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I recently came across this picture of the Boeing 787 series aircraft's incredible wingflex:

I suppose this is a consequence of using very light CFRP wings, but how does the wingflex itself improve the 787's flight performance? Do the benefits/drawbacks also apply to the 747-8 (which IIRC also uses CFRP wings)?

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    $\begingroup$ Not an answer, just a nice video on really incredible flex for the DG-1000: dg-flugzeugbau.de/Data/Videos/bruchversuch-i.wmv. They also do that for the big ´uns like the A380, which is really fearsome (but I don´t have a video link at hand). $\endgroup$ – yankeekilo Jan 10 '14 at 15:32
  • $\begingroup$ Related: airliners.net/aviation-forums/tech_ops/read.main/253605/1 $\endgroup$ – yankeekilo Jan 10 '14 at 15:33
  • $\begingroup$ @yankeekilo thanks for sharing, that was a pretty cool video. I heard that they stress the CFRP wings a lot, but not to breaking point as the shrapnel from a CFRP wing could be quite severe. $\endgroup$ – shortstheory Jan 10 '14 at 17:17
  • $\begingroup$ Just found: airliners.net/aviation-forums/tech_ops/read.main/267122 $\endgroup$ – yankeekilo Jan 10 '14 at 17:57
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    $\begingroup$ That's a dreadful image. I really doubt the wings increase in length dramatically as they flex. The wingtip's motion would surely describe something closer to an arc than a vertical line. $\endgroup$ – RedGrittyBrick May 21 '14 at 18:20
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From here:

The amount of flex is really a product of the material. The wing requires a specified ultimate strength; with metal, that translates into a given amount of flex. This can be varied within limits, but it is really the material, its stiffness to yield point ratio, and its fatigue properties, that control how much flex you are going to end up with. CFRP is a very different material, and has much less stiffness for the same yield point, and has essentially no fatigue problems. This is beneficial in that it provides a smoother ride in turbulence; the wing acting essentially like a giant leaf spring. There is some lift lost due to the nature of the curvature, though. However, this is relatively small.

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    $\begingroup$ How do you correlate yield and stiffness? CFRP has a higher specific stiffness compared to aluminum and steel... $\endgroup$ – yankeekilo Jan 10 '14 at 16:50
  • $\begingroup$ Increasing stiffness, means increasing mass, means decreasing yield/lift. This material provides high strength with a relatively low stiffness/mass, meaning a good ratio and, in turn, the consequential flex that you see. $\endgroup$ – Dan Jan 10 '14 at 16:55
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    $\begingroup$ But the flex is in the design, not the stiffness of the material. You could build much stiffer wings with CFRP. CFRP (done properly) offers both excellent stiffness&strength, with relative low breaking strain compared to aluminum. I agree on the fatigue point, though. $\endgroup$ – yankeekilo Jan 10 '14 at 16:58
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    $\begingroup$ You could build much stiffer wings with CFRP. However, the increase in mass will reduce the resultant lift more than having 'flat' wings. $\endgroup$ – Dan Jan 10 '14 at 17:01
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    $\begingroup$ My point is that CFRP does not in general show a lower stiffness for a given yield. The flex is a design decision giving the best compromise, but not inherently due to the material. $\endgroup$ – yankeekilo Jan 10 '14 at 17:58
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The wings of the Boeing 787 are so flexible because its carbon fiber material can be stretched more, and the high aspect ratio of 11 will magnify this effect. In flight, all you will feel is less shaking due to gusts, because the wing will dampen load changes more effectively. On the ground, the wing might have less tip clearance, because less in-built dihedral is needed - the rest is supplied by the wing's elasticity in flight.

The influence on performance is slightly negative, but this is a very weak effect. It can be compared to the rolling resistance of a stiff bicycle versus one with a spring-loaded frame.

The amount of bending for a given bending moment depends on three factors:

  1. Wing span: A given curvature of the wing due to bending at the wing root will cause a tip displacement which is proportional to the distance of that tip from the root.
  2. Spar heigt: This curvature grows with the inverse of the square of the spar height. A lower relative thickness of the wing will produce more bending.
  3. Spar material: The Young's modulus of the material describes how much it stretches for a given stress. More important, however, is the elastic elongation at yield stress. Carbon fiber has a higher Young's modulus than aluminium, but is elastic until rupture, so it can be stretched more and produces more bending at yield stress.

The numbers: The Young's modulus of aluminium is fairly constant for a wide range of alloys and normally 70,000 MPa or N/mm². The modulus of graphite fibers depends on their manufacturing process and varies between 200,000 and 700,000 MPa or N/mm². However, this value cannot be compared directly to that of aluminium. The final modulus of the composite depends on fiber orientation and resin content.

It is safe to assume that Boeing (or more precisely, Mitsubishi Heavy Industries) uses a modern, high-strength fiber like IM7 (pdf) (IM stands for intermediate modulus), which has a modulus of 276,000 MPa. It is also safe to assume that most of the fibers are oriented in span direction, so they can contribute fully to taking the bending loads. If we assume a conservative fiber content of 60%, the resulting modulus of the spar material should be 164,000 MPa. However, the spar is not a discrete component, but part of the wing box which also has to take torsion loads. While Aluminium is an isotropic material (it has the same properties in all directions), CFRP is highly anisotropic, and adding torsional strength will require additional fibers in other directions. Consequence: The effective modulus of the wing box in bending direction might be as low as 110,000 MPa.

In the end, what counts is how much material is there to carry the bending loads. Here the yield stress of the material comes into play: The more stress a material can tolerate before it shows plastic deformation, the less of it is needed to carry a given bending moment. To arrive directly at the maximum deformation, it is enough to look at the maximum elastic strain. With IM7, this is 1.9%, and with high-strength 7068 aluminium (pdf), it is less than 1% before the material suffers permanent elongation. This means that, even though CFRP is stiffer than aluminium, it can be loaded more and will stretch more before it reaches its limits.

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    $\begingroup$ Thank you for the answer. But my question was about the in-flight performance of the extremely flexible wings, not about why the wings flex in the first place. $\endgroup$ – shortstheory Feb 23 '15 at 6:00
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    $\begingroup$ @shortstheory: Theoretically, there is a small performance reduction due to wing flex, but this is extremely small. My point is that it mainly reduces the load factor felt by the payload due to gusts. $\endgroup$ – Peter Kämpf Feb 23 '15 at 12:34
  • $\begingroup$ But Airbus A350 that is developed using almost same materials, has the same wing flex or not? and, if not, simply "why"? $\endgroup$ – Luca Detomi Jan 18 at 9:26
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Not only the 787 with CFRP has this, all wings flex a lot as shown by the lower part of this image. B52 deformation Source: Introduction to Transonic Aerodynamics by R. Vos and S. Farokhi

These days, designers incorporate the flexing into the design, making sure that the shape in cruise is exactly as they want it. But the two graphs above show some interesting facts. On het left you can see the pressure distribution on different locations on a flexible wing, and on the right the same, but then for a rigid wing (thus, not deformed)

You can see that on the right image (around x/c=0.3), there are sharp jumps in the graphs, these indicate shocks, and lead to wave drag. On the flexible side, the gradients are less steep, meaning the shock wave is less strong. As a consequence the wave drag will be less.

Thus, based on these graphs, we can conclude that the flexible wing will have less wave drag, than the same wing that would not deform.

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    $\begingroup$ Good answer! But wouldn't the designers twist the wing just so that under load it has the desired angle of attack at all wing stations? After all, the result of flexing a backward-swept wing is to reduce the angle of attack at the outer stations. Of course the unflexed wing wing will have too much load at the outer stations. $\endgroup$ – Peter Kämpf Aug 22 '15 at 18:06
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    $\begingroup$ That was also the thing I was aiming at. Designers know that the wing will deform, and will account for this in their design such that in cruise the shape is optimal. I made the comparison with the rigid case, not only to show that the flexing is a good thing, but also to explain why. $\endgroup$ – ROIMaison Aug 24 '15 at 8:44

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