scsmith
Well Known Member
ChiefPilot posted a nice picture of the tip vortex condensing on his RV6 as he pulled up into a loop I'm guessing. See the picture here:
https://vansairforce.net/community/showthread.php?t=185852
Here is a brief treatise on wingtip design, and why the Hoerner tip works surprisingly well on rectangular wings, and what that has to do with the great picture of the tip vortex that ChiefPilot captured.
The normal thinking on good wingtip design is that you want to achieve the greatest possible effective wingspan, by forcing the tip vortex to form as far outboard, and as far aft as possible. A second goal is to help sustain a nearly elliptical lift distribution by helping the loading to shed progressively on the outer panel. Both of these objectives are based on classical linear theory. An example of a nice wingtip add-on to an existing wing to improve performance can be seen here:
(photo credit HP Aircraft LLC, original source Yasuo-Suzuki)
But there is another path to getting good performance that is particular to rectangular wings. It involves a departure from classical linear theory, where we will consider the formation and shape of the trailing wake UPSTREAM of the trailing edge, and its influence on the wing load distribution and induced drag. Where linear theory would assume that all the vorticity is shed from the trailing edge, and that immediately downstream of the trailing edge, the wake is flat (a straight extension of the trailing edge), there can be beneficial effects from having the wake form upstream on the tip side-edge and form a dramatically non-planar shape just aft of the trailing edge.
There are two effects.
First, by shedding vorticity off of the side edge well forward on the wing, the vortex induces more downwash on the outer portion of the wing as it makes its way aft to the trailing edge. For a nice, nearly elliptically loaded wing, we would not want that - we would want to sustain the loading that was designed into the wing shape using more classical methods. BUT for a rectangular wing, there is far too much loading on the wing outer panel, more loading than the ideal elliptical loading. So getting some extra downwash from the vortex shed off of the tip side edge helps by unloading the outer panel somewhat, shifting the lift distribution to be closer to the ideal.
Second, by shedding vorticity off of the side edge well forward on the wing chord, the vortex lifts up above the plane of the wing significantly -- as shown in ChiefPilot's picture -- and the resulting wake shape just downstream of the trailing edge has a very similar non-planar shape that would be produced by a wing with a winglet. This non-planar distribution of shed vorticity results in lower induced drag, in the same way that a wing with a winglet has lower induced drag. After much digging, here is a sketch from my Thesis that illustrates this:
So how do Hoerner tips achieve this? First, the side edge is fairly sharp. Unlike the well-rounded side edge that we would want for a classical tip that seeks to delay the vortex formation, instead in this case we want to encourage it. Second, by making the sharp edge follow essentially the upper surface airfoil contour, it sets the side edge at a rather low angle of attack forward along the tip (the first, say, 20% of chord), then in the mid-chord area, the sharp side edge has essentially the same angle of attack as the wing itself. This curvature allows the wing circulation to be pulled out to the tip, and then shed off the side edge somewhere forward of mid chord.
The result of all this is that rectangular wings achieve higher span efficiency than would be predicted by linear theory. Still not as high as an ideal elliptically loaded wing, but much better than would be expected.
https://vansairforce.net/community/showthread.php?t=185852
Here is a brief treatise on wingtip design, and why the Hoerner tip works surprisingly well on rectangular wings, and what that has to do with the great picture of the tip vortex that ChiefPilot captured.
The normal thinking on good wingtip design is that you want to achieve the greatest possible effective wingspan, by forcing the tip vortex to form as far outboard, and as far aft as possible. A second goal is to help sustain a nearly elliptical lift distribution by helping the loading to shed progressively on the outer panel. Both of these objectives are based on classical linear theory. An example of a nice wingtip add-on to an existing wing to improve performance can be seen here:
(photo credit HP Aircraft LLC, original source Yasuo-Suzuki)
But there is another path to getting good performance that is particular to rectangular wings. It involves a departure from classical linear theory, where we will consider the formation and shape of the trailing wake UPSTREAM of the trailing edge, and its influence on the wing load distribution and induced drag. Where linear theory would assume that all the vorticity is shed from the trailing edge, and that immediately downstream of the trailing edge, the wake is flat (a straight extension of the trailing edge), there can be beneficial effects from having the wake form upstream on the tip side-edge and form a dramatically non-planar shape just aft of the trailing edge.
There are two effects.
First, by shedding vorticity off of the side edge well forward on the wing, the vortex induces more downwash on the outer portion of the wing as it makes its way aft to the trailing edge. For a nice, nearly elliptically loaded wing, we would not want that - we would want to sustain the loading that was designed into the wing shape using more classical methods. BUT for a rectangular wing, there is far too much loading on the wing outer panel, more loading than the ideal elliptical loading. So getting some extra downwash from the vortex shed off of the tip side edge helps by unloading the outer panel somewhat, shifting the lift distribution to be closer to the ideal.
Second, by shedding vorticity off of the side edge well forward on the wing chord, the vortex lifts up above the plane of the wing significantly -- as shown in ChiefPilot's picture -- and the resulting wake shape just downstream of the trailing edge has a very similar non-planar shape that would be produced by a wing with a winglet. This non-planar distribution of shed vorticity results in lower induced drag, in the same way that a wing with a winglet has lower induced drag. After much digging, here is a sketch from my Thesis that illustrates this:
So how do Hoerner tips achieve this? First, the side edge is fairly sharp. Unlike the well-rounded side edge that we would want for a classical tip that seeks to delay the vortex formation, instead in this case we want to encourage it. Second, by making the sharp edge follow essentially the upper surface airfoil contour, it sets the side edge at a rather low angle of attack forward along the tip (the first, say, 20% of chord), then in the mid-chord area, the sharp side edge has essentially the same angle of attack as the wing itself. This curvature allows the wing circulation to be pulled out to the tip, and then shed off the side edge somewhere forward of mid chord.
The result of all this is that rectangular wings achieve higher span efficiency than would be predicted by linear theory. Still not as high as an ideal elliptically loaded wing, but much better than would be expected.
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