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I want to calculate the actual drag force that a NACA 63-412 wing would experience at a given planform area and relative wind speed. Airfoiltools gives a drag coefficient of 0.01676 for the optimal angle of attack. The drag equation states that $$F_D = \frac{1}{2} \rho*V^{2}*C_D*A.$$

What is the reference area associated with the drag coefficient above? Is it the planform area of the wing? If so, can I use the wing's planform area for $A$ in the drag equation and 0.01676 as the value for $C_D$?

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Yes, the reference area is commonly the projection of the exposed wing area on the wing's X-Y plane, the plane spanned by the wing chord and the wing span.

However, at the low Reynolds number you should find other airfoils more suitable. The NACA 6-digit range is more commonly used at Reynolds numbers > 10$^6$.

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