Well, I was speaking hypothetically.
Ahhh... mind games!
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.
That's accurate. Just so you know... I'm not trying to bicker here... this forum is fun... Ben L. put me in my place when I first got here. I wouldn't be suprised if you would do the same.
This is
my understanding of the phenomena we're writing about.
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.
You just described a 2D wing. Downwash is created, but not at the expense of lift (in other words, it is not induced). Downwash in this case is equalled by upwash. Induced drag is a differential between these two... and none exists in a 2D wing.
If you can articulate how spanwise flow is necessary for downwash, please help me here. This was your claim before.
This differential is what I am talking about... but we we're talking about induced drag, so I wasn't getting into the 2D stuff that I mentioned above because it doesn't contribute to 3D drag.
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.
I don't think I changed my explanation... maybe the verbage. Think of it this way... the cutoff tip is like a sharp bend in a pipe. It takes more energy for a fluid to get around the sharp bend than a round bend. In other words... it's more difficult for the air to swirl around that corner
at the tip (remember, this is spanwise flow we're talking about). What does this do... it effectively pushes the span and those vortices out further from each other. There will be a local separated flow bubble... but that bubble serves a purpose. Is this the best solution? No. That's why I suggested the other tips.
So, like I said, I think that we are saying the same thing... just the difference with the relationship of spanwise flow to induced drag. I contend, based on the above statements, that without spanwise flow, there is NO induced drag. Without spanwise flow, the only thing that you have is parasite drag.
Let me know if I wrote anything stupid.