Uploaded April 2019 | Updated September 2026, 2 weeks ago

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In this video, we will compute the circulation around an ellipse for an arbitrary vector field using MATLAB and Python. First we will look at the equation for circulation, and then transform it into a useful form for its calculation using a discrete vector field. Finally, we will run some code that computes the circulation for an arbitrary vector field in both MATLAB and Python.

The purpose of this code is to be able to compute the circulation, and thus the lift per unit span, of an airfoil in my future vortex panel method video/code. I will also be using it in my potential flow elementary solutions videos.

===== ERRORS =====
► The angle definitions in the MATLAB code shown in the video are incorrect. The Python version was always correct, but I was using an old version of the MATLAB code in the video by accident. The code available on my website has been updated as of 08/19/19, and both Python and MATLAB functions are correct now.
► The error is that you do in fact need a duplicate angle in order to finish the line integral around the ellipse. Without the duplicate angle, it leaves the integrated ellipse open. Including the duplicate angle ensures that the entire ellipse is integrated over (i.e. a closed curve).

===== RELEVANT LINKS =====
MATLAB and Python code from my website
► joshtheengineer.com/2019/04/01/compute-circulation-of-a-vector-field-in-matlab-and-python

GitHub: Panel Methods
► github.com/jte0419/Panel_Methods

===== NOTES =====
► I'm using the circulation defined in Anderson's "Fundamentals of Aerodynamics".
► You can use any other shape you want for the closed curve, but the ellipse is useful for my purposes.