- #1

Supercritical

So now imagine a rectangular wing in a wind tunnel where the wing spans the tunnel (essentially a 2-d wing). Parasitic drag will be disregarded.

Thus, if 1 kg/s of air is influenced by the wing, and it's deflected downwards at an average downward velocity component of 1 m/s, 1 N of lift is created. The same 1 kg/s of air deflected at 1 m/s requires 0.5 Watts of power, manifested as 0.1 N of drag if the wind tunnel freestream velocity is 5 m/s.

I can't imagine how the above scenario would fail to check out, and yet here we have induced drag in the absence of wingtip vortices (impossible according to a good deal of literature).

More importantly, however, something is preventing me from reconciling the above with the induced drag equation. Holding the mean chord, lift coefficient and efficiency factor constant, doubling the wingspan halves the induced drag coefficient (CL^2/pi*e*[highlight]AR[/highlight]), which counters the doubling of drag from the wing area term (0.5*rho*[highlight]S[/highlight]*Cdi*v^2). As a result, it would seem that by holding these items constant, the amount of induced drag a wing creates is independent of its span (the span term also drops out algebraically if you write S as b*c and AR as b/c). From the perspective of a wing in flight, then, past some finite wingspan the power imparted on air accelerated downwards from a standstill would exceed the power required to maintain flight. I can't find a way the transition to a 3-d wing rectifies the issue. There is obviously a deviation from energy conservation somewhere, but I can't find it.