Tip discussion, part II
So, we could consider 4 tip shapes, each with a different combination of planform and edge radius.
The sheared tip with a sharp side edge is the most extreme - the sharp swept edge will develop the side-edge vortex separation at the lowest angle of attack, and it will develop farther forward on the side edge, so it will form a larger, stronger vortex structure that will extend higher and farther inboard at the trailing edge.
The primary goal of a tip like this would be on a STOL airplane, to develop high lift with excellent aileron control to very high angles of attack. The outer region of the wing experiences very stron downwash from the side-edge vortex that delays stall, augmenting the flow over the upper surface of the aileron. The disadvantage of this tip is the high pressure drag caused by the large vortex separation region on the side edge. This will produce very mushy stall with very high sink rate at low speed.
History? For early examples of this tip shape, look at a Fokker Eindecker E-3 or a Moraine Saulner monoplane from WW I. Or even, look at Bleriot's 1908 monoplane. Did they understand why this tip shape worked? I don't know. More recent examples: Look at the Dornier 328 turboprop.
The sheared tip with a more full, rounded side edge, like the 715 tip, will delay the formation of the side edge separation, because of the nice generous radius edge. But as you go back toward the trailing edge, obviously the edge radius gets smaller and smaller, and at some point, it will separate. So this tip would have better climb performance than the sharp edged sheared tip, because at moderate angle of attack the flow should stay attached until farther aft, making a smaller side-edge vortex formation and less pressure drag. As long as the flow will stay attached, this tip will achieve a fairly high effective wingspan, supporting the wing lift distribution out most of the way to the tip, but looses some effective span as soon as the side edge flow separates, because of the sheared edge. At high angle of attack it should preserve the good aileron control and mushy stall/high sink rate at low speed.
The 90 degree tip with sharp edge is the Hoerner tip. The 90 degree side edge will support the wing bound vorticity out to the full effective wing span, even when the side edge flow does separate and form a side-edge vortex, because the edge is at the full span point. The vortex will not tend to wash as far inboard, and may not enhance aileron effectiveness at high angle of attack. For the same physical wingspan, this tip has more wetted area than the sheared tip.
The 90 degree tip with a full round side edge will delay/prevent side edge separation to the greatest degree possible, and maintain the highest effective wingspan. If I had a tapered wing with a nearly elliptical lift distibution, and I had to choose from the 4 tip shapes discussed here, this is what I would pick. Still better, I would alter the tip planform beyond what has been discussed here. IMHO,The best tip for an elliptically loaded wing is a 1/4 circle or 1/4 ellipse planform shape with the max span point coinciding with the trailing edge, and maintain full side edge radius, not sharp.
Two more points, one subtle.
First, The RV-s have lots of wing area - and at cruise conditions we have lots of skin friction drag. If you decide that you want to extend the wing span, without adding lots more wetted area, you need to do something like the sheared tip. To avoid the large pressure drag when the side edge separates on the sheared tip, you would make the edge radius as full and round as you can. So that is the 715 tip. I think the hope was to gain some effective wingspan at low to moderate angle of attack without adding a lot of wetted area, and gain some low speed controlability and mushy stall at perhaps slightly slower speed compared to the 415 tip. As observed here by Mel and others, these gains may be very small and hard to measure. It is very hard to accurately measure max climb rate - my hunch is that the 715 is, on balance, a bit better, but difficult to measure the difference.
Second point, and this one is subtle, advanced stuff. Generally from classical wing theory the rectangular planform would be considered less efficient than a tapered planform that better approximated an elliptical load distribution, and that is basically true. The lift distribution has too much lift on the outer part of the wing, then the lift drops off steeper toward the tips, causing too much downwash -- more induced drag. BUT.......
There is an interesting secondary effect of the side-edge vortex formation on a rectangular wing that is not addressed by classical wing theory. When you look at the vortex wake shape formed by a rectangular wing at moderate angle of attack, including the side-edge vortex formation, you find that this wake has the same non-planar characteristics as the wake from a wing with a winglet on it. The non-planar lift distribution produces lower induced drag for the same wingspan. And coincidentally, takes advantage of the otherwise less desireable lift distribution of the rectangular wing. So, while it is still true that the rectangular wing is less efficient, it is not as bad as predicted by classical theory, because it is gaining a small benefit that is beyond classical wing theory. The wingtip shape plays a significant role in this side-edge separation, and the Hoerner tip probably does the best all-around job of exploiting this effect.
This non-planar lifting effect is one of the reasons why our RV's are such nice planes. Along with Piper's and other designs with rectangular wings, they aren't as bad as one would think. If you want to learn more about this subtle non-linear effect, read my thesis, NASA TP-3598. (and write me for the errata sheet, because section 5.1 is wrong) Also, keep an eye out in the AIAA Journal of Aircraft for a good paper due out soon by Prof Dave Zingg at University of Toronto, he and a student have been studying this non-linear side-edge effect with modern CFD codes, really nice work.
Or even v-v 
