Winglets vs. Aspect Ratio

[rlc747capt]

Any Aeronautical Engineers and Test Pilots:

If Aspect Ratio is defined as: AR=b²/S or b/c, simply, then how does a Winglet increase Aspect Ratio? Is the Area of each Winglet added to the Area of the Wing or is it applied another way?

Looking Top Down at a Wing with Winglets should the Leading Edges be Toed In or Toed Out?
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If Toed In, as above, how much?
If a Wing has a 9 degree Dihedral, then should the Winglet be perpendicular to the Wing, perpendicular to the ground, or bent outward (away from the fuselage), if so how much?
Also, should the Winglet Airfoil be symmetrical or in the form of the Wing, say a NACA 2412, for example?

Would it be just as efficient to extend the wing to achieve the same Aspect Ratio?

Suppose an aircraft with a 9 degree Dihedral, a NACA 2412 Wing, 42 feet Span, and approximate 4.8 feet chord, what winglet would be suited, how much would the Aspect Ratio increase, and could you provide the math???

Last question, if Winglets reduce Roll Rate, would a reduced Dihedral or even an Anhedral compensate for Winglet negative or less than desired affects?

 

[JetAssist]

rlc747capt,

Winglets increase the aspect ratio by straightening the airflow at the end of the wing which allows the wing to produce lift out to the tip. In effect, with a winglet, you get more lifting surface on the same wing. The vertical section of the winglet does not add to the planform area of the wing. The length is determined by how the necessity to get the wingtip vortices pullet away from the horizontal section of the wing. Also by looks.

Experience has shown that winlets are tricky to design so that they actually work. A winglet is optomized to one flight condition, normally cruise, and if the shape does correct, you will not gain lifting area with the wingtip.

Another consideration on wingtips is that they add structural weight. Not just the weight of the structure of the wingtip, but the added reinforcement of the wing spar to support the higher bending load that is produced by moving your center of pressure outboard. Many winlets help aerodynamically, but create an equal weight and drag penalty such that their installation is a wash on the design. The reason so many aircraft have them is that they look modern and add sales appeal. Some also work.

Sorry for the soapboxing. I like the subject.

Jetassist