho = 1.227 kg/m^3




.. GENERATED FROM PYTHON SOURCE LINES 36-41

The 1903 Flyer's minimum speed
------------------------------

About 340 kg flying mass, 47.4 m² of wing, and :math:`C_{L,\max}` taken
between 0.6 and 1.4.

.. GENERATED FROM PYTHON SOURCE LINES 41-56

.. code-block:: Python


    weight = 340 * 9.80665
    S = 47.4
    clmax = np.linspace(0.6, 1.4, 50)
    fig, ax = plt.subplots(figsize=(6, 4))
    for label, k in [("Smeaton k = 0.005", 0.005), ("Wright k = 0.0033", 0.0033), ("modern k = 0.00256", 0.00256)]:
        rho_implied = 2 * k * lbf_per_ft2 / mph**2
        ax.plot(clmax, stall_speed(weight, rho_implied, S, clmax), label=label)
    ratio = float(stall_speed(weight, 1.225, S, 1.0) / stall_speed(weight, 2 * 0.005 * lbf_per_ft2 / mph**2, S, 1.0))
    print(f"true / Smeaton-predicted stall speed: {ratio:.2f}")
    ax.set(xlabel="$C_{L,\\max}$", ylabel="stall speed [m/s]", title="1903 Flyer minimum flying speed")
    ax.legend()
    fig.tight_layout()

    plt.show()



.. image-sg:: /api/gallery/aerodynamics/forces/images/sphx_glr_plot_04_wright_smeaton_stall_speed_001.png
   :alt: 1903 Flyer minimum flying speed
   :srcset: /api/gallery/aerodynamics/forces/images/sphx_glr_plot_04_wright_smeaton_stall_speed_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    true / Smeaton-predicted stall speed: 1.40





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

   **Total running time of the script:** (0 minutes 0.133 seconds)


.. _sphx_glr_download_api_gallery_aerodynamics_forces_plot_04_wright_smeaton_stall_speed.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/forces/plot_04_wright_smeaton_stall_speed.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_04_wright_smeaton_stall_speed.ipynb <plot_04_wright_smeaton_stall_speed.ipynb>`

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

      :download:`Download Python source code: plot_04_wright_smeaton_stall_speed.py <plot_04_wright_smeaton_stall_speed.py>`

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

      :download:`Download zipped: plot_04_wright_smeaton_stall_speed.zip <plot_04_wright_smeaton_stall_speed.zip>`


.. only:: html

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

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