Winglets certainly do change lift distributions and increase bending moments, as I found out all too well when I was assessing the effect of winglets on the F&DT characteristics of a wing a while ago, but I thought that they were installed primarily to reduce total aircraft drag by generating a net forward component of force, and that any reduction in the concentration of vorticity at the tip was achieved only as a consequence of the primary aim.
Quick review: At the tip, due to the pressure differential between the upper and lower surfaces, there is a significant spanwise component to the airflow. On the lower surface, the spanwise component of flow is outwards, away from the wing root, and on the upper surface, the spanwise component tends to be towards the root. Some bright guys, most famously Dr Richard Whitcomb, realised that since lift is defined as acting perpendicularly to the flow local of the airfoil and the surface planform, then with a bit of cunning engineering, the lift on a vertical surface at the wing tip, in a flow with a spanwise component toward the root such as occurs on the upper wing surface, could be directed "forward" - in the direction of flight, - and "inward" - toward the wing root. The forward component of lift manifests itself as a reduction in total aircraft drag. Of course, the benefit is reduced somewhat by the component of winglet drag acting aft, but nonetheless, the net result is a reduction in total aircraft drag. And as mentioned elsewhere, winglets will indeed reduce the strength of the shed vortices in the tip region, but only as a consequence of the generation of a lift force on the winglet.
Take a look at
The text is Japanese, but the sketch shows what is going on with the lift component of force.
The same sort of logic can be applied to the lower surface at the wing tip to again achieve a net drag reduction, and Whitcomb's famous winglet is proposed with elements acting in both upper surface flow and lower surface flow, shown in a sketch at
For a given angle of attack, installation of winglets can also increase lift, but since aircraft mass is approximately unchanged, the aircraft would have to fly at a decreased angle of attack to maintain the same lift as in the pre-winglet case - which further decreases drag.
Aircraft Design: A Conceptual Approach (Raymer) provides a very brief, but good, summary of winglets. It is hard to find generalised summaries on "how to do" winglets because the work is often very empirical and highly tailored to the specific wing under consideration. NASA have a lot of good reports on winglets, most of which are not available for free. Check out
But coming back to the original questions...
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?
My personal feeling is that for drag calculations, it is probably best not to view a winglet as affecting aspect ratio, but it
maybe better to consider it as affecting Oswald's Span Efficiency Factor. It depends a lot on the assumptions & methodology. Or just get yourself down to the wind-tunnel or a CFD workstation and start running some scenarios. If you like computing aircraft characteristics, then maybe look at AVL as a first port of call:
The "rules" sometimes seen giving an equivalent increase of aspect ratio upon addition of a winglet are often nothing more than a couple of empirical data points or rules of thumb. As such, they are highly specific to the types of situations for which that apply, and usually cannot be quoted as being generally applicable. A rule of thumb for a transonic airliner will not apply to a private aircraft.
Raymer quotes Whitcomb winglets as increasing L/D by
up to 20%, but what will be the increase for the specific aspect ratio, airfoil and angle of attack under consideration? It is hard to say. Later, Raymer also states that the effective aspect ratio with winglets is 20% higher that the geometric aspect ratio of the so-called "reference planform", but he clearly states that this is simply a rough approximation based on a limited range of data.
In Stinton's excellent "The Design of the Aeroplane", the author, wisely, is not brave enough to venture any generatilities. He quotes Whitcomb's rule guide that "winglets give twice the increase in span efficiency as wingtip extension for the same increase in wing root bending moment." The trouble here is that by the time you have calculated or measured the increase in RBM due to a winglet, you probably already know the change in drag and thus no longer need to know the equivalent aspect ratio.
Looking Top Down at a Wing with Winglets should the Leading Edges be Toed In or Toed Out? If Toed In, as above, how much?
The flowfield around the tip is complicated and highly specific to its wing and the angle of attack, so it is hard to generalise. Raymer gives some guidance for a Whitcomb winglet.
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?
Again, it is hard to generalise about positioning of the winglet, and so without looking at the specifics of the wing and the winglet design methodology, it is difficult to say whether the winglet should be perpendicular to the wing or canted. If you look at, say, an A340 winglet, an A320 winglet (or more correctly, tip fence), a MD-11 winglet and a B737 winglet, you can see that very different design processes have been applied to the same problem.
In general, winglet airfoils are not symmetrical, nor are they the same as the wing airfoil.
Would it be just as efficient to extend the wing to achieve the same Aspect Ratio?
No, in general the equivalent extended wing will be heavier and may be more expensive than the competing winglet design. Also, while a winglet increases the root bending moment, the equivalent increase in wing span will usually generate an even higher RBM.
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???
To do the job properly requires a little CFD and a lot of wind tunnel and flight testing. Making judgements about what is "best suited" depends on a lot of things. If you're tooled up for carbon composite moulding, you will design a different winglet than if you're using fibreglass, or fabricating from aluminium sheet.
As for "providing the math", AIAA have a lot of good papers concerning winglet analysis.
Last question, if Winglets reduce Roll Rate, would a reduced Dihedral or even an Anhedral compensate for Winglet negative or less than desired affects?
I think that it would be simpler just to increase the size and/or throw of the ailerons, but adverse yaw may result. An analysis of the increased loading on the attachments and actuators would be required.
In terms of performance gain, retrofitting winglets can increase the performance of an aircraft with a limited range of operating points, but they are unlikely to do much for a private aircraft other than make it look sexier, and, in fact, unintended consequences of retrofitting winglets may be negative. I am sure that I read somewhere about somebody adding self-designed winglets to a homebuilt constructed from a kit, and they ran into problems due to the increased bending moment on the wing. The PFA, EAA, or whoever your local home-built aircraft organisation is, would be able to advise. I think I know what they will say.
My two cents worth is that if your aircraft is unique (because you added winglets to it), then you are the person that will find any problems with it. Not good if that problem is, say, flutter, which can be an issue with winglets. However, if you are flying an aircraft that is the same as many others in-service, and especially if your aircraft is not the fleet leader, then you are protected by the likelihood that any problems with the design will be uncovered by someone else and hopefully promulgated to you before you have the bad luck to happen upon them yourself. So modification of existing designs is a serious issue, and not to be undertaken lightly. In fact, I would say do not do it!
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All of the forgoing comes with the usual disclaimers, of course. I think that it's good info, but I might be inadvertently talking rubbish. As with all freely available information, users are responsible for assessing its validity for their individual purposes.
