Following on from yesterday's posting of flow around a #ZhukovskyAerofoil, I've added #equipotential lines (blue) in addition to #streamlines (black). The two families are #contours of the #real and #imaginary parts of an #AnalyticFunction and therefore have the property of intersecting #orthogonally. The plots aren't ideal as there is some anomalous features where the equipotential lines are very close to the #aerofoil but it's still not bad.

Here, each frame is a different #wing profile, obtained this time by keeping the imaginary eccentricity of the generating #circle constant and varying only the real part.

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The #Zhukovsky #Aerofoil (sometimes transliterated as #Joukowsky from #Russian), is a 2D model of #streamlined #Airflow past a #wing. It uses #ComplexVariable and is an #AnalyticFunction (i.e. #Differentiable everywhere, save at isolated #Singularities). Take a circle in the #ComplexPlane which is not quite centred at the #origin but passes through the #coordinate (1,0) or (z=1+0i). Using the mapping w -> z+1/z, you get something that looks remarkably like an #aerofoil.

It is a #ConformalMapping meaning that angles are preserved during the mapping. In this animation, I've varied the imaginary part of the the eccentricity, while keeping the real part the same. With a zero #AngleOfAttack, you can see the change in the airflow around the #wing as its shape changes.

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