.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/aerodynamics/forces/plot_02_cayley_lift_and_drag.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_02_cayley_lift_and_drag.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_02_cayley_lift_and_drag.py:


Cayley's separation of lift and drag in level flight
====================================================

George Cayley's *On Aerial Navigation* (1809-1810) proposed the modern
aeroplane by separating the problem: a fixed wing supports the weight (lift),
and a separate propulsion system overcomes the resistance (drag). In steady
level flight lift equals weight and thrust equals drag. Here
:func:`~engineeringkit.aerodynamics.lift` and
:func:`~engineeringkit.aerodynamics.drag` turn coefficients into forces for a
light aircraft, and the required lift coefficient and thrust are traced
across the speed range.

.. GENERATED FROM PYTHON SOURCE LINES 16-21

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from engineeringkit.aerodynamics import drag, drag_polar, dynamic_pressure, lift








.. GENERATED FROM PYTHON SOURCE LINES 22-24

Lift must equal weight
----------------------

.. GENERATED FROM PYTHON SOURCE LINES 24-31

.. code-block:: Python


    weight, S, AR, e, cd0, rho = 10_000.0, 16.0, 7.5, 0.8, 0.027, 1.225
    V = np.linspace(28, 80, 200)
    q = dynamic_pressure(rho, V)
    cl_required = weight / (q * S)
    assert np.allclose(lift(q, S, cl_required), weight)








.. GENERATED FROM PYTHON SOURCE LINES 32-37

Thrust must equal drag
----------------------

Parasite drag grows like :math:`V^2`; the induced drag that comes with
lift falls like :math:`1/V^2`. Their sum has a minimum.

.. GENERATED FROM PYTHON SOURCE LINES 37-58

.. code-block:: Python


    cd = drag_polar(cl_required, cd0, AR, e)
    thrust_required = drag(q, S, cd)
    parasite = drag(q, S, cd0)
    induced = thrust_required - parasite
    i = int(np.argmin(thrust_required))
    print(f"minimum drag {thrust_required[i]:.0f} N at {V[i]:.1f} m/s (C_L = {cl_required[i]:.2f})")
    print(f"there, parasite {parasite[i]:.0f} N ~ induced {induced[i]:.0f} N")

    fig, axes = plt.subplots(1, 2, figsize=(9, 3.5))
    axes[0].plot(V, cl_required)
    axes[0].set(xlabel="speed [m/s]", ylabel="required $C_L$", title="Lift = weight")
    axes[1].plot(V, thrust_required, label="total drag = thrust required")
    axes[1].plot(V, parasite, "--", label="parasite")
    axes[1].plot(V, induced, ":", label="induced")
    axes[1].plot(V[i], thrust_required[i], "ko")
    axes[1].set(xlabel="speed [m/s]", ylabel="force [N]", title="Thrust = drag")
    axes[1].legend()
    fig.tight_layout()

    plt.show()



.. image-sg:: /api/gallery/aerodynamics/forces/images/sphx_glr_plot_02_cayley_lift_and_drag_001.png
   :alt: Lift = weight, Thrust = drag
   :srcset: /api/gallery/aerodynamics/forces/images/sphx_glr_plot_02_cayley_lift_and_drag_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    minimum drag 757 N at 37.9 m/s (C_L = 0.71)
    there, parasite 381 N ~ induced 376 N





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

   **Total running time of the script:** (0 minutes 0.198 seconds)


.. _sphx_glr_download_api_gallery_aerodynamics_forces_plot_02_cayley_lift_and_drag.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_02_cayley_lift_and_drag.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_02_cayley_lift_and_drag.ipynb <plot_02_cayley_lift_and_drag.ipynb>`

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

      :download:`Download Python source code: plot_02_cayley_lift_and_drag.py <plot_02_cayley_lift_and_drag.py>`

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

      :download:`Download zipped: plot_02_cayley_lift_and_drag.zip <plot_02_cayley_lift_and_drag.zip>`


.. only:: html

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

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