ORIGINAL: KenLitko
If you could build a wing with no spanwise flow, it would still suffer from induced drag whenever generating lift.
Actually, no it wouldn't. The only way you're going to get no spanwise flow is from a 2D wing (a.k.a an infinite wing, or some approximation thereof). The only drag that a 2D wing suffers from is parasite drag.
A 2D wing, has no induced drag because it has no induced downwash. In a 2D wing, upwash always equals downwash... this is not the case in a 3D wing. In a 3D wing, energy is lost (from lift) to the trailing vortex sheet. This vortex sheet induces downwash.
The tip vortex is simply the "rolled-up" vortex sheet caused by a 3D wing moving through a fluid. You CANNOT prevent the tip vortex, but you can modify it. Modifying it by effectively spreading it out further from the other tip (which is what a cutoff, Hoerner, or end-plate does) can reduce drag.
Well, I was speaking hypothetically. It seems to me that you're saying that a wing without spanwise flow would not have induced drag because it would have to be 2D, and a 2D wing couldn't be built. If that wasn't your meaning, please excuse me. My contention is that the downwash experienced by a 3D wing is not dependent on spanwise flow. It would almost certainly be impossible to build a wing with no spanwise flow at all, but try this thought experiment. Imagine a lifting, 3D wing, with some kind of super-duper fence system which eliminates spanwise flow at the surface. If you are a CFD guy, you can imagine instead a flow simulation of a lifting, 3D wing with a boundary condition on the wing which precludes spanwise flow. There is nothing I can see about the absence of spanwise flow in this situation which prevents the lift of the wing from causing downwash. If you can articulate how spanwise flow is necessary for downwash, please help me here. This was your claim before.
Please compare your third paragraph to your first post, in which you stated: "it is more difficult for air to swirl around the cutoff tip" as the reason that a square tip would result in lower induced drag. In my first post, I took issue with this explanation, stating: "some wingtip designs could reduce induced drag by shifting the distribution of downwash ( usually this means that the tip design pushes the center of the vortex out from the end of the wing, emulating a longer wing )". We seem to have come back to that issue, and you seem to have changed your explanation to something fairly similar to mine. In any case, it is not obvious to me how a square tip would have a beneficial effect on the downwash distribution, but I would be interested to hear it, if there is some rationale. This discussion of induced drag ignores the issue of overall drag, which is where the square tip would seem to have a disadvantage, and of which induced drag is a small component for most flight regimes.
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