Discussion in 'Aircraft Design / Aerodynamics / New Technology' started by David Teahay, Oct 14, 2018.
Bingo. Which then negates the OP's question.
It doesn't negate the OP question. He asked about an Affordaplane spar, not a typical hinged rear spar like a Cessna 150.
the rear spar is carrying the flap and aileron loads,.....so how does that relate?
You're right. In the case of the A-plane, it appears the front and rear spar are the same, meaning they have equal stiffness. (Making some assumptions about how they're strutted and attached because I'm too lazy to look.)
All that they do is change the lift magnitude & location (yeah, drag too but we're ignoring that). So they just present a few new load cases.
It's true that the rear spar--if it's really a spar, depending on which design we're talking about--carries the aileron & flap loads, but if it's a pinned wing root, the rear spar isn't carrying that load back to the fuselage via bending & shear. In that case it's really the wing skin that's holding the rear spar (which really would more appropriately be called the rear skin) and flap/aileron hinges in place because of torsional stiffness. Think of the wing like one of those textbook problems where a steel pipe is sticking out from a concrete wall and you put a torsional load on it. That's all the ailerons and flaps are doing.
But yeah, we have strayed from the OP's question a bit. I think it's been answered.
I do not see anything wrong with a little thread drift as long as the subject is the same.....But looking at Afordaplane it is fabric covered wing and strut braced. Is fabric strong enough as regards "rear skin" to provide torsional stiffness?
Fabric doesn't usually add much torsional stiffness (maybe some for small models).
So the simple ultralight wing is limited in how much cantilever overhang beyond the struts (determined by the deflection of the tube spars).
Hi,What does "s" stand for in (29),(32)...Thankyou for your time Sir
-opinion concerned with drag problem ?
=Scott Price ? (very short take off time !)
Marc, I assumed you were talking about conventional 'plank' or I beam spars, which have low torsional stiffness. If you have a very torsionally stiff front spar, you can, like R.J. Mitchell did with the Spitfire, not bother with a rear spar. Other aircraft have torsionally weak spars connected with diagonal bracing to form a torsionally stiff assembly. Those are best analysed as a single spar.
Marc, I suspect you know this as well as anyone on the planet, sounds like a you are asking this as rhetorical question. at least in terms of answering you.
So let's clarify a little. In most of these types of discussions, we are generally making the assumption that the wing stiffness is high and the wing deflects in bending without significant twist. We apply nominal spanwise air load distribution, and then find spar shear, bending moment, and deflection by integration. This is a decent approximation in most small airplanes with modest AR and span and with structural skins. Get into sailplane style wings with AR of 40 and 50, and torsional deflections can be significant.
Other cases are certainly possible. If we were dealing with a torsionally soft wing with its shear center significantly away from the quarter chord point, we will develop twist in the foil. If the twist is unfavorable structurally, we call it structural divergence.
First, what is the shear center? This is a place where if loads are applied through it, the beam will just bend and there will be no twist. Refer to Mechanics of Materials texts for how to calculate it and more discussion. Apply lift aft of that place and it will cause nose down torsion, apply lift forward of that place and it will cause nose up torsion.
An easy example is a fabric covered cantilever wing with two spars about the same bending stiffness, forward spar at 40%c and the aft spar is at 70%c, and no D-tube. Ribs and drag / anti-drag bracing tie the spars together but do not add much torsional stiffness. If the two spars have about the same bending stiffness, the shear center is somewhere around 55%c, but lift and pitching moment are normally described around 25%c. We have lift applied 30%c ahead of the shear center making a nose up moment = lift times 30%c. That moment is much bigger than the nose down pitching moment of the foil, and the wing will try to twist nose up, increasing angle of attack as you go out the wing. This increasing angle of attack towards the tip will raise loads outboard from the nominal distributions. This is structural divergence...
Now for a more typical structural arrangement for fabric covered wings. The forward spar is around 20%c and much stiffer than the aft spar at 70%c. There is also a D-tube of thin plywood bonded over the leading edge, half ribs, and the main spar. The spar and D-Tube give a lot of bending stiffness compared to the aft spar, and adds quite a bit of torsional stiffness too. This arrangement usually puts the shear center close to 25%c, so lift times distance between shear center and lift makes for a small twisting moment that might be nose up or nose down, depending upon if the shear center is just ahead or just behind the 25%c point, and pitching moment tries to twist the wing nose down as you go out the wing. This unloads the outer portions of the wing, and makes conventional analysis of the wing somewhat conservative. The D-tube makes for much more torsional stiffness than in the previous case, so in total, this wing will only twist in smaller amounts, and usually in a direction that slightly unloads the tips. The nominal spanwise air load distribution is pretty darned close so you can go ahead with nominal spanwise airload and usual integration to get shear, bending moment, and deflections as well as torsion moments, then compute stresses in any given section.
The flexibility of these wings is why so many wings built either of these first two ways are usually built with the forward spar well forward and then they are braced with forward and aft struts or otherwise braced with struts and/or wires. They usually need more support against bending and twisting deflections than they have internally. A structural D-tube helps a bunch too.
Last example is a fully structural covering, whether it is sheet metal, wood, or some composite. Now the wings are much stiffer torsionally, very resistant to torsional moments, and they are employed either with a single strut or in cantilever design. With the single strut, the spar can be lighter than with the cantilever design, but you accept more wetted area in the trade. In these wings, whether strut braced or cantilevered, they are still more structurally efficient (strength is made at lower weight) if the main spar is near the thickest point in the wing. The aft spar becomes pretty thin, serving to tie the skins together and anchor trailing edge devices. In wings of this sort, they are so stiff in torsion that main spar position almost does not matter much to torsional deflection. With laminar flow foils in either metal or wood or composite designs, the maximum thickness is usually around 30% to 40%c and the main spars are usually located there. In many of these the skins forward of the spar are thicker than the skins aft. This may be due to higher airloads forward or due to desire to shift shear center forward or both. Either way, these wings may have their shear center a little aft of 25%c but with nose down pitching moments running opposite to the torsion from slightly aft shear center, there are only small net twisting moments trying to twist a stiff wing, resulting in little torsional twist and allowing the conventional assumptions and calculations to run as good approximations to reality.
As I mentioned above, if you get into long slender wings, structural divergence is more of an issue. In the extreme, helo and gyro main rotors are very long and slender wings. They are designed with placement of shear center relative to the lifting loads and typically use zero pitching moment foils, all because they will twist incredibly if they are not designed to prevent it.
Let the questions begin…
W.J. Fike, in his Practical Lightplane Design book (available from EAA) said the typical 1940’s Cub, Aeronca, Talorcraft types had the front spar at 15% chord and rear spar at 65%. The aileron is usually about 20% chord so another false "fabric" spar is provided at say 80% chord.
A typical ultralight front spar is 0% chord and rear spar around 80% with ailerons hinged on rear spar.
As a first cut at spar sizing, remember that loads are picked up first by the stiffest structure – always. Then look at where you want to, or have to, place the front spar. The preferred location is at maximum thickness of the airfoil section because you can put the deepest spar. The second spar is usually placed just ahead of the ailerons and flaps.
Remember that spars are beams and that a deeper (or taller, if you like) section will have a higher second moment of area, aka, moment of inertia. A spar with a higher moment of inertia is said to be stiffer than one with a lower moment of inertia.
Assume that all the bending loads on the wing are carried by the spars and calculate the total bending moment for the wing. Now apportion that bending moment across both spars based upon the depth of each spar by adding the depth (or height) of each spar together and set that equal to 100%. If the front spar is 8 inches deep and the rear spar is 2 inches deep then 8+2= 10 =100%. Then the front spar can be assumed to carry 80% of the bending moment while the rear spar will carry 20%.
Then design the front spar to carry 80% of the wing bending moment and the rear spar to carry 20%. You are not done with sizing the spars due to other factors such as attach points for fittings, but this will give you conservative estimates that can be further refined.
This is basically correct.
There is no basis for this claim - upon what mathematical or engineering theory do you base this?
It does not take into account about a zillion other factors that affect stiffness, not even withstanding the fact that the stiffness of a cantilever beam is not proportional to its height, but to its height cubed.
Will putting the flying wires of my wings closer to the wing tips help increase torsional stiffness?
Yes. But then you need two or three sets of wires to support the spar tubes all along the span. (like a Quicksilver)
The wing's torsional stiffness stays the same, but you add stiffness at the point where the flying wires or struts attach. The wing will still twist in or twist out in the portion outboard of wires or struts, and the wing will still twist in or twist out between the fuselage and the flying wires. You will have far less deflection at the tips than you would had you no wires, but then, if you are designing with wires, you do not need anywhere near as much bending strength in the inboard part of the wing either.
Big thing is to design, through whatever scheme you are building with, to keep twist small. Cantilever wings usually have very beefy spars and structural skins and so have tiny twist, even with non-optimal spar placements. Externally braced wings need far less bending strength inboard, but the same amount as a cantilever wing outboard of the last bracing. The result is externally braced wings can be much lighter, with simple structures and fabric covering, but you do have to design to avoid unfavorable twist - the spar placements typically chosen do tend to reflect that need.
Get a copy of a Mechanics of Materials book, and go through the beam theory portion of the book. Learn how you calculate shear, then bending, then angle, then deflection. Cantilever wings support pretty large bending loads near the root, much lower loads outboard. Then stick in a constraint at 70% of the semi-span, and pin joint the root end, and you find that the biggest bending moments seen are MUCH smaller.
Once you get your head into beam theory, come back to us with your thinking and confusion, and we can help some more.
An older edition of Hibbeler in PDF. If you need to start with a Statics book there are also older versions of those in PDF as well. Just Google 'Statics engineering PDF' and go from there.
PDF are fine if you can't get a hard copy but there is just nothing like having the pages in front of you and older versions are cheap. There are also some good Youtube video channels. This guy may be worth a few days of you time:
This one looks pretty easy to follow as well:
What are tge things that I can do to shift the shear centre forward?
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