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Old Jul 27, 2010, 07:38 AM
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Spar Structural Design

I'm a scratch-builder, and I strongly suspect that many of my designs are overbuilt by a substantial margin. I've been trying to find a good reference for designing a weight-optimized wing spar that's still "strong enough." I came across this spreadsheet earlier today in this thread. I have no formal training in engineering, so I'm hoping someone can help me figure out how to use it. I understand (I think) what goes in all the purple boxes (using the I-beam configuration), but I don't understand how to interpret the results.

Also, supposing the spar is designed to be strong enough at the wing midline, how much (and at what rate) can it be tapered as it approaches the wing tips?

For the purposes of discussion, let's assume I'm building an unswept constant-chord wing with a midline fuselage and no struts or supports. I'd really appreciate any help or references you can give me.

Cory
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Old Jul 27, 2010, 11:25 AM
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Disclaimer: third-year aerospace engineering student here, and I only got a B+ in my strength of materials class.

Now, that looks like a well put-together spreadsheet. First you'll want to fill out the "Aircraft Data" block, putting your numbers in the purple boxes. Next, you select the type of spar you want, plug in some dimensions, and it calculates a bunch of numbers for you. They're all informative, but the one you need is the Maximum Bending Stress. This tells you how strong your spar needs to be. Down below the blocks are a bunch of materials and the strength of each. Use the "Calculation Maximum" bolded values for reference. You want to pick a material which has a higher strength than the maximum bending stress.

So in the default spreadsheet, with nothing altered, for an I-beam spar, the maximum bending stress is 3670.5 psi. Referencing the materials list, Eastern White Pine has a strength of 3600 psi. This is probably fine if you're going to be gentle with your plane, as this spreadsheet sizes spars for a 6-10G IMAC sequence. If you're going to be doing heavy aerobatics, go with White Spruce or Sitka Spruce, strengths of 3900 and 4100 psi, respectively.

Oh, and when you make I-beam spars, make sure you create a fillet along the joint with thick CA.

Oh, and as for your second question: bending stress here would decrease linearly as you move along the wing (I think) so you would theoretically be able to reduce the spar such that its strength decreases linearly in proportion (out to zero stress at the tip) but honestly, that seems like too much hassle for a model.
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Old Jul 27, 2010, 12:25 PM
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Assuming a constant chord, and no tip losses, the bending moment varies with the inverse square of the spanwise location. I.E. halfway out on each wing, the bending moment is 1/4 that at the root. Translating this into practical terms, you can get away with a linear taper of the spar caps' width (or thickness), along with (linear) overall wing thickness tapering so they get closer together towards the tip. In reality, the tip losses reduce the bending moment slightly faster than what I mentioned above.

Going beyond this means you're getting into parabolic spandrels and other such fancy, curved shapes. If you're building a constant-chord wing, that's probably not such a concern!
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Old Jul 27, 2010, 12:43 PM
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Techincally you can taper almost to a point. But realistically you still want some spar at the tips. Usually for the small amount of weight savings no one bothers since it means the spar slots would need to be tapered in width as well. But if you're making the wing in such a way that it's easy to cut tapered slots then sure, go for it. If I were doing it that way I'd opt for making the spar caps still to full depth but 1/2 as wide just so there's something to give overall strength for handling and other unforeseen loads not related to actual flying.

I'm not sure I trust his numbers for spruce all that much. I inputed numbers for a glider wing at 123 inch span, 3.5 lbs weight, 8G max load (not unreasonable to occur on a winch or during a hard pullout). Spar details were 1/2 x 1/8 caps with 1/16 webs and a total depth of 0.95 inch. The box and I beam bending stress values came out to 7907 and 8812 respectively. Both of these are well over the given max load of spruce at 4100. But I know from experience that such a wing would easily handle this amount of flight load without rupturing. So either there's some other factor missing or the items he's got in white need adjusting to suit our sizes or his numbers for max stress in the woods given are very conservative.
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Old Jul 27, 2010, 12:48 PM
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Originally Posted by Flyingwingbat1 View Post
Assuming a constant chord, and no tip losses, the bending moment varies with the inverse square of the spanwise location. I.E. halfway out on each wing, the bending moment is 1/4 that at the root. Translating this into practical terms, you can get away with a linear taper of the spar caps' width (or thickness), along with (linear) overall wing thickness tapering so they get closer together towards the tip. In reality, the tip losses reduce the bending moment slightly faster than what I mentioned above.
You're assuming a point load for the fuselage and a roughly equal distributed load on the wing right?
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Old Jul 27, 2010, 12:53 PM
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You're assuming a point load for the fuselage and a roughly equal distributed load on the wing right?
Yes, but others have given good advice above. There's diminishing returns once you get past a certain point (linear tapers, IMHO). I would not lose sleep on whether to taper my spars according to a quadratic, vs. cubic equation!
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Old Jul 27, 2010, 01:00 PM
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Yeah, far too much calculus involved to figure that out. Besides, I'd be thrilled if a fat overbuilt spar was the most critical problem on my plane.
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Old Jul 27, 2010, 02:29 PM
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I like box spars, using the same amount of material for the vertical parts, better than I beams.
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Old Jul 27, 2010, 04:13 PM
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Thanks to everyone for the replies! I ran some of my already-built planes through the calculator and confirmed that they are indeed much stronger than they need to be. Your responses made me think of a few more questions:

1. This spreadsheet seems to assume that the webs are made from the same wood as the flanges. Would it be reasonable to substitute end-grain balsa, and if so, would I have to make it thicker in some sort of proportion to its compressive strength vs the strength of the flange wood?

2. Can the shear webs be tapered in thickness toward the tips, and if so, is a linear taper reasonable? (Obviously there would be some practical limitations to how thin these can be.)

3. I currently prefer to build all-wood structures, but does anyone know where I can get strength data for unidirectional carbon fiber or fiberglass to add to the sheet for completeness?

EDIT: 4. Would the box beam shown be stronger if the webs were in between the flanges instead of flush with the top and bottom surfaces? And wouldn't the box beam outperform the I beam in torsion? Why do people seem to use I-beams more often than box beams?

Cory
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Old Jul 27, 2010, 06:50 PM
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spar design primer

may be helpful: composite spar design
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Old Jul 27, 2010, 08:21 PM
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Quote:
Originally Posted by chickenblender View Post
Thanks to everyone for the replies! I ran some of my already-built planes through the calculator and confirmed that they are indeed much stronger than they need to be. Your responses made me think of a few more questions:

1. This spreadsheet seems to assume that the webs are made from the same wood as the flanges. Would it be reasonable to substitute end-grain balsa, and if so, would I have to make it thicker in some sort of proportion to its compressive strength vs the strength of the flange wood?
Shear webs take very low compressive stress at all. You might say they take none in theory.

its sort of like the strand of silk that stops the oinne ball rolling off the needle point. As long as it never rolls very far (the silk doesn't stretch) it will stay balanced..

There's a a bit of shear in them when the whole wing bends, but that is, in my opinion, not their real function.


Quote:
2. Can the shear webs be tapered in thickness toward the tips, and if so, is a linear taper reasonable? (Obviously there would be some practical limitations to how thin these can be.)
You can, but they are not part of the overall stress calculation really. They are there to stabilise the spars, and provided they are stiff enough not to buckle under the small compressive forces that the elasticity of the main beams will impart, that's all they need to do.
[QUOTE]



Quote:
EDIT: 4. Would the box beam shown be stronger if the webs were in between the flanges instead of flush with the top and bottom surfaces?
Not much, if any.
Quote:
And wouldn't the box beam outperform the I beam in torsion? Why do people seem to use I-beams more often than box beams?
Yes a box beam is better in torsion. But a wing is not normally something that doesn't have some sort of stressed skin applied, be it as humble as doped tissue. That is far better at stiffening it torsionally than the box beam.

If you use floppy plastic coverings, a D box leading edge sheet structures gives a better aerofoil, a far stiffer wing in torsion, and the sheeting also adds to the final strength.
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Old Jul 27, 2010, 11:25 PM
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Actually the webs do see some considerable amount of compression but not much else. A typical failure mode for sailplane spars that are webbed in that box manner with the glue joints vertical is for the top spar to buckle inwards by shearing the glue joint between the spar cap and the webbing glued to the face. For this reason sailplane designers like to see full width endgrain supportive platform like webs that fit snuggly between the caps so that the top cap sees a fully supportive web joining it to the lower cap and does not have to rely on the glue other than to hold the webbing in place. Overkill for most cases but it does illustrate a key point about when an I or box beam spar flexes strongly in a thin wing.

For most power and sport models face glued webs like shown in the box spar example that use very hard balsa and good glue would be more than fine.

Chickenblender, I'm a big fan of building light but I don't tend to spare the grams when it comes to spars in models that I know will see high G loads. Yet you are sure you way overbuilt some spars. Care to bare your soul and describe a couple of examples of what you think you overbuilt? I have to admit to some serious curiosity on this...
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Old Jul 28, 2010, 01:43 AM
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Care to bare your soul and describe a couple of examples of what you think you overbuilt? I have to admit to some serious curiosity on this...
After running things through the calculator, my flange size seems to be about appropriate (about 1/2" by 3/16" basswood on my 48" sport wings), but I've been using full-width end-grain balsa webs which I learned about when I was building a Bubble Dancer sailplane wing. Total overkill on a short wing that's not going to be winch-launched.

Cory
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Old Jul 28, 2010, 12:59 PM
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Maybe not. How hard to you pull on the elevator stick at high speeds to do those impressive snapping flick rolls? Such a thing is easily as tough on a wing spar as any winch.

Yeah, I'd still agree that they are more than you need given a typical sport model's wing thickness. The deeper spacing greatly eases the loads in the caps. But all in all you're maybe only 50% "fatter" than what I would use if it were my own design. The few extra grams you "needlessly" added is a drop in the bucket. But a drop that is in the right place if you're going to drop anything extra anywhere in a design.
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Old Jul 28, 2010, 04:44 PM
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Maybe not. How hard to you pull on the elevator stick at high speeds to do those impressive snapping flick rolls? Such a thing is easily as tough on a wing spar as any winch.

Yeah, I'd still agree that they are more than you need given a typical sport model's wing thickness. The deeper spacing greatly eases the loads in the caps. But all in all you're maybe only 50% "fatter" than what I would use if it were my own design. The few extra grams you "needlessly" added is a drop in the bucket. But a drop that is in the right place if you're going to drop anything extra anywhere in a design.
Your point is well-taken: better to have extra weight in structural components than non-structural ones. This whole line of inquiry came up when I realized that my flanges were roughly 1/3 of the weight of the entire wing, prompting me to see if there were significant weight savings to be had there. Even if I keep the exact same flange size at the root but taper toward the tips, that would save 1/6 or so the weight of the entire wing.

Another thing I didn't mention is that I also used a lot of diagonal cross-braces and that there was a second smaller spar in the back. I feel confident now that I could make the same wing, at the same strength, with a single spar and some D-tube sheeting and take off 1/4 or more of the wing's weight.

Vintage1 suggested that doped tissue (or silkspan on a bigger model?) gives more torsional rigidity than plastic films. Is this the general consensus? I've been thinking about trying out silkspan recently.

Cory

EDIT: bad math is fixed
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