6.2 on page 113, which includes these seemingly arbitrary coefficients that you’re asking about.
The thickness distribution for the NACA four-digit sections was selected to correspond closely to that for these wing sections and is given by the following equation” The equation stated is Eq.
In the section about the NACA 4-digit airfoils (section 6.4, page 113) they state the following: “When the NACA four-digit wing sections were derived, it was found that the thickness distributions of efficient wing sections such as the Gottingen 398 and the Clark Y were nearly the same when their camber was removed (mean line straightened) and they were reduced to the same maximum thickness. “So first of all, if you don’t already have it, I recommend getting the book Theory of Wing Sections by Abbott and Von Doenhoff if you’re interested in wings/airfoils etc. I would try to give the explanation of how the shape works using Bernoulli's equation, but I feel I'm not adequately able to do that as I'd only be restating what I remember from reading online, and not what I've formally been taught.Here’s a response I wrote to someone who had the same question as you. That's obviously not objective proof, but you're welcome to validate this shape is the NACA 4412 yourself in you still don't believe it. I co-plotted the shape I generated against coordinates generated by an online software designed to output airfoil coordinates of NACA airfoils and they matched up perfectly. That said, I still have good reason to believe this airfoil shape works. You're right in your second comment, I just completely derped in every way while responding. Wow! I just realized that not only did I misread your original comment, after you pointed it out, my explanation was utterly incorrect (I guess that's what I get for answering technical questions immediately after waking up, lol).
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