Dave Hyde wrote in message
The generally accepted definition of the induced drag coefficient
is:

CDi=CL^2/pi/e/AR,
where CL is the wing lift coefficient at the conditions under
consideration,
pi=3.14159...
e = Oswald's efficiency factor (typically 0.8 or so)
AR = aspect ratio

Okay, thanks for all that, I think you're missing some parentheses in
there because I'm getting a quad decker formula. I always love those
formulas with a constant that has some guys name that was alive in the
last 100 years.

The _definition_ of aspect ratio is chord/span, or span^2/aero (they're
equivalent), so as area remains the same but aspect ratio increases,
induced drag decreases by 1/span^2. That's what I call a primary
effector.
If you add wing treatments like winglets, fences, etc, you can increase
the
effective AR, but the big effects are gained by working at the tips,
not across the span, as another wing typically does.

Look at the lift side. The formula becomes messier, but for a finite
wing:

CL,finite ~= CL,infinite*(1/(1+(dCL,inf/daoa)/pi/AR))

As span increases through increased aspect ratio, the finite
wing lift coefficient gets closer to the infinite wing CL.

Can we agree that this is a good thing?

Okay I'm looking at things in the infinite wing theory where the
effects due to tip/root disturbance are very small compared to the
rest of the span. So with this theoretical wing of aspect approaching
zero, 2 non-interfering wings of half span, would be essentially the
same lift and drag as one.

Perhaps this is really a discussion of how large an effect the
root/tip distubance is for a practical wing (e.g. 30' span). You'd
pointed out that proper tip treatment can help make the shorter wing
behave as if it is part of an infinite span. Seems like a fence at
the tip would be the way to go to keep the high pressure air from
spilling over into the low pressure region.

Um...you might want to review some finite wing theory.
There can be quite a bit of spanwise flow at the root _or_
the tip. When subsonic you make a bow wake. The air is moving
before you hit it, and it's not just front-to-back.

Looks like the issue is I'm talking about this theoretical wing and
you're talking about a practical one. You know, in theory, practice
and theory are the same, but in practice, they are very different. =^)

That's not a rule of thumb, that's physics. All other things being
equal, the highger AR wing *will* have less drag.

I'm talking about 2 wings that have an aspect approaching zero, versus
a single wing with aspect approaching zero as well. So the lift and
drag per foot of wing are essentially the same.

Done and done. Your turn.

I've worked for lots of companies like Boeing...

Have you ever worked in conceptual design and/or
aerodynamics?

Not of aircraft, have you? The closest thing I've done and got payed
for was the work I did on a DARPA program called FLASH. I was working
on the ailerons of the Dryden F/A-18 they were torturing.

Most of your risk aversion comments
were way off the mark. A trip to the Air Force museum
to see the Bird of Prey or the X-36 could be illuminating.

Most if not all of those X planes were R&D payed for by the you and
me, the tax payers of America. Its extremely rare for a large company
to take a "flyer" with their own money and reach very far forward.

Dave 'misconceptual design' Hyde