787 Wing - A New Twist on Structural Engineering?

(Thanks to Jon Ostrower, at http://www.flightglobal.com/blogs/flightblogger/, for the graphic!)

I was a bit relieved to read comments indicating other folks also thought the 787 wing had an unusual amount of wing deflection during the first flight video.

In particular, the aft view of ZA001's climb-out seemed to indicate an amazing curvature/bending of the wing-

Reuters video of ZA001 First Flight Takeoff
0:18 great T-33 fun- swooping in for chase during takeoff roll
0:37 front view of wing bending
0:53-1:03 amazing (apparent) wing deflection

Now, camera angles can play tricks with our perception (Bonus Prize to those who have already identified a contributing effect- see first post of this new thread).

But discounting that, I did some surfing about to investigate the 787 wing. (Unfortunately, merely on the web, not long boarding as our friend Baron is doing off the coast of Brazil this holiday season- rats! :)

It turns out, Jon Ostrower, who runs the great FlightBlogger website, has been examining this topic for some time- here is his July 30, 2008 article "A Closer Look at 787 Wing Flex" (gulp! guess we're catching up a bit! :). My special thanks to Jon for letting me borrow the graphic above and to link in to his article.

As one of Jon's commenters noted, "One wag joked(?) that the only reason MCboeing put larger windows on the 787 so that the passengers would not get concerned when the lost sight of the wingtip...."

Julius noted the landing gear issues on the first flight of the second flight test article (ZA002), which also sent me surfing- (sounds like the nose gear initially only deployed 75 degrees- the crew did an "emergency" extension (which some say, is not that unusual for first flights or after maintenance) to get it down and locked, but the situation resulted in more video coverage than usual of the landing, which shows some fairly substantial wing flex too- looks like coincident with the ground spoilers deploying- guess those things really do have a big effect on brake effectiveness (among other things, "runway friction coefficient" x "actual weight on wheels") and landing lengths. This also prompted a review of the ZA001 first landing, which shows similar "flapping" during landing. (More correctly, relaxation as the wings unload, but heck, "flapping" sounds more spectacular).

ZA001 First Flight & First Landing (check out last few seconds of video)

ZA002 First Landing

With Jon's blog substantiating our observations, let's investigate this wing flex stuff!

As well commented upon, the 787 is a constructed with composites. I'm no structural engineer, and I'm sure there are many subtle variations, but it seems the terminology of choice is Carbon Fiber Reinforced Polymers, or CFRP.

Trying to find specifications for CFRP was one of the most frustrating experiences I've had on the web- quoted strengths varied widely, and most of the reference material is only available by purchasing trade journal reprints. (Given the wide variance of the open source material, I did not have confidence I would find a definitive answer with the journal articles). There was also some information about reinforcing concrete with CFRP- which while intriguing, I thought not too applicable for our purposes. (It seems CFRP makes a dandy "wrap" for concrete cylinders and beams that make up highway supports- I think after the Northridge earthquake in the Los Angeles area, circa 1994, many of the freeway overpass supports were reinforced with this fabric).

But, with little confidence in any alternative, I resorted to our steadfast reference, Wikipedia, which pointed me to "AS4", which seems to be a representative aerospace CFRP,
Hexcel AS4.

For comparison with conventional, shall we say, "non-disruptive", aluminum construction, I found a variety of sources- it seems like 7075T6 is a good representative material,
Alcoa 7075 fact sheet.

For our study, I used the Hexcel AS4 datasheet "Typical 350ºF Epoxy Composite Properties (at Room Temperature)" values, and the compression values, rather than tension, as bending loads create both conditions, on the "near" and "far" side of the article subject to the bending load. (The compression values used in this study are somewhat lower than the "flexure" strength listed in the AS4 table, so this represents the conservative case- I suspect the flexure values are for tension side of a loaded object, such as when working with prestressed beams, e.g., reinforced concrete and such- any stress engineer types out there?).

From Wikipedia, the above references, and a few other scribbled notes over the pat couple of days, I pieced together this table. (It's in metric units. I confess, rather than demonstrating my enlightenment, it reflects my laziness in not converting to "English" units. Well, make that "American" units, as even the British use the metric system... But since we'll be doing relative comparisons, the unit's won't matter- one less thing for me to goof up! :)

So here's the deal- we'll be using three metrics (so to speak!) of performance:

Young's Modulus, which is "stiffness": the amount of load (force per cross section area) divided by the resultant strain (axial deflection per reference length).

Yield Strength, the load (force per cross section area) that produces permanent deformation in aluminum, or damaged fibers in composites. (Note: this is slightly different than "ultimate" load, which is the "breaking point"- complete failure- but we will assume the airplane is kept out of the damage region).

Density, the mass per volume (perhaps there is a slight difference between "denseness" and "density" ... :)

So, here we go, the Mr. Science overview (these numbers are approximate, and "Your Mileage May Vary", but seemed to be the most typical values I could find):

Material ....... Young's Modulus ...... Yield Strength ...... Density
7075-T6 ........ 69 GigaPascals ....... 430 MegaPascals ..... 2700 Kg/m^3
CFRP (60%) .... 128 GigaPascals ...... 1530 MegaPascals .... 1550 Kg/m^3

Note: the CFRP properties are for "along fiber" loads, not cross-loads, which are markedly lower (more about that later- #1), but for bending, this is appropriate.

A higher value of Young's modulus means a "stiffer" structure- and CFRP is about twice as stiff as aluminum. (So what's up with this goofy-looking 787 wing? Calm down- let's continue! :) At least this "reinforces" our stereotype of "composites being better than aluminum".

A lower density value is also a good thing in general, and CFRP once again demonstrated it lives up to the stereotype expectations of composite's superiority over aluminum- the latter being about twice as "heavy" (dense) as CFRP. (Well, 2700/1550 = 1.74 to be "exact". Hmmm, so far, things are distressingly stereotypical, rather than disruptive!)

A higher yield strength is also a good thing. Again, CFRP follows stereotypical expectations, with a nearly four-fold advantage over aluminum. (Okay, 1530/430 = 3.56 or so, but hey- this is "ball park stuff"! :)

So, all the material properties would seem to be just as we would expect- so why all that wing bending?? Let's consider the primary design criteria for a wing: weight and strength. Does stiffness matter? Uh, well, er, "it ought to". But for now, let's say no (we'll come back to that one also #2!)

Let's look at "strength"- what it takes to keep the wing from "breaking" (Although strictly speaking, we will use yield- the point of permanent deformation- rather than breaking strengths). To handle a given load (bending load, which is converted to axial tension and compression, in the upper and lower wing skins, and upper and lower web caps of the spars), CFRP is about four times (3.56) as strong as aluminum. So, we can use one-quarter (28%) as much, to get the same strength (resistance to yielding or damage). There are two ramifications of this- one is obvious, the other not-so-obvious.

a) Obviously, there's a tremendous weight savings! (Ah, more on THAT later #3). And figure CFRP is about half as dense (0.57), the total weight savings would be about four times two: the composite structure would weight roughly 1/8 of the aluminum wing! (Or a bit less roughly, (1/3.56) x 0.57 = 0.16, or about 1/6; More on this later #4, with some real-world adjustments...).

b) Less obviously (until we saw the videos and Jon's graphic at the top), is: DEFLECTION. Since CFRP is -about- four (3.56) times as strong as aluminum, a wing designer can use one-quarter (28%)as much. But the stiffness is "only" twice (128/69 = 1.82) that of aluminum;

SO, "one-quarter the material" x "twice the stiffness"
= TWICE THE DEFLECTION
(Okay, (1530/430) x (128/69) = 0.52 the stiffness = 1.92 the deflection)

MYSTERY SOLVED ! (Yeah! Well, basically...); Viola!, as one public icon of past exuberantly, and famously, (mis-)proclaimed. (Which icon? I'm not so sure :)

NOW, back to those pesky "later" items mentioned above (#1, 3 & 4; #2 follows later):

#1) "CFRP properties are for "along fiber" loads, not cross-loads, which are markedly lower..."

#3) there's a tremendous weight savings

#4) the composite structure would weight 1/6 of the aluminum wing ...some real-world adjustments

All three of these items can be summarized in one discussion: how much additional material is required to compensate for the anisotropic (directionally dependent) properties of fiber reinforced materials, versus the isotropic (universal in all directions) characteristics of aluminum, and most metals for that matter. (There are some metallic structures, particularly crystalline turbine blades, that are not isotropic, but such exceptions are rare- and expensive).

Wings are subject to complex loads (different than "wing loading", weight/area). Obviously, with the shear, bending, and torsion, the load paths are complex, and this is one area the anisotropic nature of composites can create problems. Consider just how unidirectional composite strength can be: the shear strength of a single-direction layup is only 81 MPa for 90-degree cross load, or a mere 4% of the 0-degree tensile strength os 2205 MPa; and shear strength is only 128 MPa, or 6% of the 0-degree tensile strength. (By comparison, aluminum is equally strong in any axis, and the shear strength of 7075T6 is 331 MPa, or 65 percent of the 503 MPa yield strength in this ASM spec sheet, which is some 20% stronger than the yield strength listed in the Alcoa spec sheet, which did not list shear strength, but to compare "apples to apples", the ratio of shear to tensile strength for 7075 seems to be 65%).

To address complex load paths, CFRP must could be constructed with complex fiber orientation, for maximum strength and minimum weight. This would require individual strands to be oriented in the unique desired directions. A more practical, and less expensive, alternative, is to use CFRP with the familiar 0 degree/90 degree weave orientation. To maintain full strength in either direction (0 and 90 degrees), twice the material is required (the intended 0-degree plies, PLUS plies oriented at 90 degrees). And to handle loads at 45 degrees (as shear strength is weak), plies in both directions must be stronger (read: more- by a factor of the square root 2 = 1.41, or 41%, if my trigonometry is correct). So, potentially, to make a CFRP structure as "isotropic" as aluminum, would require about 2(for 90 degree loads) x 1.41(for 45 degree loads), or about 3 (2.82), times as much material as a "simple" anisotropic structure, and the marvel of a CFRP structure weighing 1/6 that of aluminum now becomes about half (0.47) as heavy. Still an impressive weight savings! And most assuredly, the design engineers will strive to minimize such wasteful excess.

(The ply orientation issue could have other solutions; one might be using 0-60-120 or 0-45-90 degree plies, rather than thicker 0-90 degree plies. The various solutions would result in slightly varying weights, and strengths in off-primary axis directions. It seems I've seen broken composites, and the jagged edge seemed to have fibers pointed in multiple directions- not sure if that is a result of the damage, or the inherent weave pattern of the composite fabric fibers).

Our visual observations of the 787 wing flex, does seem to substantiate this ball-park estimation, of roughly twice the wing flex of an aluminum wing. Regarding CFRP manufacturing and design allowances to handle the anisotropic limitations, Dow Chemical has an interesting article, which states "The key drivers for using CFRP are light weight (50 percent lighter than steel and 30 percent lighter than aluminum)", which would seem to indicate a lot of material is going into making composites act more isotropic (plus, probably some conservative design practices with the still relatively new technology). The Dow claim of only a 30% weight savings over aluminum (rather than our 50%-ish number above) seems to be proven in aviation- there seems to be no real-world weight savings of composite airplane versus aluminum, so far anyway. Perhaps CFRP manufacturing and design allowances to handle the anisotropic limitations (??)

Besides weight, excess material imposes, ah, excess cost. Boy, I thought the mechanical properties of CFRP was hard to find- the cost was even more proprietary and elusive. (Please see accompanying post at the top of this thread).

#2) "Does stiffness matter? Uh, well, er, "it ought to". But for now, let's say no"

One of the advantages of a "flexy" wing is absorbing gust loads and provides a better ride, and improved fatigue life for the rest of the airplane. (With a flexible wing, the overall upward velocity is not changed in response to a sustained updraft, but the rate of upward velocity change is slightly more gradual (and prolonged), so the vertical acceleration is smoother, and forces -and stresses- are lower). This allows components to be made less robust, and lighter.

On the other hand, one of the more alarming presumptions regarding the appearance of unusual/"excess" flex in a wing, regards susceptibility to flutter. And this might be where composites/CFRP shine. The X-29 forward-swept wing program was feasible because of the torsional stiffness of a composite wing. It would seem the 787 is benefiting from this as well, not that it is vulnerable to the inherent wingtip divergence the X-29 had, but still, that flexy wing needs to be resistant to torsion/bending coupling.

Jon's FlightBlogger website has the scoop on this too; some early 777 testbed work for variable camber effects, and his Better Know a Dreamliner - Part Two - ZA002 post yesterday, ("Airplane Two will have the second most hours of the six flight test aircraft and will first participate in the initial airworthiness and flutter clearance, as well as stability and control testing...High speed air testing is also expected to be a significant part of ZA002's aerodynamic check-out along with wing twist that will be measured"). With fly-by-wire controls, and tailored twist characteristics from CFRP construction, this should go smoothly. (Then again, how often have we heard "it's only software" :)

One last (thank goodness!) item to consider is fatigue life. This turned out to be disappointingly proprietary or buried exclusively in subscription trade magazines. The best I could find was Wikipedia CFRP, "Carbon fiber-reinforced polymers (CFRPs) have an almost infinite service lifetime when protected from the sun, but, unlike steel alloys, have no endurance limit when exposed to cyclic loading". So the "flexy" composite wings should not fatigue as aluminum would exposed to such large deflections. (One wonders about fuel and hydraulic lines though, but I suppose these are of a relatively small diameter such that bending will result in a low stress and strain).