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Old Apr 06, 2012, 08:02 PM
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How does Winglet toe-angle affect Yaw stability

I am designing a 30 degree swept back flying wing with airfoiled winglets and am trying to figure out the best toe-angle for the winglets in terms of minimum drag and best yaw stability.

There seems to be very little information on the web about winglets and toe (incidence) angles used. The Whitcomb winglet calls for a toe-out of 4-7 degrees, while other papers say the optimum angle is a toe-in of 9 degrees.
The Rutan Long EZ winglets look to be near straight but I cant find the exact angle on the web.

From my research it appears that toe-out is decreases cruise drag, while decreasing Yaw stability, and toe-in increase cruise drag but increases Yaw stability.
I realize that the optimum angle will be different for every aircraft and at different speeds, but I am just trying to get a sense of weather to toe-in or toe-out?

Flying Wing modelers seem to use toe-in angle to increase yaw stability. Has anyone flown enough wings to notice the difference in yaw stability for different winglet toe angles?

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Last edited by alexlb; Apr 06, 2012 at 08:41 PM.
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Old Apr 06, 2012, 08:25 PM
RPM314 is offline
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well, toe in would be good for stability if you think about it like dihedral/anhedral. (toe in, relative to flow as viewed from the top, is the analouge to dihedral as viewed from the front). I don't have any evidence, so don't build it as toe in based just on me.
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Old Apr 07, 2012, 03:31 AM
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Basing the assumptions mostly on the drag force (which could be valid considering flat plate style winglets on a zagi type model). "Say you are yawed slightly clockwise in the airstream. The tips will be aft of the CG. With toe-in, the right tip (downwind) would be parallel to the airstream and do nothing. The left tip (upwind) will present its outside face to the airstream which will cause a counterclockwise torque tending to yaw the wing back to a parallel orientation to the airstream." This is assuming the left tip only experiences drag (acting towards the rear with half-span as your moment arm), creating a large restoring torque. This could be true if you have a Zagi with flat plate type winglets, where you get separation, low lift and high drag. However, if you consider a nice airfoiled winglet, the story could be quite different. A good foil would produce mostly lift and little drag. The lift that the left winglet experiences points inward towards the CG (perpendicular to the airstream), and the moment arm is very small, creating very little torque. Tow-out on the other hand, the left tip (Upwind) would "do nothing", and the right tip (downwind) would present its inside face to the airstream creating lift outwards, this time with a larger moment arm creating more restoring torque.

I set off to figure this out myself and I came up with a few diagrams. I plotted the Resultant forces (resultant force of lift and drag assuming L/D =20) There is one figure with no toe, one with toe-in and one with toe-out.
I know this is contrary to common RC flying wing knowledge, but the attached pictures demonstrate that assuming good airfoils and no separation, toe out is "more stable"
Let me know if this makes sense.
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Old Apr 07, 2012, 04:24 PM
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Toe-out is unstable. Toe-in is stable and self correcting. With toe-in, if the plane yaws left, the right wing tip gets more drag and the left wing tip gets reduced drag thus making the plane yaw back to the right.
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Old Apr 09, 2012, 06:57 AM
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I don't know a thing about wings but have seen the finless wings tips cut inward leaving the flat exposed to the airstream in yaw to self correct. I found it impossible to make a swept forward wing tailess or with tip fins is why I researched the topic. I do find the fin angles to be informative, thanks guys.
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