saman,
Thanks for refreshing my memory.
You said:
Methinks induced drag will change with flap deployment!
I noticed you said "change", not "increase" or "decrease".
Made me think...
Take an untwisted rectangular wing planform, so the span-wise lift distribution is definitely not elliptical. Now simply lower the inboard part of the trailing edge as a simple flap, increasing the lift over the inboard part of the wing.
The span-wise lift distribution will now be closer to the elliptical than before, so under otherwise the same conditions (same speed, so same Cl, and AR unchanged) the
induced drag should actually decrease (k closer to 1).
That's what KristianNorway mentioned in the first post.
On the other hand, of course, if you do the same thing in the Spitfire, you move away from the ideal lift distribution, so the induced drag increases.
Do you agree?
CJ