Structural Design considerations for reinforcing a fuselage??

subtitled : a second short course in designing composite structures?

Original Question edited for simplicity

Don -

I laid up some "lite" (what it said on the package) FG cloth over a part similar to the forward fuse on the Electra (3/32 balsa). The glass extended from the forward box between the two bulkheads past the second to an essentially cantilevered portion. I performed a highly scientific stress test on the glasses and unglassed portions of the side (I bent it with the glass in tension until it broke), and there wasn't much difference between the two (they felt about the same when they broke).

What I am trying to accomplish with the glass is this: I have reinforced the bottom of the box ahead of the LE bulkhead with 1/4" tri stock in the bottom corners, and I want something to carry the load across the second bulkhead (located about at the LE). I expect the load to be mostly compressive here from a hard landing, but maybe bending will be significant, too. OTOH, the fuse side should be plenty strong in shear, so bending loads shouldn't be an issue. Is one layer of "lite" glass sufficient? I've had several people say I should glass the fuse, but I'm afraid that much of that may be a knee-jerk reaction -- there seem to be two types of people: "build strong" and "build light". I'd like to do both.

TIA,

- Chris

Response

From : Don Stackhouse

Chris,

Good question, no simple answer. The nose of a model glider during a bad landing is one of the most complex stress analysis problems you can find in this hobby. It is sensitive to a huge list of variables, and it's almost impossible to address without making some fairly sweeping simplifying assumptions.

***WARNING***
Someone once made the accusation that if you asked me what time it was, I would tell you how to build a clock. Actually, they were wrong. I would first tell you how to design a clock. Be forewarned before reading further! In case this discussion gets shared with others who do not have an engineering background, I will also try to start with very basic explanations of the principles involved. Please bear with me if I explain something that you already know.

First, determine the loads on the nose. Well, how hard are you planning to crash? At what pitch, roll and yaw attitude of the model and the model's flight path (those two are almost never the same) relative to the ground? How hard is the ground? What speed, and at what flying weight? What are the model's dimensions and the distribution of mass within the airframe? These are the primary variables defining the load applied to the nose. Because of that first question in particular, whatever you come up with will be a judgement call at best.

Most of the design work actually comes down to making sure that whatever loads you design for are being carried efficiently by making sure that all of the components in the structure are doing their fair share of the work, and that the overall structural concept does the best job of absorbing those loads of any of the options available.

So, back to your balsa box fuselage with a hatch in the top of the nose. There's basically 3 kinds of serious impacts it will see, and 2 of those behave about the same. In the cases of both a cartwheel and a vertical impact, most of the loads on the nose are basically compression. In the case of a shallow diving impact, like a "dork" landing, the nose sees some lengthwise compression, but also a lot of upward bending. This bending is stronger as you approach the wing, which is why the failures from this load generally occur near the leading edge. The fuselage in this situation sees compressive loads on top, tension on the bottom, and shear in the middle. Failures will usually be either a tension failure on the bottom, probably just behind the triangle stock you installed, or a buckling failure in the compressively loaded upper edges of the fuselage sides in the open bay in front of the wing leading edge.

Let's take a moment here (the time kind, not the stress kind) and talk about material properties. All materials have an ultimate strength in tension, and another (usually lower) strength in compression. The tensile ultimate is the load at which the material lets go completely, snaps, parts company with the other end, etc. The compressive ultimate is the load at whch the material crushes, like a lump of modeling clay under a brick (NOT like a pop can - we'll discuss that one in a minute). If you divide the load (pounds) by the cross sectional area (square inches) of the part carrying the load, you get the load per unit area ( pounds/sq. inch, or "psi."), which we call stress.

In addition to the ultimate stress, many (but not all) materials have a yield stress. If you apply and release a load to a material and it returns to the same shape and size it started with, the material is behaving "elastically". At some load level it takes a permanent set and returns after loading to some other size and shape. The stress level where this change first starts to occur is called the "yield" stress. As with ultimate stresses, there can be different yield stresses for tension and compression. Shear stresses also typically have ultimate and yield values. In addition, many materials, including wood and most composite materials, have properties that are dependent on the direction of the load relative to the fibers.

Stiffness is the measure of how far the material deflects under a given load. Typically the stiffness of a material is specified in the books as a deflection-to-stress ratio for stresses within the elastic range, and is called a "modulus". The stiffness in tension and compression is typically called the "elastic" or "Young's" modulus. There is also a modulus for shear. The Young's modulus for steel is typically about 30,000,000 psi, which means that a piece of steel 1" long with a 1 square inch cross-sectional area would hypothetically stretch 1" under a 30,000,000 pound tensile load. Of course the stress in this case is far beyond the elastic limit (the yield stress), so it might be a better example to say that it would stretch .001 inch under a 30,000 pound tensile load!

Back to fuselage failure modes. Another possible failure is a shear failure in the fuselage sides. There are 2 kinds of shear going on here. There is the vertical shear load that connects the upward force of the ground on the end of the nose with the downward force from the vertical decelleration of the rest of the model. There is also a horizontal shear connecting the tension forces in the bottom with the compression forces on the top, that are the result of the upward bending moment in the nose (which is there because the contact with the ground and the decelleration forces at the c/g are separated by a distance, called a MOMENT arm). Since the fuselage sides in this area are normally horizontal grain, the horizontal shear due to the bending moment is what usually splits them, plus any vertical tension forces from the nose's top edges trying to buckle them upwards away from the bottom. If you made the fuselage sides with the grain vertical they would probably fail in the other direction due to the vertical shear load. Glassing the fuselage sides will help prevent this kind of splitting, but there must be enough glass there to carry a significant load.

To answer that question we need to get some material properties. I'd like to thank Larry Hardin for sending me this chart he put together from WACO's technical newsletter, some from an article in "Sport Aerobatics", and some from his aero engineering texts. I've also added some properties for e-glass cloth in epoxy:

material	Sp Gravity	Modulus	Strength	Yield Strn.	Strgth.	Stiffns.
		x 1000000	x 1000 psi	x 1000	/Weight	/Weight
S-glass	2.50	3.6	188	52.22	75.20	1.44
Kevlar	1.44	8.8	198	22.50	137.50	6.11
Spectra	0.97	18.1	315	17.40	324.74	18.66
Graphite	1.81	21.6	137	6.34	75.69	11.93
Spruce	0.40	1.6	10.2	6.38	25.50	4.00
Balsa	0.14	0.5	2.2	4.40	15.71	3.57
Basswood	0.37	1.5	8.7	5.80	23.51	4.05
Alum 2024-T4	2.77	10.5	40	3.81	14.44	3.79
E-glass cloth	2.50	2.3	33	14.3	13.2	.92

Comparing the data for E-glass and balsa, we can see from the strength column that glass is about 15 times stronger than balsa. This means that if you added about .006" of glass cloth to a piece of 3/32" balsa you would approximately double the tensile strength of the part. Your "lite fiberglass" might be 1/2 oz., 3/4 oz. or 2 oz. per yard cloth, depending on their definition of "lite". As a general rule of thumb, glass cloth has a thickness of about .001" for each ounce per yard of cloth weight. If you have a micrometer, you can stack up about 4 layers of dry cloth, measure the thickness and divide by 4 to get the thickness per ply.

Incidentally, this thickness is about what you would get in a vacuum bagged layup, and is also representative of the fiber/resin ratios used in the table above for the material properties. If you do a wet layup without the vacuum bag or other means of compression your thickness per ply will probably be about 2-4 times as thick. The simple way to deal with that is to work out the required layers of cloth for dry fabric, not the finished layup thickness. It's the number of fibers per square inch of cross section that counts. If the laminate "puffs up" with extra resin during layup, only the resin quantity changes, the number of fibers remains the same. You pay a weight penalty, but at least you have enough fibers present to carry the specified load.

Now let's assume that you've measured your glass and discovered it is 3/4 oz./yard, or about .0008" thick. This is equivalent in strength to about .012" of extra balsa, so a single layer of this added to your 3/32" (.093") glider nose makes its strength equivalent to about .105" balsa, a 13% increase. This isn't much of a difference, which probably explains the results of your experiment. The other thing to note is that the strength to weight ratio of E-glass is slightly worse than balsa. The reason we use e-glass anyway is because it's cheap, and provides a lot of strength in a small space. If tensile strength alone were the only consideration, you could build an equivalently strong nose from all balsa, but it might be as thick as a football.

In you case, the specific question is how much glass do you need across the underside of the leading edge bulkhead to be equal in strength to the section in front of it that has the 1/4" triangle stock? Well, the triangle stock adds approximately the same amount of balsa as an extra .03" thickness in the bottom sheeting, or about .002" of glass. This means you need about 1 layer of 2 oz., or 3 layers of 3/4 oz., or 4 layers of 1/2 oz. glass across the underside of the bulkhead.

Sounds ok so far, except there's something we've left out: strain to failure. For e-glass it's 14.3, but for balsa it's only 4.4 . This means that at the load where the balsa lets go, you've only used about 1/3 of the strength of the e-glass. If you want the fuselage bottom under the bulkhead to be as strong as the section ahead of it, you need 3 layers of 2 oz. glass! Not only that, but the load continues aft of the bulkhead, so you need to run the glass aft too, or else put triangle stock in the area under the wing. This will do a fairly good job of carrying the loads past the wing saddle, and your fuselage will now break at the trailing edge.

So far we haven't made a very convincing case for glassing the nose. Now let's talk about that pop can.

When you crush a pop can ("soda" can if you're from the Philladelphia area), it fails in what we call "buckling". Buckling occurs under compression loads in relatively long, slender structures, and is entirely independent of the material's strength. That's right, if the dimensions are identical, a piece of the hardest tool steel will buckle at the same load as a soft piece of coat hanger wire. In structures subject to this, the failure typically occurs at stresses far below the compressive yield strength of the material.

When buckling failure occurs, there is usually no warning. When the critical load level is reached, the structure loses its ability to support itself, and simply collapses. It's sort of the structural equivalent of a bad tip stall.

The parameters that control buckling failure are length of the unsupported sections, the type of support at each end of the unsupported sections (is the connection rigid, or does it act like a hinge?), the size, shape and construction of the cross section, the straightness of the unsupported section, and the stiffness (not strength!) of the materials involved.

The sneaky thing about buckling failures is that the apparent damage is frequently not in the same place as where the failure occured. Have you ever spiked a model into the ground nose first, and found a lengthwise split in the top of the front end of the nose? The top edges of the nose sides in the hatch area probably buckled outward, pulling the top of the nose apart. This is also a common contributing factor when the leading edge bulkhead comes loose from the fuselage sides. If you find cracks in the fuselage sides at the leading edge bulkhead, or in the fuselage bottom at the same place, there's a good chance that the real failure that started it all was buckling of the fuselage sides in the middle of the unsupported edges in the hatch area. Look closely at the cracked areas. If the crack looks like the material was pulled apart (loose, torn, ragged fibers like the end of a broom) or simply crushed (little wrinkles running across, not lengthwise), it might be simple tension or compression; however, if you see compression failure on one side (probably the inside), and tension failure on the other side, the break occurred in bending. That bending was probably the side effect of a buckling failure nearby.

To fix the problem, first find the location of the buckling failure. Any increase in bending stiffness of the unsupported section, reduction of the unsupported length or lengthwise curvature in the unsupported section will improve things. In the case of the top edges of the nose in the hatch area, the addition of an extra bulkhead in the middle will reduce the unsupported length. If the sides are curved outward, re-shaping them to something straighter will help. Thicker or stiffer material in the fuselage sides will improve their bending stiffness. This is where your "lite fiberglass" comes in. The nose has already been designed and built. You don't want to re-do it, or make it look like a football with extra balsa. The problem is, the sides of the fuselage will probably buckle long before the full strength of the balsa has been used. The key is to make the sides stiffer in bending by applying a layer of glass to the inside and outside of the fuselage nose. Since the two layers are separated by the thickness of the balsa, which gives them more "leverage", this is much more effective than applying the same total amount of glass to the outside only.

The other benefit from glass on the nose is splitting resistance. If the nose has curved sides or bottom and is subjected to a compressive load on the nose, there are circumferential tensile stresses around the nose. We sometimes call these "hoop" stresses, like the stresses carried by the hoops around the outside of a barrel. Note that with the exception of the glass cloth and the metals, the material data in the table above is for uni-directional material. In other words, the strength of the wood is given with the load parallel to the grain. Your balsa nose probably has the grain running lengthwise, and if there are any hoop stresses in the vicinity they will probably be across the grain. The cross grain strength of balsa in particular is quite variable, depending on grain patterns, proccessing variables, past history, etc., but in any case it's very low. Let's assume just for the sake of argument that it's 10% of the along the grain properties for the wood in your model, so that glass is 150 times stronger in that direction. In this example, a single layer of 2 oz. glass would approximately quadruple the splitting resistance!

So much for the simple part of the discussion. at this point we get into stress concentrations around hard points, notches and corners, the effects of changes in load path, and all those other little complications. If you don't have access to finite element stress analysis, your best bet is probably to study all the failures you can find, or else do a lot of crash testing of dummy noses. I use the computer to get in the ballpark with it, but it seems like no matter how much you try to analyse it, you will still find surprises in service. Engineering is still in many ways far from an exact science!

There are rarely any simple answers in engineering, but in this case it appears that glass in the right places and the right amounts can be worth the trouble. It can also be a lot of un-necessary extra weight if you use it incorrectly. Each situation will be different, and you probably need to see a few broken parts to figure out if glassing makes sense, and exactly where to put how much. Rather than running outside to do a lot of crash tests on your model, I would suggest talking with any other Electra and Gentle Lady owners you can find, and find out where theirs tend to break. They may or may not have good suggestions on how to fix them; your main concern should be figuring out from this discussion and their descriptions which loads and failure modes tend to cause most of the problems. Once you understand that, the best way to add reinforcement should be fairly clear.

If it was simple we wouldn't have anything to talk about.

Good luck!
Don Stackhouse @ DJ Aerotech