Originally Posted by Mathy
Lift coefficient with flaps may be about 2.0 whereas on retraction 0.5 is nearer the mark
With the same wing (same reference area), the same airspeed and the same weight?
Even if the wing reference area is indeed changed to reflect the flap extension (if it was me, I wouldn't bother and just change the coefficients) I somehow doubt the factor four change in lift coefficient.
Back to the original question.
As is way too usual when asking very general questions, the answer is: "it depends".
What is high alpha? For which wing? Which flap configuration and setting? You will be able to find cases where induced drag is lower with flaps and there will be cases where the induced drag is lower clean.
We know that wing load distribution will change radically. As ChristiaanJ pointed out, we also know that this
will affect the wing efficiency factor in the induced drag equation significantly. However, there is no general answer to just
how this factor will change.
Now, if you specify it to a L1011 at 18 degrees of AoA I'm sure someone will be able to provide you with a definitive answer.
