by how much will single-slotted Fowler-type flaps increase the drag coefficient of an aerofoil?
is sin theta the flap angle?
it says the change in drag coeffcient is equal to, so do i add this on to the original drag of the aerofoil?
How can that equation be valid at such large angles? I would expect flow separation to come into play long before you reach 90 degrees of deflection.
I can only comment that McCormick have plots of measured and theoretical values up to 90 degrees with no (visible) discontinuities and that this approximation is for the drag coefficient, not the lift which would be a different matter.
You need to know fuselage aerodynamics before calculating flap affects.
Typically it is the drag curves that are in error, not the lift (because of the estimation of drag due to shear stresses). So if the drag agrees well, the lift is probably very good too.
The equation you provided is interesting.
It appears to apply to a wing, not a wing section, but doesn't account for wingspan, or how far outboard the flaps extend. So, use with caution.
By "lift ... would be a different matter" I was referring to CL for simple unflapped airfoils not having an accurate analytical model for AoA above the AoA for maximum CL. There you would not expect such analytical models to be valid for high AoA.
Another point to make to argue for the validity of high deflection angles in the approximation, could be to say, that the flap deflection angle is not the same as angle of attack and that high deflection angles not necessarily imply equally high AoA for the flap airfoil since it lives in the downstream from the wing airfoil.
I see that Theory of Wing Sections (which McCormick references for some of his airfoil data) has some drag data that maybe could be used to verify this drag approximation.