I have a foam wing biplane I am building (Graupner Sunwheel) , and the wings flex more than I would like.

I have decided that I am going to reinforce my wings with .007 x 0.25 inch carbon fiber strip that I have previously acquired.

The question is...... should I glue the carbon fiber to the underside of the wing flush (with the wide side, i. e. flat side glued to the wing) or should I cut a "slice" and slip the carbon fiber in perpendicular to the wing and glue, i.e. skinny side .007 perpendicular to the wing surface?

From : Don Stackhouse

I'm not personally familiar with the Sunwheel, but from what I can tell from photos on the web, it appears to have thin sheet-foam wings like the Lite Stik's. If that's the case, neither of those two proposed methods is going to be an effective use of the carbon.

When something bends, there are compressive stresses on one side (for a wing under positive "G", that would be the upper surface), and tensile stresses on the opposite side. Of course that also means that somewhere in between those two extremes is a place where the tensile and compressive stresses are exactly zero. However, the shear stresses will be highest at that point. This place in the structure where the stresses make the switch between tensile and compressive is called the "neutral axis".

For a homogenous structure (i.e.: made out of material that all has the same stiffness, like the foam of your Sunwheel's wing), you can find the approximate location of the neutral axis with nothing more than a piece of cardboard and the edge of a ruler (one of those triangular shaped engineer's rulers works best). Cut the exact shape of the wing's cross-section out of the cardboard, then balance it on the edge of the ruler, perpendicular to the direction of the bending load (so in this case, parallel to the chord line). The line that the cross section balances on is the neutral axis. If the wing has an undercambered airfoil shape similar to the Lite Stik's, then the distance from the neutral axis up to the high point of the airfoil will probably be about the same as the distance from the neutral axis down to the leading and trailing edges.

One absolutely crucial detail should be immediately obvious. The material in the wing that has the most "leverage" is the material that is farthest from the neutral axis, in this case the high point of the wing on the compression side, and the undersides of the leading and trailing edges on the tension side. This is the material that will try to work the hardest to carry the load, and therefore will also probably have the highest stresses. On the compression side this is probably where buckling (for buckling failures) or crushing (for compressive failures) will originate, and on the tension side this material is where tensile failures will probably start. This is also the most effective place to add reinforcements, which is why I recommended that arrangement in my comments above.

Note also that one of your proposed locations for adding the carbon strip, the underside of the wing near the high point, is probably very close to the neutral axis. A reinforcement added there has almost no leverage, and therefore will not add very much strength.

Inserting the carbon strip into a vertical slit in the wing gets the top edge farther from the neutral axis, so some of the carbon is in a place where it can do some good. However, a great deal of the strip is below there, close to the neutral axis, and not very effective. Also, there is some question about how well that top edge will be supported in buckling by the foam on either side of it, since it will be carrying more than its fair share of the load, and also has less support due to the free edge right at the point of greatest stress. This is still not a good way to use the carbon.

Also, using a single strip of carbon does some funny things to the load and stress patterns in the structure. This is typical whenever you add some material to a structure that is much stiffer than the rest of the material in the structure. Carbon fiber is many times stiffer than plastic foam, and so a single strip of it will tend to pull the neutral axis very close to itself, no matter where you put it in the structure. If you put it on the upper surface at the high point, the neutral axis will be very close to the top of the airfoil, so the distance from the neutral axis down to the leading and trailing edges will be much greater, giving them much more leverage. The real effect of adding the carbon will be to make it easier for the foam on the other side of the neutral axis to carry the tensile loads.

The other option, adding carbon to the leading and trailing edges, pulls the neutral axis closer to them, giving the compressively loaded foam at the airfoil's high point more leverage. However, given that the stiffness and crushing strength of the foam is probably not even as good as its tensile strength, this still doesn't really help all that much.

In any of these approaches, the wing will get stronger, but not by nearly as much as the carbon's natural strength and stiffness might lead us to expect. It's an ineffective use of the carbon's abilities.

If you REALLY want to make the wing stronger, you need to put carbon where it can do the most good, and that means in places where it can carry both the compressive and the tensile loads. If you wanted to use the same total amount of carbon, you would need to split your strip of carbon in half down the middle, then split one of those two strips in half, so you end up with a 1/8" wide strip and two 1/16" wide strips. Put the two narrow strips along the underside of the leading and trailing edges, and the 1/8" strip inlaid into the top surface at the airfoil's high point. This arrangement puts the neutral axis halfway between the upper and lower carbon strips, giving all of the carbon plenty of leverage, and giving the wing a huge boost in strength and stiffness. The bad news is that the foam will be doing almost nothing at this point. However, this arrangement will not weigh any more than the other options you were considering, and the wing will be so much stronger that you really won't care that the foam is now just along for the ride.

Of course none of this will be as simple and effective as adding some flying wires. The legacy we got from the Wright brothers' wind tunnel was thin airfoils. These work well at low Reynolds numbers (such as models, and in their wind tunnel), but not so well at full-scale Reynolds numbers. However, it took a couple of decades for folks to fully realize this, and in the meantime those thin airfoils were too thin for cantilever spars. Thus, even the monoplanes of those early eras had to have external bracing. The nice thing about external bracing (i.e.: struts and wires) is that they typically have much more leverage to work through than a cantilever spar can even dream of. As a result, a lot of weight can be saved. For example, a full-scale Bucker Bu133 Jungmeister aerobatic biplane has a gross weight of 1290 pounds, and is stressed for plus and minus 12 G's, yet each of its four wing panels, covered, painted, ready to hang on the airplane, only weighs 25 pounds.

The only negative to wire bracing is the greater parasite drag, but for a park flyer that spends most of its time at low airspeeds, the induced drag is more important, and the parasite drag (within reason) is less of an issue. Even on full-scale airplanes it wasn't as much of an issue as you might think. The switch to cantilever monoplanes instead of wire-braced biplanes occurred when the airlines first started to fly in bad weather on instruments, and started to se their first regular encounters with in-flight ice. It's fairly easy to add de-ice boots to wings and tail surfaces, but pretty impractical to add them to all those bracing wires.

In the case of the Sunwheel I would recommend one possible mod. It looks like the interplane struts are located about halfway out from the fuselage to the tip. This leaves a great deal of unsupported tip out beyond them. If you add flying and landing wires, I recommend moving the interplane struts (and the associated anchor points for the outboard ends of the wires) to about 2/3 to 3/4 of the way out from the fuselage towards the tips. This will reduce bending stresses on the unsupported tips, without increasing them too much on the inboard portions of the wings.

I know that carbon fiber is good in tension loads, but not compression.

This is a bit of erroneous folklore. Carbon is actually very good in compression (almost as high in compressive strength as it is in tension), and fiberglass is relatively good in compression as well. However, just as is the case with most materials, they must be properly supported against buckling failures. Most of the so-called "compressive" failures you're likely to see are actually buckling failures, and are typically the result of poor design, not a lack of compressive strength in the material itself.

Kevlar is the material that is most notable for actually having poor compressive strength. Its tensile strength is actually higher than carbon, but its compressive strength (note, we're talking about pure compressive crushing here, not buckling) is less than 40% of the compressive strength of ordinary hardware-store-variety "E" type fiberglass. If your application sees very high tensile loads with little compression (such as most propeller blades), Kevlar is often an excellent choice, but for compressive or bending loads (bending typically results in compression on one side of the structure), Kevlar may have problems. I've been told that it's because the Kevlar molecule actually has a "kink" in it, causing the molecules themselves to buckle under compressive load, transferring the load to the matrix material, which then crushes. Oddly enough, the Kevlar fibers still retain nearly all of their tensile strength after this happens, so the structure still holds together if you put it back under a tensile load. Subsequent flexing then causes the now loose, unsupported fibers to saw and chafe against each other, resulting in very slow crack growth.

In my "previous lifetime" in the propeller business, I saw this happen in the original propeller spinner dome design for the Lear Fan, which had been designed from Kevlar. We were seeing very slow-growing cracks around the blade cutouts due to compressive failure in the compressively loaded zones when the dome surface flexed in that area from vibration. The epoxy matrix would crack at the microscopic level, then continued vibrational flexing would cause the Kevlar fibers to saw through each other, resulting in the cracks. I redesigned the dome using carbon fiber, which could handle the compressive component of the flexing stresses, and the problem went away. However, on carbon fiber spinner domes I did use a layer of Kevlar on the inside surface (which sees a tensile stress when the dome is impacted on the outside) for impact strength and for vibration damping (the other thing that Kevlar is especially good at).

Don Stackhouse
DJ Aerotech