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Bending beam wing structural design

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DaveD

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Net twist forces are tiny compared to vertical and fwd bending. The only catcha is that torsional stiffness (even at a low strength) is still critical.

For a design like yours (or mine), having the wing box carry-through either going intact through the fuselage, or having the fuselage fully operating as a torsion-stiff construction is virtually unavoidable.
That's reassuring, I was just thinking the wing box carry through may have to be the way to go... keep all the torsion in the wing and out of the fuselage.
 

wsimpso1

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Matthew,

It appears that no one has answered your questions...

I do not know of any real world examples myself, but it would work. The reason I would do it another way is because other approaches will be lighter and more rigid too.

This scheme with the spar at about 0.5C means that the beam is at a thinner section than it could have been. Structurally, I like the thickest part of the wing for the spar.

Next, having the pinned connections at the leading and trailing edges means that you have to drive a lot of structure into places where the depth of the wing is small - all of the vertical loads generated by the wings must be funnelled to the pinned joints, while you already must have a significant shear web in the spar. It just adds weight.

The best way is not so hard to scheme out. Main spar at either the 0.25 C (to minimize pitching moments) or 0.375 C (to minimize spar weight) or somewhere in between. Attach the main spar to the fuselage with pin joints plus a drag spar at about 0.75 C that is attached to the fuselage with a pinned joint to react off the pitching moments but no bending. The main spar can be kept to min weight, the drag spar can be pretty darned light until right at the root, almost all of the lifting loads are ine the main spar which is already beefy, and it is simple to setup and rig.

Now that also gives pros and cons, but let's go further.

This setup can be a one piece wing with one or two spars through the fuselage (many aerobats like this) attached with two big pins and two small pins. No bending moments in the fuselage, only lift forces plus reacted bending moments. Jon Staudacher's and Greg Panzl's unlimited aero birds do this. Lighter than everything else, but harder to build (a 29 foot spar and all of that wing to get perfect) and can not be corrected for roll-off by rigging the wings - gotta adjust flaps and/or ailerons differentially to trim out roll. If the bird is to sit on its gear in your shop with the wings off, the gear has to be fuselage mounted.

You can do the wing in two pieces with the main spars overlapping each other, and still attached with only two beefy pins (each spearing both spars and mounts in the fuselage). The drag spars terminate in a beefy hardpoint at the fuselage with two small pins. This is used in a lot of sailplanes, Lancair's four seat airplanes, and others. Easier to build one wing at a time, but a little heavier. Because you are building one wing at a time, your various fixtures can be used for both, ensuring that they be as identical as you can make them. If the bird is to sit on its gear in your shop with the wings off, the gear has to be fuselage mounted.

You can do a three piece wing with a center section that extends beyond the fuselage, landing gear in the center section, and outer panels with main spars that overlap the center section main spar. A little heavier, but it simplifies ground transport and landing gear arrangements. This does drive a substantial drag spar in the center section to carry loads from outer panel pitching moments to the fuselage, but a tricycle gear will need that drag spar for anchoring anyway, and adds structure to the cockpit area. This is the Lancair two seaters, the Long EZ/Cozy/Speed Canard/Velocity, and the Defiant.

Now if this does not drive some questions...

Billski
 

cluttonfred

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Thanks, Billski, for the thoughtful response.

On the pin locations I took Raymer's sketch to be a schematic only to illustrate the bending beam bit and not an intentional location for the spars. I think I would want to make my actual design a generous box spar with pin joints between spar and longeron each side, maybe just one long pin left and right, and either one joint along the centerline or overlapping half spars as you describe. The centerline joint would be heavier but easier as the box spars could simply continue to the centerline to be joined by top and bottom fittings and a single vertical pin. Depending on the airfoil, with a 3' wing chord I should be able to fit a box spar about 6" high and 9" deep in a thick (18%) airfoil located about 20%-45% chord.

I am definitely looking at a two- or three-piece wing as one of my basic design principles is the ability to build and, ideally, store the aircraft in a small space--I am using a 20' ISO shipping container as the basic definition of that space. Even without proper folding wings, the arrangement I described above would allow the wings to come off in two pieces by removing two hinge pins, left and right, one centerline pin in the bending beam, and, say, two "pip" pins connecting the ailerons. With a mid- or shoulder-wing design and the wing simply sitting on the top longerons, everything would easy to access and inspect.
 
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autoreply

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You can do a three piece wing with a center section that extends beyond the fuselage, landing gear in the center section, and outer panels with main spars that overlap the center section main spar. A little heavier, but it simplifies ground transport and landing gear arrangements. This does drive a substantial drag spar in the center section to carry loads from outer panel pitching moments to the fuselage, but a tricycle gear will need that drag spar for anchoring anyway, and adds structure to the cockpit area. This is the Lancair two seaters, the Long EZ/Cozy/Speed Canard/Velocity, and the Defiant.

Now if this does not drive some questions...

Billski
Interestingly enough, once you move to proper (higher) aspect ratio's, 3-piece gets lighter as 2-piece. I think the Mü31 saves 15-20% in wing weight by going 3-piece over a traditional 2-piece wing. No of control connections gets halved, save for the number of load paths.
 

DaveD

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You can do a three piece wing with a center section that extends beyond the fuselage, landing gear in the center section, and outer panels with main spars that overlap the center section main spar. A little heavier, but it simplifies ground transport and landing gear arrangements. This does drive a substantial drag spar in the center section to carry loads from outer panel pitching moments to the fuselage, but a tricycle gear will need that drag spar for anchoring anyway, and adds structure to the cockpit area. This is the Lancair two seaters, the Long EZ/Cozy/Speed Canard/Velocity, and the Defiant.

Now if this does not drive some questions...
Sure will!!!

Why does a three piece wing drive a bigger drag spar in the center section? Obviously there will be torsion loads due to pitching moments, but they shouldn't be any different in magnitude for a three piece, two piece or even single piece wing...
Is the drag spar requirement due to a different structural configuration in the outer and inner panels, say 'D' cell in the outer transferring to a torsion box in the inner?
I suspectl I may be missing somthing, and that always worries me!!!
 

cheapracer

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You can do the wing in two pieces with the main spars overlapping each other, and still attached with only two beefy pins (each spearing both spars and mounts in the fuselage). The drag spars terminate in a beefy hardpoint at the fuselage with two small pins.
Ashley, I have an example .....
 

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wsimpso1

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OK several things to comment on and a couple questions to answer.

The OP showed us a sketch of a wing structure where the lift and pitching moments are carried between wing and fuselage at pinned joints away from the spar, and the spar carries bending moment only. BoKu pointed out that Van’s airplanes both pin the spars together and pin to the fuselage with the same pins. +1 on BuKu. We need to understand the difference between the two schemes in order to discuss them. The OP carries all lift plus pitching moments and rolling moments between fuselage and wing through pins near the leading and trailing edges. The alternate scheme pins the main spars to the fuselage, carrying lift and rolling moments, while pitching moments are carried through a drag spar fitting.

Next, the wing attach scheme Cheapracer shared (page 1 of this thread, post #9) is scary. Let’s describe it in words and then talk about the issues. It uses a vertical bolt at the root and a vertical bolt at the airplanes buttline. Loads in a system where the beam is solid across the airplane are easy. Fuselage mass times the g’s it is under produces load in shear of the beam and is reacted through the brackets. The bending moments produced by the wing making lift over its length will be carried in the beam between the root brackets. The beam inside the fuselage will have moment but no external shear (but the web will see internal loads that make shear).

Let’s start by assuming that the root mounts will stay together and will move elastically, and look at the centerline bolted joint. What is it doing? If the airplane is carrying lift but no roll moments, both wings are pulling and the inner ends will move the same amount up and down. Now deflect an aileron or encounter turbulence. The wings make different amounts of lift , and the ends will slide vertically relative to each other. Now what else is going on? Well, the net wing root bending moment also has to be carried either through the middle of this beam or by the root fittings or both. Quite frankly, you will not carry the wing bending moments at the root and through the fuselage. That centerline joint would be carrying big moments, and the brackets and bolts would have to be big indeed. A simple bracket and single bolt? Nope. Maybe a beefy joint with many bolts or a knuckle joint on top and bottom with a pair of bolts in multiple shear.

Now let’s consider the fuselage wall. The hardpoint at the fuselage wall or longeron would have to do one of two things – be torqued enough to produce clamp loads high enough to prevent joint slip OR have large enough clearance and allow the joint to slip.

With the tight system, the spar bending will deflect the fuselage walls with the spar. Bolts will have to be large enough and torqued highly enough to make clamp loads high enough to produce enough friction to bend the walls. So to size the bolts, you would start with the bending angle change of the spar, bending stiffness of fuselage walls to compute the friction force, then the clamp load is the friction force times the coefficient of friction, then the clamp load works back to bolt size and torque necessary. And the spar has to stand that clamp load as compression of the shear web. Certainly doable, but the system would have to be pretty beefy and heavy. Repeat after me “weight is the enemy”.

With a loose system, the spars slide on the brackets, the system requires no torque, no real clamp load, and things slip under load. So they would have to stand the sliding without being damaged, much less galling and sticking, which will both precipitate failure of the parts sliding and raise loads in the fuselage walls. Again doable but big and heavy. An additional issue is that if the spar movement exceeds the clearance between the bolt and brackets, the bolts will see shear equal to the bending moment divided by the spar depth. To resist that would require some pretty massive bolts and brackets.

This all seems pretty heavy and complicated to build compared to just making the main spars run a couple more feet and put a single pin joint in longitudinally at each root. No bending moments in the mounts, just the lifting loads. All bending in the beams, which are designed for that at pretty low weight.

Once you attach the main spars to each other with a pair of longitudinal pins, you can do one of two easy things:

Also run those pins through root fittings, then react pitching moments by connecting the drag spar to the fuselage with a hard point and a single pin on each side.

React lift and pitching moments to the fuselage with hardpoints and simple joints at the drag spar and leading spar, while letting the beam float.

The reason I feel that the latter of these two schemes is heavier is because lift has to find its way to the fittings and then be carried there instead of through the main spar and its fittings. Little needs to be added to the main spars to carry this load, so we are talking a net weight increase to do the scheme brought up in the OP. Now it does have the advantage of being EASY for airplanes where wing mount/dismount is frequent, but a lot of sailplanes pin the main spars to lift tabs too.

The three piece wing arrangement (look at my build photos) puts a beefy main spar in the fuselage and the wing outer panels overlap with longitudinal pins. My airplane has the middle 96” of wing built to the fuselage. The center section drag spar has to reach 26” beyond the fuselage to where it picks up the reacted pitching moments from the outer panels. This makes bending moments in the spar. The center section drag spar also picks up much of the landing gear loads, and then spreads this to the fuselage. In total, this makes for more joints and more structure, but it allowed me to build in the spars and landing gear, so I accepted the weight delta.

I am curious how a three piece wing can be made lighter than a two piece, as it has more connections, more beam length in total, and reacts loads in more complicated manner, which usually means more weight. When Jarno says it, I believe it, but, I am curious as to how that is achieved.
 
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cheapracer

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hing moments are carried through a drag spar fitting.

Next, the wing attach scheme Cheapracer shared is scary. Let’s describe it in words and then talk about the issues. It uses a vertical bolt at the root and a vertical bolt at the airplanes buttline.
Nope, 100% wrong. I didn't even notice those vertical bolts before you mentioned it, not standard and the owner must have added them for some feeling of security but pretty useless.

The wing securing bolts are horizontal and a single bolt goes through a wing, frame load plate and the other wing on each side. If you look again you will see the horizontal bolts.

This is the setup, and all signed off by an engineer btw ...
 

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wsimpso1

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I was looking at the first page of this thread, post #9, and it has vertical bolts with a spars joined near the centerline. The spars in the photo on post number #28 are a whole 'nother deal.

Billski
 

autoreply

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I am curious how a three piece wing can be made lighter than a two piece, as it has more connections, more beam length in total, and reacts loads in more complicated manner, which usually means more weight. When Jarno says it, I believe it, but, I am curious as to how that is achieved.
It only works when the spar is a significant part of the wing mass. In composite planes that means AR>>20

1/3rd out from the mid plane, local bending moment is only half of root bending moment, so a 1/3rd span midwing and two 1/3rd span tips would have roughly the same weight for the stub spars etc, if we assume that this perfectly scales with local bending moment. Further out is obviously lighter.

Further considerations are simpler controls (one driven flap if you have flaps on the mid wing and ailerons on the outer wings), no need for a complex and heavy "torque connection" (a continuous wing skin is much lighter) and lots of other details like less control connections etc.

This might be a nice render of the earlier mentioned Mü31. Two extra ribs in the mid-wing and that's all you need.


Here some build pictures:
Innenflügel

I have it from a good source for example that the Binder EB29 (EB29 Einsitzer), that has an 8-piece wing (respectively 82, 56, 17 and a few kg) could easily loose an easy 50 kg for both inner panels (164 kg together). In this case panel length (over 10 meters) is prohibitive though:
 

DaveD

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I suspectl I may be missing somthing, and that always worries me!!!
All becomes clear. I was picturing a centre section that was still a bending beam arrangement thus the drag spar was pin jointed a the fuselage sides and therefore didn't carry any bending loads. I should have picked up that you called it a drag spar... A rear member that doesn't carry bending loads is usually just called a shear web, my bad!
 

cheapracer

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I was looking at the first page of this thread, post #9, and it has vertical bolts with a spars joined near the centerline.
9 paragraphs devoted to bagging out a crappy 5 minute Sketchup illustration? WTF?? :roll:

You might have just simply asked for some more detail or opened a line of discussion.
 

Riggerrob

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All vans RV designs, except the 12, use this wing design. A single carry through spar structure with a single fore and aft bolt. The aft bolt keeps the angle of incidence of the wing correct while for fore bolt keeps the LE from rising or falling.
...................................................................................................................................................................................................................................................................................................................................................................................................................................... DeHavilland's Beaver (float plane) is similar in that it has 3 wing spars: front, main and rear. The forward-most spar is in the leading edge. The front spar carries wing pitching loads down to the engine mount via steel tubes. The main spar is in the deepest part of the wing, where it can be strongest and lightest. The rear spar carries aileron and flap loads. Most of the Beaver's cabin are is made of a steel tube roll cage wrapped in sheet aluminum.
Also note that most Cessna float planes are retro-fitted with V-tube that distribute wing loads from the front wing spars to the firewall. Floatplanes take a lot of beating on landing.
 

wsimpso1

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Ok Cheapracer, you put on an illustration, treated it like it was serious and asked for discussion. Being as forums are not about one-on-one discussions, but a public way to disseminate info, and people are on here trying learn what makes sense and what is not as good, I felt that I should point out what was poor about it, why it was poor, and how to do it better. Otherwise, someone reading this might think that the single vertical bolts and centerline joints are an OK idea.

I try not to ridicule, but instead try to respectfully describe things on their merits. Your response was to post photos of a mounting system that is completely different from what was originally posted, and then ridicule me in an attempt at discrediting me. These are the tactics of the bully.

None of us are obligated to help anyone on here, we do it out of generosity. I will choose not to be generous with you. I may not be the only one...

Billski
 

Riggerrob

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If your design has a high wing, just stick with the bending beam. Think of a bending beam the same way you think of the wing center-section in a Boeing airliner. The big Boeings make a huge boxed beam with the wing top skin as the top spar cap, the front and rear spars as the spar webs and the bottom skin as a giant spar cap. A large boxed bending beam is great at absorbing all the torsional, drag and bending loads. A giant boxed beam is the lightest way to build a high aspect-ratio, cantilever wing. The disadvantage is that weight increases dramatically if you try to fold it. Far simpler to build your high-wing with a monolithic bending beam. To fold it into an ISO container, just raise it a few inches and pivot it 90 degrees (ala. V-22 Osprey or Backyard Flyer). With your wing laying parallel with the fuselage, chord becomes insignificant. Unfortunately, then the length of the ISO container limits your wing-span. You can only fit a 19 foot wing-span into an ISO 20 container. Nineteen feet is enough wing for a single-seater. But if you decide to build a 2-seater, then you will need to buy an ISO 40 container. You can pivot and store a 39 foot (monolithic) wing in an ISO 40 container. Thirty-nine feet is more than enough wing for all but the lowest-powered 2-seaters and will gracefully lift most 4-seaters.
 

Riggerrob

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The closer the wing joint is to the center-line, the heavier it has to be. Consider that the bending moments on a wing spar resemble the depth of the cables on a suspension bridge: full depth at the towers, but rapidly tapering to thin halfway across the river. To help you visualise the loads on a wing, try to picture the geometry of a typical strut-braced, high-wing light plane. The triangle formed by the wing, wing-spar and fuselage are a crude approximation of the bending loads on the wing. Notice that few struts extend more than 2/3 of the half-span because bending loads are so light on the outboard third of the wing. IOW, the worst bending loads are on the wing root, ergo wing spars are always thickest and heaviest at their roots. Now let's relate those loads to wing spar joint loads, which are greatest thickness at the center-line and insignificant at the wingtips. Let's start by considering the Scheibe Bergfalke glider. The 1960-vintage BF has wooden wings that meet at the center-line. They have massive steel doubler plates on the wing roots. A single, large-diameter, steel pin is inserted vertically to join the wing halves. The wooden wing roots just lay in "cradles" formed by the steel tubes that make up the fuselage sidewalls. Also remember that any joint has to be built three or four (including a fudge factor for manufacturing tolerances) times stronger than a simple, straight spar. All that steel is heavy. Secondly, we will consider a two-piece wing that overlaps the entire width of the fuselage (24 inches on a single-seater or tandem-seater). Many fibreglass gliders just have small steel pins protruding from the inboard ends of their wing half-spars. Those small pins are strong enough to transmit all of the bending moments to the opposite wing half-spar. Any removable pins only have to prevent the wings from vibrating loose. Even a flexible Kevlar strap could prevent the wings form vibrating loose. Next, we consider the bending loads on airplanes that have a 7 foot wide center-section permanently glued, nailed, bolted, riveted or welded to the fuselage. Seven feet is narrow enough to fit in any trailer, even an ISO container. Seven feet is wide enough to carry most of the fuel tank and undercarriage loads. But a 7 foot center-section also moves the joint out past the worst bending moments, so the joint can be significantly lighter than a center-line joint. Finally, we will look at the wing-fold on a CF-18 fighter plane. No-one expects to trailer a CF-18 after it leaves the factory. So the only width limitation on a CF-18 is the width of elevators on aircraft carriers, so they put the wing-fold mechanism more than half-span out from the fuselage, because that is the lightest place to fold a wing. Am I making sense?
 

Riggerrob

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Also consider that several sailplanes have three-piece wings that allow them to quickly fold and hide in Cessna-sized hangars. Consider the modern Stemme S-10 which has roughly a 15 meter wing span. The Stemme's outer wing panels fold just outboard of quarter-span, so folding them suddenly reduces the wing span to less than the 10 meters needed to fit into a Cessna-sized hangar. The wing-tips almost bump the fuselage when folded. By putting the joint well outboard, it is considerably lighter. Also note that the outer-wing spars insert/overlap into the wing center-section by about a meter, lightening the joint even more.
 

Riggerrob

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Now you are starting to talk about a 3-piece wing like the ICON amphibian. Judging from photos, the ICON has a bending-beam center-section roughly 7 feet wide. The center-section has no leading edge. Since the forward edge of the center-section as at the deepest part of the wing (near 25 percent chord) it can be deep and comparatively light -weight. Since the center-section is skinned with fibreglass (generic term) the front and rear spars and wing skins work together to carry bending, torsional and drag loads to the fuselage. The ICON's center-section is joined to the fuselage permanently at the factory. Meanwhile the outer wing loads are carried by a huge D-spar. The D-spar is made of the main spar and wing-leading edge. Since the D-spar is at about 24 percent mean aerodynamic chord, it is also the deepest possible to carry bending loads gracefully. The D-spar also overlaps the center-section for most of a meter, so most of the loads can be resolved by comparatively small pins. I have not looked closely at an ICON but imagine that 3 or 4 pins could carry all the loads: 1 pin where the leading edge meets the fuselage, 1 or 2 pins at the corner where the inner and outer panels meet (25% MAC) and a 4th pin at the rear spar. Any locking mechanism could be comparatively light since all it has to do is prevent the outer wing panels from vibrating loose.
 

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Ok Cheapracer, you put on an illustration, treated it like it was serious and asked for discussion. Being as forums are not about one-on-one discussions, but a public way to disseminate info, and people are on here trying learn what makes sense and what is not as good, I felt that I should point out what was poor about it, why it was poor, and how to do it better. Otherwise, someone reading this might think that the single vertical bolts and centerline joints are an OK idea.

I try not to ridicule, but instead try to respectfully describe things on their merits. Your response was to post photos of a mounting system that is completely different from what was originally posted, and then ridicule me in an attempt at discrediting me. These are the tactics of the bully.

None of us are obligated to help anyone on here, we do it out of generosity. I will choose not to be generous with you. I may not be the only one...
My feelings exactly. I was also concerned by that sketch of a really bad spar joint. I knew that if I said anything, Cheapracer would attack the messenger, so I didn't bother. Billski was honest, constructive and informative in his response. Cheapracer's earlier comment that Billski was "100% wrong" is ludicrous. Billski was 100% correct, as he usually is when it comes to structures. Belittling Billski's response was bad form.
 
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