Winglets vs. Aspect Ratio 2

[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?

 

[tailless]

In order:

For AR=b^2/S, the area of the winglets is added to the area of the main wing, and the height of the winglets is added to the span.

Toe in or out is determined by how much lifting load is acceptable at the extreme of the wing. There's a good explanatory article (PDF format) which can be downloaded from the Boeing web site. <

http://www.boeing.com/commercial/aeromagazine/aero_17/winglets.pdf>

The cant of the winglet, vertical or off vertical, is dependent upon the winglet design itself.

Winglet airfoils require special design considerations because the angle of attack of the wing changes with the coefficient of lift. This is especially true with swept wings.

Winglets are used on commercial aircraft because they are a means of reducing drag without increasing the wing span. Boeing has found them to be relatively inexpensive to retrofit, as well.

Sailplanes can utilize winglets to improve gliding efficiency. While they were originally used to enhance the performance of gliders in the 15 meter class, they're now being found on unlimited class sailplanes as well. See M.D. Maughmer's article in the November-December 2003 issue of Journal of Aircraft (Vol. 40, No. 6).

Adding span is generally better, but there are aerodynamic and structural considerations which make winglets more attractive, especially in light of current technologies.

If the aircraft designer is attempting to optimize the lift distribution for a new design, adding span and adding winglets are both viable options. See <

http://www.glide.dyndns.org/on-the-wing4/>.

We know of no mathematical process(es) which will accurately answer your specific question. This is the realm of CFD software and wind tunnel testing.

Winglets on swept wing commercial aircraft do not adversely affect roll response if properly designed. See the Boeing Aero article cited previously. On sailplanes, winglets can actually improve the roll rate. See the Maughmer artcile cited previously.

Winglets increase the effective dihedral of swept wings. See <

http://www.b2streamlines.com/EffectiveDihedral.pdf>.

 

[rlc747capt]

Tailless,

I appreciate your insight and references, but I feel your answer is too simple. I believe there is more to it that can be directly/mathematically calculated, in theory, before reaching the Wind Tunnel. From what I have read, it seems Wing Aspect Ratio before Winglet Application has a bearing on the &quot;after-market&quot; or &quot;retro-fitted&quot; Winglet.

I am familiar with winglets, from an operational point of view, as I flew the Classic 747-200, 747-300, and new generation 747-400, as a Captain.

The 747-400 has a different wing, but, I felt it was more stable, in all regimes, and it developed a heck of a lot more ground effect . . . and I always made fuel enroute, far above the flight plan.

My interest is in Rectangular Wing Planform, for the moment. I am considering modifying an RV-6 or RV-8 Wing, to increase Aspect Ratio, and am considering a Winglet, but how much of a Winglet is the question. If a Winglet increase effective dihedral, then maybe a slight amount of anhedral would be in order. The RV-6 has a NACA 23013.5 Wing, a 4.809 AR, 110 sq ft S, and 4.783 b, for example. But, how did Boeing Engineers come up with a 6 foot Winglet for a 211 to 213 foot wing span? Considering that, with a wing that is 41.666 feet, it seems a 6 foot Winglet would be ridiculous.

I know a Winglet generates Lift/Drag and a Forward Lift Component, but I feel a cambered Winglet that is parallel could generate as much Lift/Drag as a symmetrical Winglet, with toe-in. See my point or confusion. These should be predictable, mathematically.

 

[Minifloresta]

Dear rlc747capt,

Allow me to join this discussion briefly because the subject is somehow familiar to me. My company studied many different winglet configurations - some of them were cfd´ed, some of them were actually flight tested to reduce induced drag on a business jet that was derived from a regional jet.
The RV-6 is an excellent design, but let me just call your attention to a few things:

- Winglets, like wing extensions, produce bending moments, and - depending on the design - some twisting moment (the 747-400 winglets obiously do not induce any significant twist moment, but the BBJ winglets certainly do), and they are NOT negligible. I am not familiar with the RV-6 airframe but if this extra bending moment is not properly analysed and the wing not reinforced accordingly, you may have trouble in the form of cracks, loose rivets, and so on.
- Winglets sometimes change directional stability to some extent, making dutch roll behavior a little different.
- There is winglets and winglets. In other words: if not properly designed they may end up being just extra weight and drag. A good CFD analysis by somebody familiar with the subject is advisable.
- The extra ground effect you´ve noticed on the 74 is sort of expected. The winglets are equivalent to increasing the wing span, and a longer wing does increase the ground effect. However: sometimes changes to the downwash pattern at the horizontal tail due to the presence of the winglets may require different elevator inputs during flare, and the pilot MAY feel like there is more ground effect. I can not say if this is the case with the 74.

These statements are based on our experience with regional, business and short haul jets that are far smaller than the 747-400 (our largest aircraft - to be first delivered next year - carries 108 pax) and far larger than the RV-6 but as the laws of nature equally apply to all aircraft, perhaps the info here is useful to you.

 

[aerodog]

With due respect to the mathmatical formulas dealing with winglets, one should not lose sight of the basic function of a winglet.

It is acting as a fence to keep the high pressure air on the bottom side of the wing from mixing with the low pressure air on top of the wing.

This in turn tends to square off the spanwise lift distribution curve and making the outboard wing panels more efficient.

And as Minifloresta has correctly pointed out, this shifts the center of lift farther outboard and increases the wing bending moment at the root.

Various older airplanes have used end plates to try and achieve the same result but they paid a drag penalty due to interference drag between the end plate and the intersections of the upper and lower surfaces of the wing. Winglets try to provide this barrier with minimal drag.

All things being equal, winglets should be of more help to low aspect ratio wings than high aspect ratio. So I am a little suprised to hear they would put them on a sailplane.

 

[MintJulep]

Pretty much every high-performance glider designed in the past 10 years uses winglets.

 

[joekm]

"I appreciate your insight and references, but I feel your answer is too simple. I believe there is more to it that can be directly/mathematically calculated, in theory, before reaching the Wind Tunnel. From what I have read, it seems Wing Aspect Ratio before Winglet Application has a bearing on the "after-market" or "retro-fitted" Winglet."

Your insights are pretty much correct. Winglets will make a wing behave as if it had a larger aspect ratio but there is more to it than just adding the winglet area. This is done by interfering with the tip vortecies at either end of the wing. This, in turn, reduces the downwash on the wing in a manner that's roughly similar to a longer, thinner wing of the same area. Just slapping some fins on the side won't do it, it has to be "dialed in" as it were. Then you also have your induced twist, etc. that was mentioned in a earlier post.



--
Joseph K. Mooney
FAA DER Structures

 

[MintJulep]

Mark D. Maughmer at Penn State is widely respected with regard to winglet design. This may lead you to some answers.

http://www.aero.psu.edu/maug.html

 

[Minifloresta]

Winglets are certainly more useful on low aspect ratio wings, but there is a reason for gliders to use winglets: International competition categories are based on maximum wingspan. The standard class, for example, is limited to a 15m span(about 49ft). So the winglet in these cases is a way of having a more efficient wing without exceeding the maximum span.

 

[FastMouse]

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

http://www002.upp.so-net.ne.jp/a-cubed/aero-misc/winglet.html.

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

http://www.aerodyn.org/Drag/tip_devices.html.

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

http://ntrs.nasa.gov/.

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:

http://raphael.mit.edu/avl/

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.