Jay wrote:

Okay, I think you nailed the departure of my logic from yours. I
don't believe that span is in the formula (at least not in high
order).

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

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?

In the lift case, there is *some* easily realizable benefit.
A forward surface like a canard can be used as a big vortex
generator to keep flow attached over the 'main wing' and
increase lift/delay stall. That's why you see a lot of close-coupled
canards on fighters these days.

There's also the trim drag benefit of another surface if
that surface can be configured to reduce the total downforce
required to trim. That's another reason for canards and
relaxed stability airliners. This benefit is usually
not as pronounced as the high AR benefit.

Imagine that you're an air molecule; how do you know if
you're 5' or 10' along the wing? You don't, when the wing comes
along, you just move along the bottom or zip across the top.

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.

I know that the rule of thumb is higher aspect, higher efficiency
(L/D), but this is only part of the story. That rule makes an
assumption of a single wing.

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

Okay, why don't you start off by
showing me how span comes into the relationship of air moving over a
wing's airfoil.

Done and done. Your turn.

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

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

Dave 'misconceptual design' Hyde