Hi, I am John Farley's 'winglet man'. I have direct experience in winglet design at a major airliner OEM and also for light aircraft and sailplanes, amongst other aeronautical adventures.
Before getting into specifics, let's first consider what the winglet is doing, aerodynamically. So, a thought experiment - you're sitting in a chair somehow suspended in space at 5,000' (the height is unimportant, but let's say we're high enough to be out of ground effect, which really kicks in a heights less than half the wingspan of the aircraft). The atmoshere is still. An airliner flies by, before disappearing off into the distance. You can't hear it anymore, but you can feel the air around you moving, having been disturbed by the passage of the aircraft. What's going on?
If you could see the air, you'd be able to see a general downwards motion in the area where the aircraft flew, and a gentle upwards movement to either side of this area. You might notice that the velocity of the air moving downwards is greater than the gentle upwards moving air at either side - and in fact here is our first finding - the net vertical momentum change of the air disturbed by the aircraft must equal the weight of the aircraft. Newton's second law and all that. You will also have noticed, with your air-x-ray specs, that there are two powerful horizontal tornadoes roughly where the wingtips passed by - the 'tip vortices'. These were caused by the airflow at the wingtip rolling up, moving from the higher pressure side on the lower surface around the wingtip, to the lower pressure side on the upper surface. They are an inevitable by-product of generating lift.
Now, if we somehow knew the veolicty of every air molecule disturbed by the aircraft, in both vertical and horizontal directions, we could do some sums. We could calculate the net vertical momentum change - which will equal the weight of the aircraft. The net horizontal momentum change, assuming we've done our sums correctly, and the airliner wasn't sideslipping, should be zero. Let's also work out the kinetic energy of the air in this y-z plane (y being the horizontal direction, and z is upwards), which is 1/2 * m * delta-v^2, summed over all the particles affected. It will work out to be some value. Next, consider what happens if another airliner of the same weight, but double the wingspan, passes by. The net change in vertcial momentum of the air will be the same (same weight), but a greater volume of air behind the wing is affected, because the wingspan is larger, so the vertical velocity change ('downwash') is smaller. Therefore when we calculate the kinetic energy in the y-z plane again, we get a smaller number. Cool!
Any aeroplane that moves along through the air causing less kinetic energy behind it, all other things being equal, must have lower DRAG. Specifically induced drag. That's our second finding - and one that glider pilots have known since the 1930s - that There Is No Substitute For Span. The greater the wingspan, the lower the lift-induced drag. And considering that the induced drag of an A340 cruising along at FL370 is 40% of the total drag, it's an important item to minimise.
We have't mentioned winglets yet, have we? Don't worry, they're coming.
If span is so good, why don't airliners have very large spans, say of 100m? Well, we'd need bigger airport terminals and taxiway spacing for starters, but the other reason is that as the wingspan goes up, so does the wing weight, for a fixed wing area. So we have drag going down with span, and weight going up - at some point there is a 'sweet spot', where things are optimum. A slightly greater span means the induced drag is a little less, but carrying around the additional wing weight isn't worth it in terms of Direct Operating Cost, which is what the airlines care about.
It is common for this 'optimum span' to be larger than what the airports can cope with, and for the A380, which was designed to fit within an 80m x 80m box, the optimum span was actually somewhere between 82 and 84m, although the DOC-span curve was pretty flat between these values. So - how do we 'involve' more air in the generation of lift as our aeroplane flies along? What about bending up the wingtip? We could even call it a winglet!
Let's go back to our chair again. This time an airliner flies by, same wingspan as the first one, same weight, but this one has winglets fitted. The air still gets a net 'push' downwards to equal the weight of the aircraft, but this time the tip vorticies are slightly weaker and in fact, slightly larger. Same overall vertcial air momentum change, but lower kinetic energy. Each winglet has 'diffused' the powerful tip vortex vertically, along the height of the winglet, and in fact the designer of that winglet probably tailored the aerofoil shapes, chord and twist along the winglet to generate a particular level of lift at each station, (the 'lift distribution') in the cruise condition.
So, lift distributions then - every first year aeronautical engineer undergraduate will be taught that for minimum induced drag of a flat wing (no winglets), one must achieve an elliptcial lift distribution. Some elegant maths will be produced with pi and other numbers, good stuff. But, what's the optimum lift distribution for a wing with a winglet? Or a 'wingtip fence', like on the A320? We need to go and read two 1960's NASA reports: (1) A 1962 NASA Tech Report R-139, by Mr. Clarence Cone 'The Theory of Induced Lift and Minimum Induced Drag of Nonplanar Lifting Systems', and (2) A 1968 NASA Contractor Report CR-1218 by Mr. J L Lundry 'A Numerical Solution for the Minimum Induced Drag, and the Corresponding Loading, of Nonplanar Wings'. These give us these optimum distributions and the induced drag reductions we can expect to gain, for any configuration of 'wingtip device'. No magic there, just sound maths and a brilliantly simple way of finding the answer without today's computer programs.
The reports show that the optimum lift distribution for a wing with a winglet, for the same overall lift, has slightly lower lift at the inboard end and significantly more lift at the outboard end, plus some inwards-pointing side load on the winglet itself. Interestingly the winglet doesn't directly add to the lift very much - because it's close to vertical, it's 'lift' has only a very small upwards component - but the 'blocking' effect out the outer wing increases the lift there considerably. The overall effect is larger, less intense wingtip vorticies, for the same overall lift - same vertical momentum change, lower kinetic energy.
Back to the original question regaring why some modern aircraft have winglets, whilst others (B787, B777) don't. I see this as really two questions:
1. Why do some new-design aircraft have winglets, whilst other new-designs do not?
2. Why do some in-service aircraft sprout winglets?
I think the second question is easier to answer, so let's do that first. Company A designs and builds a jet airliner, without winglets. Everybody tries their best during the design and stressing of the wing, but when designing details like stringer and skin thicknesses, some conservatism inevitably creeps in. We can't have a LIMIT:ULTIMATE factor of less than 1.5, can we? So a bit of rounding up goes on here and there, with the result that when the wing is tested, it breaks at say 156% of LIMIT load. Everyone feels relieved and goes for a beer. The airliner goes into production, and a few years later, some bright spark in the project office works out that the extra 6% 'fat' in the wing might be used up by sticking a winglet on, along with some local strengthening at the wingtip (and whereever else is critical for those additional bending loads). Remember that the increase in bending moment at the wingtip is infinite - we had zero BM before, now we have some. There is a surge tank out there, with minimum wall thicknesses, but it will need reinforcing. A few hundred lbs of reinforcement goes in along with the winglet, the LIMIT:ULTIMATE is still just above 150% - on paper - there's no need to break another wing since we can clear this modification 'by analysis', and hey presto we've reduced the induced drag by, say typically, 5%. Minus a bit of extra wetted area for the winglet, and our overall drag standard is still 2% better than before (bigger gains for bigger winglets). Everyone's still happy, and more beer is drunk. Marketing types invent a name for their winglet, to differentiate it and make it 'special', calling them 'sharklets' or 'advanced blended winglets' or whatever. This is my take on the BBJ/737-NG, 757WL, 767WL, A320NEO and others.
New design airliners are slightly different, because the winglet has to 'pay' for itself from day 1, in terms of direct operating cost. This means that the additional bending, shear and torsional loads imposed on the wing by the winglet have to be accurately calculated, as do the aeroelastic effects - the wing bends and twists a little with the winglet flight loads, not to mention flutter margins. And the weight prediction modelling has to be REALLY GOOD. The specific load cases that design certain parts of the wing structure can play a part - for example, if large areas of the wing are designed by the 2.5g manoeuvre case, a winglet that moves the aerodynamic centre at the wingtip further aft (wingtip fence for example) can cause the wing to twist off more at the 2.5g manoeuvre point, washing it out more. This shifts the spanswise centre of lift inboard at this design point, reducing the bending loads; winglet-induced aerodynamic load relief, if you like. This effect may not be the same from project to project, short haul to long haul (short haul aircraft do more cycles, so fatigue and damage tolerance may be the critical design case). The optimum span for the airliner may not be constrained, like it was for the A380, so there may be less gain to be had, if any, for the clean sheet design with optimum wingspan. Of course, when the machine is built and tested, it eventually becomes old, and tricks like question 2 can come into play.
I'll close by talking about winglet effects at different airspeeds. Clearly the winglet has to pay for itself in the cruise, as that is the point airliner wings are optimised for. For a long range aircraft, this is especially important. But at lower speeds, the induced drag forms a greater proportion of the total drag. So a winglet that cuts 5% from induced drag in the cruise (say 2% net total drag reduction, if cruise induced drag is 40% of total drag), will cut say 4% of the aircraft drag at a low speed point, where the induced drag is 80% of the total aircraft drag. So winglets are great for low speed - takeoff lengths, first and second segment climb. A poor winglet design with almost no cruise drag reduction might still be worthwhile, if airport access - second segment climb for example - is limiting.
I hope this helps.
On Glide
Last edited by On Glide; 9th Mar 2012 at 10:34.