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# Joukowski Airfoil Performance

The Joukowski transformation is a great way to study basic airfoils using potential flow. It gives a nice way to derive the Kutta condition, as well as the classic lift slope $dC_L/d\alpha \approx 2 \pi$. But in all those demonstrations, I never saw the lift and drag curves of the Joukowski airfoil! Luckily, I have XFOIL to remedy that problem. I’m comparing the symmetric NACA to Joukowski airfoils at a Reynolds number of 1 million, for thicknesses of 10%, 15%, and 20%.

First, have a look at the 20% NACA vs Joukowski airfoils:

The Joukowski airfoil’s max thickness is behind that of the NACA airfoil, and afterward thins quickly, reaching a cusped trailing edge. Time to look at the forces!

The thinner airfoils stall sooner, as expected, whereas thicker airfoils can maintain the pressure gradient. It looks like the Joukowski airfoils have a higher L/D generally. Neat. They also have better behavior when it comes to the moment: no big discontinuities.

Overall, there isn’t a huge difference. Of course, a cusped trailing edge (like the Joukoski airfoil’s) is hard to build and maintain in reality. Still, it’s nice to take a look at the standard theoretical tools and see how they compare to the engineering baselines.

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