I was thumbing through Martin Simons book model Aircraft Aerodynamics book 4th ed & came across the induced drag coefficient equation presented as: Cdi = k * (Cl^2 / 3.142 * A) where
Cdi is the vortex induced drag coefficient
K = “a correcting figure to allow for wing planform, for a well designed wing it is only a little over 1.0”
Cl = lift coefficient
A = aspect ratio = span^2/area

It goes on to describe the nasty stall characteristics based on Cl distributions of different planforms like these bad boys:
http://www.faatest.com/books/FLT/Cha...ngPlanform.htm

I know the elliptical wing thing was beat to death in past RCU posts (which I’ve read). Simons says pretty much the same thing: “mathematical analysis & experiment show that the only type of wing that will produce at all speeds constant downwash & load distribution matching the area is one with elliptical planform area” ....“To aim for an elliptical area distribution is not quite the same as saying the wing should be a perfect elipse. It may be so, but any other form which gives a chord at each point the same as the pure elipse will have the same effect.”

That’s all fine & good, but I see an equation where ‘k’ & ‘A’ have identical impact; increasing A by 10% reduces Cdi by the same amount as increasing k by 10%.

So lets say for arguments sake I humbly accept the elliptically based wing, that freezes A in the equation. Now I have created 3 wing planforms, A, B, C. All have the same span, chord, area & aspect ratio. A is a perfect elipse, B is a straight trailing edge derivative, C is an arbitrary wonky shape. Both B&C were derived from elipse A by meeting the criteria “gives a chord at each point the same as a pure elipse”.

So am I to assume that the k value shape factor is the same, therefore A,B,C have the identical Cdi values based on the equation? Or does k encompass some other geometry parameters that makes these planforms different? Where does one find a table of ‘k’ values? Who generated them & how? Simons says "k in this equation is a correcting figure to allow for wing planform. For a well designed wing it is only a little over 1.0". Unfortunately he doesnt go on to show corresponding values or variations thereof.

Using the same methods, I could actually generate very bizarre looking shapes. I could pull the tips back to something approaching the Sabre jet in the example which has stall approaching the tips from the rear. Yet these are all based on the same elipse. Something tells me they can’t all be ‘equal’, but where in the equations does that come out or am I misinterpreting something?