A mistake which is often made for the NACA 4412 is that the calculations are made for the zero line but that the real blade angle is set from the flat lower side. So if you do that, you make a mistake of 2°.
The potential for this error is there, yes, but even a rudimentary reading of airfoil aerodynamics emphasizes the importance of the
chord line as the definition used for all parameters including angle of attack and force coefficients. I trust that anyone who is taking the time to study these airfoils will come across the chord-line definition, and understand that the "flat bottom" is just a surface, not the reference.
There is a lot to be gained, for those interested, in the original work, still available in print and on line.
https://ntrs.nasa.gov/search?q=abbott%20von%20doenhoff%20Summary%20of%20Airfoil%20DataThe follow-up book Theory of Wing Sections is still in print by Dover Publications.
https://store.doverpublications.com/0486605868.htmlEven with high-school mathematics you don't have to be a passive user of airfoil designs. Instead, you can select and configure them for specific uses. Even the simplest NACA 4-digit airfoils permit this to some degree (admittedly the 5-digit and 6-digit airfoils are more versatile). Airfoil systems contemporary with NACA like Goettingen ("GOE") do not have systematic configurations quite like the NACA did (to my knowledge - correct me with documentary references if you can). Subsequent airfoil designs like Wortmann, Lissaman and Selig develop higher performance, but are less transparent in their means of development, configuration, or selection. Today it seems, even to many engineers, that airfoil selection and design is now a dark-art, while 80 years ago it was plain science.
(I was clicking at the same time as Kitestrings - you fixed it first!)