Lift Strut and Cabane Strut loads

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Fenix

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The Pietenpol plans call out strut materials that are no longer available. Of course there are materials that have been “shown to work” as substitutes without failing but I don’t know that there has ever been an analysis done of the Piet struts. I am embarking on such an analysis for three reasons. I want to learn how to do this (the biggest reason) and also because it might reveal some answers that are not already well known and lastly because a Piet is on my list of future projects so these answers will eventually be specific relevance to me.

I have been studying truss formulas and I think I understand enough to calculate the load paths through the spars, lift struts and cabane struts but do not fully understand how to handle the two separate spars that are used in wooden wings. So next on the list of things to understand is the chordwise lift distribution of an airfoil which should allow me to know how much lift to assign to each the fwd and aft strut. Note I have recently discovered “Javafoil” (but not yet began to use it) which should help me some on this matter. But I am wondering if there is a “rule of thumb” for the lift distribution on the fwd and aft spar configuration found in wooden wings (at least those that are fabric covered). I know that the lift distribution will change (maybe a lot which will rule out a rule of thumb) with various airfoils and the spars are not always located at the same % chord and the lift distribution changes with angle of attack. I would expect the critical lift distribution would be the one that occurs at high AOA as it is this high G condition that is going to be where things fail. I also expect any “rule of thumb” (if such exists) may be conservative and state , for example, the aft spar generally does not exceed 45% of the total load and the fwd spar generally does not exceed 65% of the total load…. (where the totals exceed 100% - that being the conservative part). Such a conservative rule of thumb would be useful as I am not trying to optimize this design.

So the direct question: How to assign the lift loads to the fwd and aft spars of the pietenpol or of fabric skinned dual spar wings in general. Again I anticipate the lift distribution at high AOA is the relevant distribution to this analysis.

Note: I am going to assume that the total lift is transferred through the lift struts and that none of the lift is acting on the cabanes. It is my understanding that a small amount does actually act on the cabanes, but that most of it acts on the lift struts. I will be conservative and assume it all does. A future project is to learn to determine how much acts on the lift struts and how much on the cabanes…..

I will assume in this case that the weight of the wings do not act on the lift struts (I’m not sure about the center section weight and the fuel in the center sections. It may depend on whether it is a “one piece wing” or “three piece wing”. The conservative approach is to assign that weight to the fuselage for now. Another future project is to understand this though).

Once I understand the load distribution on the fwd and aft spar I can calculate the tension on the lift strut and the compression on the wing spars and the compression on the fuselage members up to the cabanes and the compression in the cabanes as “independent systems” – one being the forward and one being the aft assemblies (or at least that is my current level of understanding). Also the tension across the fuselage between the lift strut attach points on the fuselage can be calculated, but these are of less concern because the material for this can be “per plan” (white ash) unlike the struts which materials are no longer available.

Now to throw in a kink. Mostly just to increase learning, not that I’ve seen Piet’s built this way or intend to. But I also have interest in also a Parasol version of the MiniMax (V-Max specifically) where this understanding will be relevant. The Piet has parallel lift struts that attach to the fuselage in two different locations (that being of course what makes them parallel). If the rear strut were attached at the fuselage at the same point as the fwd strut (as is done on the Minimax line of airplanes) you have what I will call a “V-strut”. It is my expectation (subject to verifying mathematically) that this change in the rear strut will increase the compression on the rear spar because the angle of the strut becomes shallower as it now has “two angles”. One the original angle between the wing spar and the strut at the strut attach point of the wing and also another angle where the aft lift strut is also “swept fwd” and no longer parallel to the rear spar. I’ve not sure about the change in the compression of the rear spar (not yet done the math) but I am confident it will also create a compression load between the rear spar and forward spar where the struts attach to them. The Piet, even with parallel struts, has a compression member at this location but I think it is there due to compression loads created by the drag/anti-drag wires. (These loads are also a future project.)

What I am really unsure about is how this will change the compression loads in the cabanes. As I stated above, with the parallel lift struts I expected the compression loads of the rear lift strut to be reacted by the aft cabane and the forward lift strut to be reacted by the fwd cabane. Changing from parallel struts to a “V-Strut” seems to me that all of the compression loads created by the lift strut assy will be reacted by the forward cabane strut. If the forward cabane takes on a lot more compression in the V-Strut design I have to wonder if the fwd spar also sees an increase in compression…?

If this is true then the fwd cabane strut would have to me much stronger than in the parallel lift strut configuration and the rear cabane strut could be almost non-existent. I suppose the rear cabane may be loaded only in tension of the small amount of lift that exists at the wing root?

While we’re at this point in the “logic” I’ve been wondering about the “net loads” on the cabanes. They are obviously under compression from the lift strut loads but they also are “lifting” a small amount of the fuselage (the part that is not lifted by the lift struts). So it seems they are reacting compression AND tension loads at the same time (which seems weird to me) and the only resolution that makes sense to me is that the small amount of tension created by lifting the fuselage could be subtracted from the compression loads given a net load that is a compression load, but slightly less than it would have been had the cabane not also been doing a bit of lifting. Did I explain that well enough to follow? Is that how it works? If so, in practical application the “lifting tension” loads could be ignored and the cabanes would be conservatively designed to simply handle “all of the compression”.

Finally once all of the strut loads are calculated there must be some reference table that shows the tension and compression (and then to learn more about Euler) strength of common materials, diameters, wall thickness of streamlined and round (for the budget conscious) tubing. Wicks and AS&S have tables that show the weight per foot, but not the strength, of these materials. There are probably lots of these references. Does anyone have a favorite that just makes a good “shop manual”?

My primary goal is to learn about this so please feel free to comment on any of the above. Am I on track at all in the “logic path” or am I not even close? Any “re-direction” or “further explanation” would be appreciated. Also, I have been through a number of “so called beginner” books but even they are hard to follow. Perhaps someone knows of a book that is really geared toward the type of subjects dealt with in my post, and at a beginner level. It seems most of what I’ve read is written for engineers, who don ‘t need to read it because, well, they’re already engineers.
 

wsimpso1

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Fenix,

Best if you do engineering by referring to engineering texts.

First stop is visit your envelope. Va at max g is high angle of attack, so the wing is at higher AOA and thus rotated nose up about 15 degrees. This makes the whole structure stiffer and stronger, so is usually not your worst case, but is worth evaluating. Usually Vd is worst case. Airspeed (and q) is higher, AOA is lower, and we usually computed EI of the wing from chord line.

Next stop is TOWS. No airplane designer should be without it and follow on documents if your foil is not covered in TOWS. Every foil has Cl, Cd, and Cm. They are charted in TOWS and elsewhere as Cl and CM vs AOA and Cd and Cm vs CL. That gives you Cl and Cm. Multiply by q (dynamic pressure) and ds (local wing area) to get local lift and pitching moment (and drag if you want to, but it is small compared to lift and pitching moment). Distribute lift spanwise based upon your personal perspective. Some like uniform for its simplicity, but it exaggerates loads on much of the wing and strut system. I prefer elliptical (because that is how wings work) with the mod to include deflected ailerons. Some folks are philosophers and just have to go Schrenk. Pick one and have at it.

Next stop is the Statics text of your preference. Let's understand that the Lift, Pitching Moment, and Drag computed from these coefficients are based upon 1/4 chord. Why there? Cm does not change much if centered there. So, if you put your forward struts on at .25c, it basically carries the lift, leaving the aft struts to carry the reaction from the pitching moment. Since your forward strut has to go to the spar, and the spar may not be at .25c, you know forces and moments applied at .25c, you will have to compute additional reactions for the shifted point of action.

Next stop is your Mechanics of Materials text and its chapters on beam theory. You have the distributed loads on the wing. From the tips to the lift strut mounts, lift accumulates from the tips to the mount, and moment is the sum of the bits of lift times the distance from them to the point of interest. Numerical integration works well for this. Properly proportioned, the max bending moment between strut and root end mount never gets higher again than at the strut mount point. Every place you have a lift strut or cabane a new big shear gets dropped in on the shear plot which is numerically integrated to get the bending moment and pitching moment plots. Had enough yet?

You are not done yet, but the above has to be done or you do not have loads yet. The bending moment of the wing outboard of the root fittings (cabanes on a bipe or parasol) is basically reacted by the lift struts. If your wing has bending stiffness throughout the span, some bending will be carried between the cabanes and can be subtracted from the moment that the lift struts carry. The bending moment of the whole wing (as modified for the center section) produces a vertical reaction at the lift struts, but being a slender element, it can only carry load along its length, so do some trig to get the actual much higher load in the lift struts. The horizontal component of that force produces compression in the associated spar between lift struts on top of whatever bending loads go in these spars.

Now, we have the information to wrestle with a flexible wing supported by lift struts and cabane struts. Here is the fuss. Is the scheme you selected statically determinate? Back to mechanics of materials book. If yes, then you can work out loads using truss theory. Trouble is the wing is flexible and the lift and cabane struts all deflect under load too. Which changes the loads. Doing this by computing spring rates and deflections and iterating until it settles down might do it. You probably should repeat the load analysis every time you adjust the section on any of the pieces because the relative stiffnesses change, which changes the loads...

Once you have the positive g situation figured out, you get to figure out the negative g situation. Load schemes are similar, just of opposite sense, and now the lift struts are in compression. So they have to not buckle. My favorite is Shigley on this - there is a chapter that includes Euler and Johnson criteria for columns. And that may define the lift struts more than the positive g loads do.

Can you make some simplifying assumptions? If you figure out the stiffnesses to bending deflection from the wing is really low compared to the strut stiffnesses, you might be OK assuming the strut ends do not move and just do the bending moments in the wing with fixed mounts. But if the wing and struts have stiffnesses that are comparable, this assumption might lead you poorly. I have never bothered with these calcs here, so I do not know how valid such assumptions would be.

Anyway, you have a ways to go before handling that. As a closing point, Bernie Pietenpol designed several successful airplanes. He did not have computers or spreadsheets or calculators. I suspect he had a slide rule. Because we do not hear of Bernie's airplanes breaking up, I suspect that the pieces he used were more than stiff enough and strong enough, but we have no idea how overbuilt they were. You could use his parts as basis and then select new again that way. That will likely be heavier still. Or you could do all of the above educating and work to define the loads more finely, then select the lightest section that will work. Or maybe you will find out that checking the failure modes at the fasteners drives you to bigger sections...

If you are good with SolidWorks or other modeling and FEA, you might be tempted to just model each spar and strut as sets or the whole wing and all struts as a unit. Sounds like a lot of work too, but that will really refine the loads at each of the connections.

I personally would be inclined to make the standard substitutions for the cabane struts that have worked fine in Piets and be happy.

Good luck.

Billski
 

Fenix

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Billski thank you for your considerable response.
Yes I could simply make the substitutions that others have made, but then I would not learn anything, which is the point of the inquiry.
OK, so every time I take a peek I am reminded that engineering is not simple, however I still don't think it is time to buy a TV and watch Kardashians. Hundreds of thousands of people have understood it, and a few have had to actually figure it out. While anyone who understands a topic can make it appear infinitely complex, there are a few who understand it to the degree that they can explain it to those who do not yet "know it".
So perhaps I picked a poor "starting point". If I was interested in being able to answer all of the questions I posed in the original post, what would be a good starting point?
Maybe the "first stop"? I understand the concept of "the envelope" and Va at max G but not how this "makes the whole structure stiffer and stronger". I understand Vd and airspeed and q but not "we usually computed EI of the wing from chord line. "

In regard to the "next stop" I don't know TOWS and Google does not return a meaningful response.

I don't expect this to be easy, and I don't have to learn it all this year (though my fuel remaining is far less than my fuel used). I've spent 3o years making planes look like the blueprints and now I'm interested in understanding why the prints look as they do. If I have "jumped into the middle" with the inquiry above I'd be appreciative to anyone who could point me to a more appropriate starting point.
 

Riggerrob

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"Billski thank you for your considerable response. .... Hundreds of thousands of people have understood it, and a few have had to actually figure it out. While anyone who understands a topic can make it appear infinitely complex, there are a few who understand it to the degree that they can explain it to those who do not yet "know it".
... That is the difference between an average professor and a great professor. ...

"So perhaps I picked a poor "starting point". If I was interested in being able to answer all of the questions I posed in the original post, what would be a good starting point? ...."
TOW = Theory of Wing Sections, a classic text book on airfoil design and variables. It mainly covers "classic" NACA airfoils. For more recent airfoils, buy a copy of Harry Riblett's book on airfoils from the Experimental Aircraft Association.
 

Riggerrob

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I am more curious about World War One Fokker parasol wings that are basically cantilever, but supported by 4 struts at the root. The 3 forward struts form a triangular pyramid to support the main spar. Unlike regular cabane struts, they do not meet in the middle, rather, they attach to the main spar about a fuselage width outboard. IOW Fokker cabane struts attach to wings at about 3 times the width of the fuselage. Meanwhile a single rear strut supports the rear spar.
My curiousity is based upon a wing-fold scheme more like the Backyard Flyer, where the entire (cantilever) wing pivots to lay longitudinally parallel to the fuselage ... to allow storage in a trailer about 8 feet wide.
 

Tiger Tim

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Fenix, are you on Facebook? There are a couple of Piet groups on there who would have your answers and enough Air Campers have been built by all types of people over the years that it’s almost a sure thing that the engineering has already been done. Just start asking around.
 

wsimpso1

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Maybe the "first stop"? I understand the concept of "the envelope" and Va at max G but not how this "makes the whole structure stiffer and stronger". I understand Vd and airspeed and q but not "we usually computed EI of the wing from chord line. "
Books mentioned are all in the Design - Technical References Technical references - Books, technical papers, software, etc..

Our frame of reference has lift is in the vertical direction and drag is in the horizontal direction, with positive lift up and positive drag to the right. At Va, the wing is at stall AOA and so is tilted with its chord line around 15-18 degrees up from horizontal. Lift and bending are in the vertical plane.

Beam theory uses I, second area moment of inertia, to describe the resistance to bending of a cross section. I is the sum of the integral of dA*y^2 integral means to sum up, dA means the small areas that make up the whole of the area of the cross section, and y is how far from the neutral axis each tiny area is. Compute dA*y^2 for each small area and add them all up. There are formulas for common shapes. Neutral axis is the centroid of the beam vertically of the beam. The upshot is an area has little effect near the middle of a beam, and a lot more effect if it is farther from the neutral axis. That is why beams are frequently a thin web and two beefy caps.

If you calculate I of the elements resisting bending based upon the wing at zero AOA you will get one number. Rotate the wing to stall AOA and the main and drag spars will be separated vertically, the neutral axis will move up some, and I will get a lot bigger. How to calculate I and how to rotate a section and then calculate I for that case is covered in whatever Mechanics of Materials text your chose to work from.

Bend a beam with lift, and the top of the beam is compression, the bottom in tension. These stresses are sigma = M*y/I, where M is the bending moment, y is the distance from neutral axis, and I is talked about above.

Tilt up to stall AOA at Va, and I gets bigger a lot faster than y does, so stresses are lower at Va than they will be at Vd, with much lower AOA to make limit loads. So we usually do the work at Vd, and we usually skip worrying over AOA for computation of y and I...

In regard to the "next stop" I don't know TOWS and Google does not return a meaningful response.
See the technical references for Theory of Wing Sections, known affectionately as TOWS or Abbott and von Doenhoff. It covers theory of foils and wings, has a catalog of airfoil shapes and wind tunnel data, chapter on high lift devices (you know, flaps and ailerons) and is generally a wealth of information on how foils work. My copy cost $12.

"Welcome to the Monkey House"

Billski
 

Dana

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Billski gave a complete answer, I’ll just try to clarify a couple of points. The relative loads in the front and rear spars (and thus struts) you get, as he said, by resolving the lift and moment through and around the quarter chord point. No, the lift struts don’t handle all the weight, you figure it as a distributed load and resolve it out at the center and strut attach points. If it’s a three piece wing you figure it as pin joints at the wing roots; if it’s a one piece wing it will be statically indeterminate but analyzing it as the same as the three piece is reasonable, if conservative. The distribution of the loads between cabane and wing struts is a function of the spanwise lift distribution. If you assume a rectangular lift distribution it will be conservative for the wing strut loads; if you figure an elliptical distribution it will be reasonable for the cabane strut loads.

In flight, the wing weight isn’t carried by struts at all; the wing supports itself and the struts (cabane and wing) carry the weight of the aircraft less the weight of the wing. Of course, the weight of the wing does have to be figured for landing loads, but that’s probably less than inflight loads at the maximum negative g loading.

V-strut vs. parallel won’t have an appreciable effect on the cabane strut loadings. What a V-strut will do is increase the chordwise compression between the strut attach points on the wing, and increase the spanwise compression in the forward spar while decreasing it in the rear.

Riggerrob already said that TOWS is Theory of Wing Sections, a necessary reference. Bruhn’s Analysis and Design of Flight Vehicle Structures (or the earlier … of Aircraft Structures) is one of the classic texts on aircraft structures and includes tables of strength data for various elements including streamline tubes. But yes, both are written assuming some basic engineering knowledge; they’re generally used as third year engineering texts. Raymer’s Simplified Aircraft Design for Homebuilders is often recommended though I don’t know how far it gets into structural design; I haven’t read it myself.
 

TFF

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Historically the Piet is an old design that has enough charm to be built, as was, today. V strut allowed easier boarding and got rid of the drag/ anti drag wires that all parallel struts seem it need. Getting people in also helped simplify the airplane with just a hair more complexity. Cub style became standard.
The FokkerEV/DVIII forward upper bracing is doing exactly what cross wires between the cabane struts do, which is keeping the struts from paralleling across the fuselage. There was already a wing hard mount that could be tied into, so that makes it easy. Making it wide like that also made a nice unobstructed view to aim the guns.
 

Fenix

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Thank you all for your inputs. All add to the picture. To respond to a variety of points above and hopefully move myself forward:


First of all TOWS = Theory of Wing Sections. Got it! Thanks. I ordered this but was also able to "preview" it online. Yes it looks like a book that much of its content is something I won't understand until a bit later. (3rd year engineering textbook was mentioned above). I also have Raymer's books, both the "full one" and the "for homebuilders" version. But also as mentioned above, structures are not a big part of what Raymer talks about and I have (perhaps poorly) chosen it as my "starting point".

Billski, I think I am following your inputs on relevant angles of attack. I had stated that I thought the most important distribution of loads to the fwd and aft spars (chordwise lift distribution) was the distribution that occurred at high angles of attack because that is where things break. If I understand you correctly you have corrected me in that while hi G loads is where things are likely to fail this need not be high AOA. It need not be Va at near stall AOA but could also be a much lower angle of attack, for example it could be Vd at the AOA that gives Max G (let's say 4.4G in this case). Furthermore you state that the high q and lower AOA is usually a more critical event than Va and approaching a stall. So it seems that I must concern myself not only with distributed loads on the fwd and aft spars at high AOA, but also all the way down to the AOA that produces Max G at Vd. Whereas Va is calculated to be the speed at which 4.4G (for example) is created just before stall AOA I don't expect that Vd is calculated to be the speed at which Max G occurs at 1 degree AOA but rather that it is more a function of q (and likely some other things). So the question this logic would create is how to determine what AOA is going to create Max G at Vd. I suspect this is a complicated answer that involves things like Coefficient of lift and can be better found after TOWS is read and understood. If there is a "rule of thumb" minimum AOA that is considered to be needed to create Max G at Vd then that would be the bottom end of the AOA range at which the lift distribution between the two spars would need considered/analyzed for my current purposes.


My aside into the V-Strut design is because of my interest in converting the Hi Wing MiniMax to a parasol wing. (Yes I have lots of projects – I don’t spend the entire year at one address and need a project at each location). This design already has a V-strut and I don’t see any reason to complicate things by changing that to a parallel strut so, to calculate the cabanes needed I need to be able to work with the V-strut arrangement. I could attempt to just “replace” the “A pillar” and “B pillars” (at least that’s what they’d be called in automobiles) with a metal cabane that had at least as much tension and compression strength as the original “pillars” but these pillars are a build up box of spruce members and plywood. I’m not sure the tension and compression capacity of these members is equal to the simple sum of their parts, and if tables exist for the tension and compression capacity of rather thin plywood. I could just use the cabanes from the Pietenpol, a much heavier plane, either that which is calculated to work or that which has been shown to work in flying airplanes (of course the latter assumes the aircraft in question has actually pulled the rated G’s. Theoretically this was done in Phase 1 flight testing, but I suspect that quite often this never occurs) but I’m not sure that this can be assumed to be a “safe exchange” given the Piet has parallel struts and the Minimax has a V-strut. Dana, thank you for your inputs on this topic, which make sense in most respects but still it “seems like” the front cabane would be more heavily loaded. Of course it doesn’t matter that it “seems like” this if it is in fact not the case, still the quest to understand drives me forward……

Perhaps, as Billski illustrated in his original response, this matter about strut loads is not a good starting point. So let me take a (perhaps) “smaller bite” and focus on lift distribution only. This will also be relevant in my “other project” of wing rib testing which I’ll discuss in a different thread.

Dana, you mentioned elliptical and rectangular lift distribution. I think I know what you are referring to, but maybe this is a good time to be sure I am on track at “square 1”. There is frequent mention of “elliptical wing loading” or “elliptical lift distribution” even in regard to pilot training. I think I now understand what is being referred to, but I was confused (I think) for a long time because of the early descriptions (in classes related to pilots, not engineers – at least in the class I was in) and the frequent reference to the Spitfire with its elliptical wing planform and how it was ideal because elliptical wing loading was the most efficient. For a few decades I thought elliptical wing loading was referring to planform and now I think this was a misunderstood point all along.

Please refer to the attached diagram which is supposed to represent a high wing strut braced aircraft (with a really thick wing apparently). The high wing and strut braced factors don’t really matter. It is now my understanding that the “ellipse” in the matter of elliptical lift distribution, is the ellipse shown by the red lines in B and C. It is not the elliptical planform but the “imaginary” ellipse on a chart showing the lift distribution that is being referred to. Is this correct? Actually it is only half an ellipse (the top half seemingly) and given that the left and right side of the planes will pretty much always be identical (not in Rutan’s Boomerang I suppose) we could really say we are dealing wing only a quarter of an ellipse.

If this is the case then the I would assume that “rectangular lift distribution” would be like that shown in “A” and does not really exist because there is always (except in a few oddball designs like flying donuts and such) less lift at the tips due to spanwise flow, that being which results in wingtip vortices. This being the case “rectangular lift distribution” is not what is found on a “Hershey bar” wing and really is only a theoretical idea that does not exist on any wing design or planform.

Then you have “linear lift distribution” which is shown in D which also probably does not happen in the real world.

Now ellipses are not all the same (as I recall it has to do with the spacing of the foci, among other factors) so you can have more than one lift distribution that would still be called elliptical – say by comparing B to C. It would seem that, due to the flow off the wingtips that most wings would exhibit some shape of an ellipse and things like taper, wingtips, winglets, wing fences, wing twist and so on all work together to create just exactly what shape of ellipse is created by any wing design – and that Schrenk’s approximation is one method by which the “proper ellipse” is determined for a given design.

So, in short, is the above what is being referred to in the commonly appearing phrase “elliptical distribution”? Is it the “imaginary ellipse” indicated by the red lines of B and C?


Returning again to chordwise lift distribution it seems a key point is understanding what is meant by “resolving the lift and moment through and around the quarter chord point.”

I think I need to understand what this phrase means as a starting point. I would appreciate any further explanation given.

Thank you
 

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Dana

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The most used part of TOWS is probably the airfoil data. The graphs are mostly reproduced from earlier NACA reports, but it’s nice to have them all in one place.

Va is simply the slowest speed where you can achieve the limit load factor (4.4g or other value). At higher speeds, that limit load can be achieved at lower and lower angles of attack. Vd is [somewhat] arbitrary; it’s the highest speed planned during testing, and Vne will be less than that.

The front cabanes will be more heavily loaded, but that’s because the center of lift is closer to the front spar, not because of the lift strut configuration. Parallel or V, the rear strut carries the same vertical load, the only difference is that the V-strut will tend to pull the wing forward a bit due to its angle, somewhat reducing the load on any internal drag bracing.

Yes, “elliptical lift distribution” refers to how lift lessens as you move outward, due to tip losses. An elliptical wing planform (aka Spitfire) is a way to reduce induced drag at the expense of stall behavior and building simplicity. A taper wing is a compromise between rectangular and true elliptical wings.

Chordwise lift distribution: The center of lift moves depending on AOA. Rather than having to calculate where it is at different times, it’s converted to assume the lift is always through the quarter chord point, along with a pitching moment. So when the center of lift is aft of the quarter chord point (as it nearly always is), you have a negative (nose down) pitching moment about the c/4 point. That c/4 point is somewhat arbitrary, but it’s chosen because it’s an even fraction and the pitching moment doesn’t change much relative to that point.

So, assuming for the sake of discussion that your front spar is at the quarter chord point (in reality it will almost certainly be farther back), you figure all of the lift acts at that point, and the rear spar only carries a load equal to the pitching moment divided by the distance between the spars. That’s a gross oversimplification but hopefully you get the idea.
 

BJC

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Good info above.

One additional comment about Va for the casual reader; it varies with aircraft weight. When the aircraft is lighter, Va is lower.


BJC
 

Map

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Good inputs from everyone.
When calculating loads, simple and conservative is best. The purpose is to address the worst case that is likely to happen in flight. So it is not that important to get the lift distribution (spanwise and chordwise) exactly right, but make assumptions that are probably a little higher than what may actually happen in flight.
For example an aileron deflection changes the lift distribution, down increases lift on the outboard wing and increases the bending moment on that side. This may act in combination with gust or other maneuvering loads.
Before computers, many designers apparently were very conservative in their loads analysis, so their structures ended up sturdier and heavier than required, but apparently quite durable.
 

Protech Racing

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Folding wing planes with lift struts, swing the wing from the rear mount. And often the V strut is anchored in line with the rear spar. How much load is on the front strut and wing, when pulled rearward to the rear spar anchor?
 

BJC

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One additional comment about Va for the casual reader; it varies with aircraft weight. When the aircraft is lighter, Va is lower.
For the uninformed reader, why?
For the casual reader; someone who may not be familiar with the subject. There are many readers here who are not pilots, but are interested in sport aviation.
It also changes with altitude does it not?
If referenced to CAS, it does not change with altitude.


BJC
 

Fenix

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Chordwise lift distribution: The center of lift moves depending on AOA. Rather than having to calculate where it is at different times, it’s converted to assume the lift is always through the quarter chord point, along with a pitching moment. So when the center of lift is aft of the quarter chord point (as it nearly always is), you have a negative (nose down) pitching moment about the c/4 point. That c/4 point is somewhat arbitrary, but it’s chosen because it’s an even fraction and the pitching moment doesn’t change much relative to that point.

So, assuming for the sake of discussion that your front spar is at the quarter chord point (in reality it will almost certainly be farther back), you figure all of the lift acts at that point, and the rear spar only carries a load equal to the pitching moment divided by the distance between the spars. That’s a gross oversimplification but hopefully you get the idea.
Your input was very helpful Dana. The above referenced quote is "making some lights come on" but I need to think a bit more about it to get a full grasp.

By the "quarter chord" do you mean 25% of the wing chord?
So I get that this is a "tool" to simplify managing the chordwise lift distribution and a gross oversimplification is good at this point. I can refine it once I grasp the basic concept. One thing that confuses me is if the spar actually WERE at the quarter chord and all of the lift forces were seen to act there then the front spar would be loaded with the total lift created by the wing. Then if there were a pitching moment (which would exist if the center of lift were not actually at the quarter chord, which you indicated it probably would not be, so there would be attributed a pitching moment, that this moment would then put some load on the aft spars making the total forces on the spars greater than the total force generated by the wing. I mean if the fwd spar was assumed to carry all of the lift force and the rear spar also had a force on it the sum of the spar loads would not be equal to the total wing force generated. So I'm missing something in my understanding.

Finally, in the quarter chord plus moment method I assume the calculated moment must change with AOA changes to properly reflect the change in lift distribution?
 

Fenix

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When calculating loads, simple and conservative is best. The purpose is to address the worst case that is likely to happen in flight. So it is not that important to get the lift distribution (spanwise and chordwise) exactly right, but make assumptions that are probably a little higher than what may actually happen in flight.
For example an aileron deflection changes the lift distribution, down increases lift on the outboard wing and increases the bending moment on that side. This may act in combination with gust or other maneuvering loads.
Before computers, many designers apparently were very conservative in their loads analysis, so their structures ended up sturdier and heavier than required, but apparently quite durable.
Good point. While I also want to learn to understand the distribution of lift spanwise and chordwise (and I think I almost understand Schrenk now) for the purpose of calculating strut loads I was actually at first thinking I could just assume a likely "worst case" such as that the front spar (of a fabric covered wing) would never exceed, say 80% of the wing lift, and the rear spar would never exceed, say 70%. Of course this is 150% so both would not happen at the same time, but each spar and strut assy must be capable of "taking its turn" at reacting the most extreme load it would see.

I suppose it could be assumed that each spar would never exceed 100% of the total load factor, and basically design the strut system of each spar so that it was capable of handling the entire job of lifting the plane at gross wt and max G. I don't intend any spar changes so it can be assumed they are OK - even though they likely are not engineered to take the "entire load". I would end up with struts that were capable of handling much more load than they would actually see (engineering each to carry the full load by itself when (I assume) this extreme case could never be achieved in the flight envelope). So if the struts are even twice the strength they need to be, that is a few pounds (which is of course not ideal but acceptable) added to the plane. Having the struts capable of 200% their loads is better than having them at 90% of the intended load for sure! Also, with no math at all and just "doing it blind" or "by eyeball" the tendency would likely be to "add plenty" to the struts and perhaps have them unknowingly capable of 500% or even 1,000% of what they need to be. This is pretty crummy/crude. So I think there is some value of just doing the math for each strut system to assume its spar is carrying the full force of the wing. Perhaps it is commonly known that 100% is way too conservative because it may be known (to those that know such things) that exceeding, for example, 75% of the total force on any one spar is the most that will ever really occur. If there is such a number less conservative than 100% yet still "known to be safe" I'd be interested in such inputs. I also expect that the "worst case" percentage for the fwd spar is not the same as the assumed "worst case percentage" of the aft spar.

Caveat: Above Billski stated, as best I understand it, that the total loads on lift struts are not equal to the total lift generated by the wing because they also react bending loads on the spars. If this is the case, then my logic above will not assure that the struts are adequate. Is this matter of "bending loads" on the spar being reacted by the struts something that also needs to be understood before this analysis can proceed?
 

Fenix

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In the furtherance of understanding spanwise distribution analysis I tried to work out some Schrenk approximations on the Pietenpol and MiniMax wings per the attached document I found on Schrenk approximations. It probably comes as no surprise that there was little difference between the two as they have similar aspect ratios and are both rectangular planforms. Is the Schrenk analysis usually even applied to rectangular wings or it it really just intended for tapered and/or elliptical wings?

I'm not exactly sure what the diagrams mean, but maybe someone can comment on them or let me know if they appear to have obvious errors.

Since I am also building a custom taper wing for my RV-4 I did Schrenk diagrams on them also. They are also attached FWIW.
 

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Dana

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By the "quarter chord" do you mean 25% of the wing chord?
So I get that this is a "tool" to simplify managing the chordwise lift distribution and a gross oversimplification is good at this point. I can refine it once I grasp the basic concept. One thing that confuses me is if the spar actually WERE at the quarter chord and all of the lift forces were seen to act there then the front spar would be loaded with the total lift created by the wing. Then if there were a pitching moment (which would exist if the center of lift were not actually at the quarter chord, which you indicated it probably would not be, so there would be attributed a pitching moment, that this moment would then put some load on the aft spars making the total forces on the spars greater than the total force generated by the wing. I mean if the fwd spar was assumed to carry all of the lift force and the rear spar also had a force on it the sum of the spar loads would not be equal to the total wing force generated. So I'm missing something in my understanding.
Yes, "quarter chord" is 25% of the wing chord.

A "moment" is also called a "couple". Think of it as two equal but opposite forces some distance apart. The sum force in any direction is zero, but the twisting force still exists.

So, for example, assume a wing with two spars, one at the quarter chord point and one three feet farther back. Let's say the actual wing lift (Cl * q * wing area) is 100#, and that the center of lift is one foot behind the front spar. You now have a negative pitching moment of 100 ft-lb, which works out to 33.33# on the rear spar (100 ft-lb divided by 3 ft). That 33.33# is subtracted from the 100# on the front spar, so the front spar carries 66.67#.

A force at any point is equivalent to an equal force at any other point plus a moment around that other point. If there is no acceleration, the vector sum of all forces and moments is zero.

This is covered in "statics", a first or second year engineering class (before you get into aerodynamics and structures).
 

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