aerodynamicsdrag
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 $C_D$?
OK, I figured out all my mistakes and the results seem sensible now.
I was using wrong formulas and, first of all, was not using imperial units which is necessary with UIUC's data. The right formulas are:
$F_T(RPS) = C_T \rho n^2 D^4$,
where: $\rho [\frac{slugs}{ft^3}] = 0.0023769$ is air density, $n[RPS]$ is prop angular speed in revolutions per seconds, $D[ft] = \frac{10}{12}$ is prop diameter. For calculating torque, the below formula must be used:
$\tau(RPS) = \frac{C_P \rho n^2 D^5}{2 \pi}$.
The results obtained seem sensible and in synch with e.g. Drive Calculator data. Some graphs and screenshots below. Of course, the results are all in imperial units, I converted them to SI for graphs.
$C_d$ is a function of speed via the Reynolds number. See here and here.
For some numeric values for the $C_d$ vs. $\rm Re$ use the following from here of which you take the log values to interpolate.
The kinematic viscosity of Air is $\nu = 14.8\; \rm{cSt} = 14.8 \cdot 10^{−6}\; \rm{m^2/s}$. At a speed of $v=20\;\rm{m/s}$ a ball with diameter $d=5\,\rm{cm} = 0.05\;\rm{m}$ has Reynolds number of $\rm{Re} = \frac{v d}{\nu} = 67400 $.
When you look at the $C_d$ vs. $\rm Re$ graph you get $C_d = 0.47$. The area of the ball is $A=\pi \frac{d^2}{4} = 0.001964\;\rm{m^2}$ so the drag force is
$F_d = \frac{1}{2} \rho A C_d v^2 = \frac{1}{2} (1.2\;\rm{kg/m^3}) (0.001964\;\rm{m^2}) (0.47) (20\;\rm{m/s})^2 = 0.2215\;\rm{N}$
Best Answer
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$^6$.