# Lift Strut and Cabane Strut loads

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#### wsimpso1

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Now I see I made an "error in logic" in the above referenced description.
The above statement: "The connection of the lift strut at the fuselage will also create a compression force upward between the strut attach to the fuse and the wing root fitting" is not correct. This upward acting force on the fuselage bracket where the lift strut attaches does NOT create a compression load between this bracket and the wing spar root to cabane bracket above it. Instead, this upward force on the bracket is reacted by GRAVITY. Duhhh.... This is (in part) where the fuselage is lifted from. This must have been "cringe worthy" to the readers who recognized this error.
Hmm. Let's just lay out a 2D expansion of this case:

If the airplane is flying at some steady speed, g, etc, the fuselage weight times the load factor is carried to the wings. The fuselage pushes down on whatever fittings it has to connect to the wings, and the wings lift up. In the vertical direction, the sum of these forces is zero;

Then the airplane is flying straight ahead and not rotating in the axes, net loads in the lateral direction is zero. This means the loads are symmetric, left and right, and that the detail loads at each wing mount and strut mount are also symmetric. That does NOT define lateral loads;

What do we know? If we sum moments about the wing root mount from lift, we get a moment about that spot. Since we prevent the wing from rotating about the root fittings with a strut, we can compute loads where the strut hangs on the wing. Take the moment we just calculated above and divide by the straight line distance between root fitting and strut connection to the wing, and we have the force perpendicular to the line between root and strut connection. If you have dihedral you may have to divide by the cosine of the dihedral angle to get the true vertical force there;

Since the strut is at some known angle from vertical and the strut is generally flexible enough that it is modelled as pin jointed at both ends, we can assume that the strut carries all load along its long axis. The load vertical and the load horizontal are in proportion to the angle of the strut. Tangent of the strut angle from vertical gives us the proportion;

At the strut mount on the wing, we have a given downward force (that keeps the wing from rotating upward) and a horizontal force that is usually bigger than the vertical pulling the wing towards the root. At the other end of the strut we have forces of same magnitude but opposite direction;

The horizontal force from having the angled strut is resisted at the root fitting, and the spar between strut and root is thus in compression;

Last up is that unless the wing lift and weight balance on the strut mount of the wing, there will be net rotating moments about the strut mount on the wing. This moment can be calculated by summing moments from lift and from distributed weight of the wing times load factor about the strut mount. Understand that much but not all will cancel. Then divide by the distance from strut mount to root fitting, and that is vertical reaction at the root fitting.

You can check your work by checking that the sum of vertical forces at the root fittings is equal to lift created by the wing. You can also check that the moment about the root fitting from lift and from horizontal forces at root fitting and fuselage strut mount cancel.

Once you have the 2D loads straight and working and know the strut tension for a case, you can displace the strut fitting forward or aft, view it all from above, compute the angle from lateral, divide the strut load by the cosine of that angle and get the linear force in the strut. By viewing it all from above, you can also use trig to get the forces in the fore-aft direction at both ends of the strut and into the wing and fuselage.

I shall look at the rest of the post during my next break from making parts. I have a piece of acrylic that has been preheated to 240F for 22 hours to drive off moisture. Now I get to warm that piece of acrylic to 360F and see if it will vacuum stretch form over a buck. Wish me luck.

Billski

#### Pops

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In forming acrylic, I have never had any success, but I didn't do it in a full moon. Sort of like designing a prop.

#### wsimpso1

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Billksi, you said: The forces in those three directions sums through vector addition to equal the force in the strut. Fx^2 + Fy^2 + Fz^2 = Ftotal^2

I was not aware of this "formula" but it makes sense. It is, of course, a great tool for checking your conclusions. And so far my new conclusions are consistent with this "test".

Yes, as you've explained above, I had several things wrong with my understanding when I began this.
Well, you do know that for a right triangle with sides a and b perpendicular to each other, a^2 + b^2 = c^2 right? That is in plane geometry, you know, 2-D. More general case is 3-D and then you have what you cited above. It still works. The proportions Fx/Ftotal, Fy/Ftotal, and Fz/Ftotal are called the direction cosines of the force at some 3-D angle. If the strut is able to carry significant moments and react them at the ends, all of this breaks down, but for pin mounted struts and cables, it means loads and directions are all related by the angles...

#### wsimpso1

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I may still have this wrong but this describes the new current state of my understanding on this matter. The attached spreadsheet (with multiple tabs at the bottom) shows the progression of this understanding and what I believe to be the forces on the cabanes and lift struts, which was the point of this inquiry from the start. So I guess, in simple cases, I have arrived at that goal - unless I still have some things wrong.
Looked it over. Made a couple minor revisions, marked with yellow background, attached. You accumulated the raw bending moment calcs from the root, they accumulate from the tip.

The one that bugs me is that to make it a decent exercise, you made it unrealistic. If the span is 348", make it 348". If the center 24" is separate, so be it, do the analysis for the 348" wing, and run the sums from BL174" to BL12", calculate the lifts to where the cabanes pick up the outer panel... It will work fine. Lift from the center section can be run and put in seperately.

The next steps would be:
• To do the angled cabane struts, which is the vertical parallel strut loads corrected for angle;
• To include the down load in each spar from the strut on each, The shear diagram will have a step change there, and then you accumulate bending anew from the revised shear diagram.
Billski

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#### Fenix

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In forming acrylic, I have never had any success, but I didn't do it in a full moon. Sort of like designing a prop.
I had to vacuum form a "plastic" lens cover for my landing light in the wingtip I made for a tapered RV-4 wing. I knew nothing about such when I started and tried several things. (Learned a lot along the way. At the time I did not know of HBA to ask questions, would have saved me a lot of trials....) Finally I got a serviceable cover. I think the final product was "PET-G" IIRC. Lexan did not work out well. Also I found the mold had to be soooooo smooth for clear lenses. Like coats of fiberglass resin wetsanded with 1000 grit and then polished. I never did try it under a full moon - maybe that is what I was missing.....

Anyway, the point of this thread drift is how beneficial HBA is as a place to share information among those of us who mess with planes!

#### Fenix

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Well, you do know that for a right triangle with sides a and b perpendicular to each other, a^2 + b^2 = c^2 right? That is in plane geometry, you know, 2-D. More general case is 3-D and then you have what you cited above. It still works. The proportions Fx/Ftotal, Fy/Ftotal, and Fz/Ftotal are called the direction cosines of the force at some 3-D angle. If the strut is able to carry significant moments and react them at the ends, all of this breaks down, but for pin mounted struts and cables, it means loads and directions are all related by the angles...
Yeah I knew A sq plus B sq equals C sq and the "handy" 3,4,5 triangle. That is how I sorted out the "formulas" for the struts. Then I discovered youtube videos on trusses...... Mine worked but were not the "convention". For example I was multiplying by the cosecant when others divide by the sin. But it is the route my "logic path" took me to arrive at a formula that made sense.
The fact that x squared plus y squared plus z squared equals force squared (or something like that) was not in my Trig class (that I can recall). I guess that is probably in the first chapter of "statics" (another new term this month). I have found a "statics course" online which I plan to run through, but right now I feel I am gaining traction on these struts (thank you contributors for your help) so the course will have to wait a bit - until I get stumped.

#### wsimpso1

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For example I was multiplying by the cosecant when others divide by the sin. But it is the route my "logic path" took me to arrive at a formula that made sense.
Secant IS 1/Cosine, Cosecant IS 1/Sine. The only reasons to have Secant and Cosecant in my mind is that before computers and calculators, we had trig tables and sliderules, and already having the sine or cosine inverted simplified things a bit.

The fact that x squared plus y squared plus z squared equals force squared (or something like that) was not in my Trig class (that I can recall).
High school Trig is generally taught in 2-D, as is most of high school Geometry. You have moved on to 3D when you start talking about cabane struts that are neither parallel or vertical, lift struts with lower mounts slid forward or aft, and wings with dihedral.

I guess that is probably in the first chapter of "statics" (another new term this month). I have found a "statics course" online which I plan to run through, but right now I feel I am gaining traction on these struts (thank you contributors for your help) so the course will have to wait a bit - until I get stumped.
When you get into statics, they will show you how to apply forces that are equivalent to moments and vice versa, and then get into directions defined by direction cosines, forces applied in directions, and then forces times distances, all in a general sense. It all seems kind of cumbersome until you internalize that the easy way you had looked at it before is the special cases of having forces and distances perpendicular to each other. So then, you will start looking for ways to apply all of this using forces perpendicular or parallel to arm lengths so you can do it more inuitively. Then when you have no choice, you can go cross products... You may not know what I am saying now, but you will.

Billski

#### Pops

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Billski-- Your post are so good and you are a very good teacher, have you ever thought about writing a book ? I know there are a lot of good books but you do a good job of teaching. Not everyone with knowledge are good at teaching that knowledge.
And Thank You for all the time and effort of putting your post on this site.

Dan R.

#### Fenix

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Looked it over. Made a couple minor revisions, marked with yellow background, attached. You accumulated the raw bending moment calcs from the root, they accumulate from the tip.

The one that bugs me is that to make it a decent exercise, you made it unrealistic. If the span is 348", make it 348". If the center 24" is separate, so be it, do the analysis for the 348" wing, and run the sums from BL174" to BL12", calculate the lifts to where the cabanes pick up the outer panel... It will work fine. Lift from the center section can be run and put in seperately.

The next steps would be:
• To do the angled cabane struts, which is the vertical parallel strut loads corrected for angle;
• To include the down load in each spar from the strut on each, The shear diagram will have a step change there, and then you accumulate bending anew from the revised shear diagram.
Billski
I made the noted changes to the document and added the page for my analysis of the V Strut. After wrestling with it a long time a sort of simplicity of understanding finally came to me and suddenly it became much shorter than it had been. It is attached here for review and criticism from any who are so inclined. Also attached are some diagrams that make it easier to follow the Excel sheet.

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#### Fenix

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For the interest of those following along or that may come along later to try to use this thread for learning:

In the last post I attached a spreadsheet showing the forces I arrived at on the lift struts and cabane struts in a parallel strut and V-strut configuration. In regard to the V-strut configuration I had not yet connected the load path from the two ends of the rear strut which runs from the fuselage strut attach fitting up and aft to the rear spar. This is where I pick up:

In thinking about it I (perhaps incorrectly) surmised that the wing with this forward pulling force from the angled rear strut must exert the same forces on the fuselage (or wing center section) regardless of how it was internally constructed, or if it were chiseled from a single chunk of aluminum, carbon, or granite. The forward load on the wing, parallel to the aircrafts longitudinal axis, had to transfer to the wing root and then the center section as a force in the same direction of the same magnitude. I then considered that the wing, being “pulled forward” at its midpoint would act in a “moment coupled” manner and put tension on the aft spar carry through and compression on the fwd one. Taking the distance from the wing root upon which the rear lift strut was acting and the spacing between the spars I easily computed the equal and opposite loads that would be transferred to the center section spars.

That left the matter of how these loads are actually transferred through the wing itself, which depends on wing design. The simplest load path I considered was a compression member from the rear lift strut at the rear spar to the forward spar, and then a tension cable (part of the drag truss presumably) from the front spar strut attach inboard and aft to the rear spar root fitting. Calculating the tension on this cable and the compression loads it would put in the forward spar these loads all matched the loads imposed on the center section under the “billet aluminum (or granite or carbon) model and also “obeyed” the “sum of the square of forces” rule. I then considered a diagonal member of the drag/anti drag truss that did not go from the rear spar root to the front spar strut attach but rather to a point on the front spar well inboard than the lift strut attach fitting. This meant that a bending load would be imposed on the front spar (that the D-tube leading edge would have to withstand) and then deliver this load to the diagonal member which joined the fwd spar to the aft spar root fitting. This resulted in forward loads that were greater than those imposed when the tension cable ran from the fwd spar lift strut fitting back to the rear spar root fitting, but most of these were reacted by aft forces of the front spar rotating around the point at which it engaged the diagonal member, leaving the net fwd acting force the same as that created by the aft lift strut in the first place. So I conclude that the forces I am calculating that go into the center section are correct and these are what I need for the current strut (cabane in this case) analysis. The loads inside the wing will be a part of the drag/anti drag truss analysis later.

So I was thinking in another 30 minutes I would resolve the loads from the aft spar root fitting down to the fwd (and only in the V strut design) fuselage strut attach fitting. It did not work out that way….

I began with a compression member transferring the loads from the aft spar root fitting fwd to the front spar. Consideration must, at some point, be given to transferring the load from the inboard portion of the wing to the outboard rib of the center section. But in the end result I placed the fwd acting load in the outboard surface of the center section pushing fwd on the front spar. From here I considered transferring them forward with a compression strut to the top longeron at the firewall (and then back down and aft to the lift strut fitting. I also considered the other method common in the PIetenpol (and other aircraft) of reacting this fwd load with a tension cable running from the front cabane at the wing down and aft to the rear cabane at the top longeron, and then down and forward through the fuselage to the lift strut attach fitting.

In either method I was confused by the discovery of a “rotational force” which I guess is to be expected when the aft lift strut pulls forward “up high” and backwards “down low”. Attached are some drawings of working through this. My “conclusion” (subject to error) is that this “rotational moment” does not actually impose any loads in the cabanes or struts because they are not reacted. These forces just try to rotate the fuselage pitch down (I guess to be expected when the fuse is lifted from a point fwd and aft of the CG in the parallel struts and is changed to being lifted by a single strut attachment forward of the CG) and are reacted by the empennage down force. I suspect a “visceral understanding” of what is taking place will come about in analyzing the beam that is the fuselage.

My question would be is my diagram correct that the only relevant loads for the cabanes and struts or cables limited to the compression of the forward diagonal strut that runs down to the top longeron at the firewall or the tension in the cable that runs from the top of the front cabane to the bottom of the aft cabane? From there of course there are relevant loads but these are in the side of the fuselage where any member placed to deal with these loads also supported by the fuselage plywood skin.

Secondly what would be the considerations if both methods were used? I mean if both the diagonal compression strut down and forward were used and also the tension cable down and aft? My thought is that “technically” each would share half the load and thus the forces in each would be half of those if only one or the other structure were used. My other thought is that this likely introduces a “common rule” in design about multiple load paths when consideration must be given to conditions such as the rigging tension or material stiffness of one load path might be greater or lesser than the other and thus find itself absorbing all of the load until it deforms enough to allow the “other structure” to begin assisting with the loads. By time this occurs the first member to take the load my already have failed and thus in cases of multiple load paths either path must be designed to take all (or at least most) of the load on its own. Or something like that……..

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#### Fenix

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In the attached document I have attempted to correct the situation Billski pointed out where I had "artificially eliminated" the center section from the wing span calculations. In the attached I believe I have made the formula more realistic and then, as suggested, considered the effects of tilting the cabane strut outward as is also done to make a wider center section (and thus a larger fuel tank within). The attached diagram calculates the loads created by the tilting of the cabane.

Again, any corrections or comments are appreciated. Especially the corrections!

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#### wsimpso1

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I began with a compression member transferring the loads from the aft spar root fitting fwd to the front spar. Consideration must, at some point, be given to transferring the load from the inboard portion of the wing to the outboard rib of the center section. But in the end result I placed the fwd acting load in the outboard surface of the center section pushing fwd on the front spar. From here I considered transferring them forward with a compression strut to the top longeron at the firewall (and then back down and aft to the lift strut fitting. I also considered the other method common in the PIetenpol (and other aircraft) of reacting this fwd load with a tension cable running from the front cabane at the wing down and aft to the rear cabane at the top longeron, and then down and forward through the fuselage to the lift strut attach fitting.

In either method I was confused by the discovery of a “rotational force” which I guess is to be expected when the aft lift strut pulls forward “up high” and backwards “down low”. Attached are some drawings of working through this. My “conclusion” (subject to error) is that this “rotational moment” does not actually impose any loads in the cabanes or struts because they are not reacted. These forces just try to rotate the fuselage pitch down (I guess to be expected when the fuse is lifted from a point fwd and aft of the CG in the parallel struts and is changed to being lifted by a single strut attachment forward of the CG) and are reacted by the empennage down force. I suspect a “visceral understanding” of what is taking place will come about in analyzing the beam that is the fuselage.
First, I have not done this particular system before this thread came along, but I am trained and experienced at general structures and know what wings can do for making loads. So let's get down to it.

You seem to be getting all wrapped around the axle on this. Allow me to simplify it a little for you.
• The wing of a fabric covered parasol is usually three pieces attached to each other by four hinges with axes parallel to the long axis of the airplane.
• Each of these three pieces is pretty flexible in torsion and the hinges can carry a lot of load in all three translation axes, but can not carry any moment in the roll axis.
• The cabane struts can be visualized as simple vertical rods fixing the hinge positions between center section and outer panels. The lift struts fix spots outboard on the spars. Depending upon how far outboard the lift struts connect to the spars, the load at the cabane end of the other panels might be up or down. The load at the cabanes from the center section will be lift. Sum the forces from outer and center sections to get total vertical loads on cabanes.
• A consequence of the lift struts not being vertical (no place to anchor them) is that there is a big compression load in each spar between the lift struts.
• Pitching moment gets reacted along with simple lift loads.
• Now we have drag load and it evil cousin, anti-drag, which is forward component of lift, most visible at high alpha. We have to keep the wings from flopping fore and aft. This is usually done by some combination of angling the cabanes, cross bracing the cabanes, angling the lift struts. Drag and anti-drag show up in these pieces.
• Vertical loads in angled (non-vertical, non-horizontal) elements are increased - divide by cosine of angle from vertical converts vertical load to strut load. Similar approaches work on other loads.
• If a load is only tensile, you can use wires, but since negative g and landing loads are real, wires usually have to be used in pairs. Wires are tensioned until no slack exists and can impose bigger loads on surrounding restraining elements than base loads. The loads in each element then becomes the static loads from the wires being tightened PLUS the live loads calculated from flight.
• Where a set of cabanes is either wire braced or diagonally braced with other struts, you may turn it from a set of slender columns into a solid chunk. Now you might model the cabane set as that solid chunk with four connections above and four more below...
My question would be is my diagram correct that the only relevant loads for the cabanes and struts or cables limited to the compression of the forward diagonal strut that runs down to the top longeron at the firewall or the tension in the cable that runs from the top of the front cabane to the bottom of the aft cabane? From there of course there are relevant loads but these are in the side of the fuselage where any member placed to deal with these loads also supported by the fuselage plywood skin.
Four vertical cabane struts will wobble left-right, fore-aft, and twist without other elements. Yes a diagonal member like you put in forward will stabilize it - the wire will keep it from wiggling. Both the diagonal strut and cross bracing will stabilize it against fore and aft loads. You may want to put in a diagonal element from side-to-side too.

Secondly what would be the considerations if both methods were used? I mean if both the diagonal compression strut down and forward were used and also the tension cable down and aft? My thought is that “technically” each would share half the load and thus the forces in each would be half of those if only one or the other structure were used. My other thought is that this likely introduces a “common rule” in design about multiple load paths when consideration must be given to conditions such as the rigging tension or material stiffness of one load path might be greater or lesser than the other and thus find itself absorbing all of the load until it deforms enough to allow the “other structure” to begin assisting with the loads. By time this occurs the first member to take the load my already have failed and thus in cases of multiple load paths either path must be designed to take all (or at least most) of the load on its own. Or something like that……..

Doing this in a way that does not tangle you up requires some bookkeeping. I like Excel, with a line for every element, whether it is streamline tubes, wing inputs, top longerons, or wires. Each gets its ends coordinates input, direction, force imposed from each source, and some relationship to the others. Complicated, but remember they did all of this with sliderules back in the Golden Age of Flight.

Welcome to the Monkey House.

Billski

#### BJC

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Bill:

I second the suggestion someone else made: a compilation of your explanations all in one place would be a very good primer for people interested in understanding airplane (or other) design.

BJC

#### Pops

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Talking about sliderules and the Golden Age of Flight. One of my favorite books that was given to me from my old flight instructor from 1937 is Aircraft Structures by Niles and Newell published in 1929. Niles-- Stanford University professor. Newell-- MIT professor & Department of Commerce. A general overview. 4130 is still 4130 and wood is still wood.

#### bifft

##### Well-Known Member
One of my favorite books that was given to me from my old flight instructor from 1937 is Aircraft Structures by Niles and Newell published in 1929.
I found a 1944 edition of this in a used bookstore and can also recommend. Very easy to follow.

#### Fenix

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You seem to be getting all wrapped around the axle on this. Allow me to simplify it a little for you.
• The wing of a fabric covered parasol is usually three pieces attached to each other by four hinges with axes parallel to the long axis of the airplane.
• Each of these three pieces is pretty flexible in torsion and the hinges can carry a lot of load in all three translation axes, but can not carry any moment in the roll axis.
• The cabane struts can be visualized as simple vertical rods fixing the hinge positions between center section and outer panels. The lift struts fix spots outboard on the spars. Depending upon how far outboard the lift struts connect to the spars, the load at the cabane end of the other panels might be up or down. The load at the cabanes from the center section will be lift. Sum the forces from outer and center sections to get total vertical loads on cabanes.
• A consequence of the lift struts not being vertical (no place to anchor them) is that there is a big compression load in each spar between the lift struts.
• Pitching moment gets reacted along with simple lift loads.
Perhaps I explained my understanding poorly. What you said (quoted here) makes good sense (thanks to all the help here over the past 3 weeks or so) and I didn't think anything in my excel sheet or comments was contrary to any of the above. The final statement "Pitching moment gets reacted along with simple lift loads" could mean two things to me. I understand that the pitching moment of the airfoil (represented by Cm at the quarter chord) gets applied to the simple lift loads on the spars. This pitching moment is "coupled" (I think that is what you call it) and adds to one spar (fwd or aft) and reduces net lift from the other. This effects what you calculate for your spar loads, but ultimately these lift loads on the spars simply get taken to the cabanes and lift struts (and put bending in the spars which is a topic for later).
In my spreadsheet I had calcualted all the forces in the spars in the parallel strut but when changing to the V strut I had calculated the same loads but did not resolve the load path through the wing and fuselage to react the portion of the tension of the angled aft lift strut between its two end fittings. When resolving this load path I calculated the "coupled" load acting across the center section (reacted by same loads from the other wing) as well as a force from the wing acting forward which is normally reacted by a diagonal strut that goes from the wing down to the firewall at the top longeron. When resolving this force through the fuselage to "connect it" to the strut fitting on the fuselage (the other end of the angled lift strut) I realized a "rotational moment". I think this is simply because the center of lift of the wing is aft of the point at which this lift is applied to the fuselage, that being the forward lift strut fitting near the bottom longeron generally below the front spar. So far I have dealt only with compression and tension on columns so the moment was a new encounter for me, but one I anticipate I will get a better understanding of when I look at all the up and down forces on the fuselage.

• Now we have drag load and it evil cousin, anti-drag, which is forward component of lift, most visible at high alpha. We have to keep the wings from flopping fore and aft. This is usually done by some combination of angling the cabanes, cross bracing the cabanes, angling the lift struts. Drag and anti-drag show up in these pieces.
• Vertical loads in angled (non-vertical, non-horizontal) elements are increased - divide by cosine of angle from vertical converts vertical load to strut load. Similar approaches work on other loads.

If a load is only tensile, you can use wires, but since negative g and landing loads are real, wires usually have to be used in pairs. Wires are tensioned until no slack exists and can impose bigger loads on surrounding restraining elements than base loads. The loads in each element then becomes the static loads from the wires being tightened PLUS the live loads calculated from flight.
That's a good point I had wondered about. The "pre-load" or "tensioning" of the wires (that seems it need not be a lot more than taking out the slack as they will get plenty tight when "worked") are added to the loads created by flight.

Four vertical cabane struts will wobble left-right, fore-aft, and twist without other elements. Yes a diagonal member like you put in forward will stabilize it - the wire will keep it from wiggling. Both the diagonal strut and cross bracing will stabilize it against fore and aft loads. You may want to put in a diagonal element from side-to-side too.
After calculating drag and anti/drag forces on the cabanes and adding these loads to the loads from lift I expect the final (are there more?) loads to consider are the lateral loads (that will cover all 3 axes) which I believe are created by asymmetrical lift. This is where I expect the "diagonal element" will be quantified. The pietenpol uses x cables in front of and behind the front seat. Basically x bracing both pairs of cabanes laterally. My Hatz uses what it calls "roll wires" that cross laterally but instead of crossing "right in front of your face" they cross from the firewall to top longeron fitting up and over to the opposite tip wing fwd spar to cabane fitting. So yes, they run not only left and right, but also slant fore and aft. I suspect running them this way will impose higher loads in them (that whole cosine thing) but intend to calculate them in both arrangements as I'd prefer to run them like in my Hatz, a bit further out in front of the pilot's face.

Finally my other question about dual load paths was just in regards to design in general when a single force is reacted by two separate structures. For example an object with a downward force, say a bowling ball in earth's gravity, could be set on top of a column and supported by the compression of that column. It could also be suspended from the ceiling by a cable. In either case the column or cable would have to be able to support the gravitational force from the mass of the ball. OR - you could do both, the column and the cable. In such a case do you engineer it so each has to be able to carry only half of the force of the ball? My "guess" is that this is not a good idea because of one of the structures is "stiffer" than the others (or if the cable was not tensioned properly) the member that was supposed to carry half of the force is unexpectedly carrying more or all of the weight.

In a similar airplane related example: My Hatz has parallel flying wires acting as the primary lift strut to the top wing. They run about 3 inches apart from each other. I have often considered that if they were unequally tensioned that one would carry much more than half of the load of that wing, and maybe all of it and it may or may not be designed to "act alone". So I wondered if in mechanical design there was some "rule of thumb" for "redundant load paths" where each one should be able to carry, say, 70% of the total load. If each had to be designed to carry the total load it seems there is little reason to install both structures or "pieces" unless you think one may get "shot out" such as in a combat aircraft.

#### Fenix

##### Well-Known Member
HBA Supporter
Talking about sliderules and the Golden Age of Flight. One of my favorite books that was given to me from my old flight instructor from 1937 is Aircraft Structures by Niles and Newell published in 1929. Niles-- Stanford University professor. Newell-- MIT professor & Department of Commerce. A general overview. 4130 is still 4130 and wood is still wood.
Thanks for the referral Dan. I found an old copy on Amazon. It will be here next week : )

#### Dana

##### Super Moderator
Staff member
That's a good point I had wondered about. The "pre-load" or "tensioning" of the wires (that seems it need not be a lot more than taking out the slack as they will get plenty tight when "worked") are added to the loads created by flight.
Not quite. Preload is necessary, not only to give the structure rigidity, but to prevent metal fatigue in the wires and fittings. There is a good discussion of this on Ron W.'s Fly Baby page.

#### BJC

##### Well-Known Member
HBA Supporter
I know of one Pitts (no, not mine) whose owner broke the upper spar by tightening the flying wires too much.

I also have watched the flying wires turn into a 5 or 6 inch blur from slackening at -6 g.

Metal javelins look cute, but locally fatigue the wires, so stick with wood.

BJC

#### wsimpso1

##### Super Moderator
Staff member
Log Member
The final statement "Pitching moment gets reacted along with simple lift loads" could mean two things to me. I understand that the pitching moment of the airfoil (represented by Cm at the quarter chord) gets applied to the simple lift loads on the spars. This pitching moment is "coupled" (I think that is what you call it) and adds to one spar (fwd or aft) and reduces net lift from the other. This effects what you calculate for your spar loads, but ultimately these lift loads on the spars simply get taken to the cabanes and lift struts (and put bending in the spars which is a topic for later).
I have trouble helping you for a couple reasons. The formal training and book learning on this uses a particular very specific taxonomy that allows us to know what we are saying to each other. I suspect that words I know the meaning of are not meaning the the same thing to you. My basis for this belief is that I explain something, and you come back with a description that does not really fit... Sort of like playing the telephone game. So, I try to explain the topic a different way in the hope of being understood on what can be a tough topic to grasp. Please do not think that I am catching errors, I am trying to make sure that the concepts are getting through in the first place...

In my spreadsheet I had calcualted all the forces in the spars in the parallel strut but when changing to the V strut I had calculated the same loads but did not resolve the load path through the wing and fuselage to react the portion of the tension of the angled aft lift strut between its two end fittings. When resolving this load path I calculated the "coupled" load acting across the center section (reacted by same loads from the other wing) as well as a force from the wing acting forward which is normally reacted by a diagonal strut that goes from the wing down to the firewall at the top longeron. When resolving this force through the fuselage to "connect it" to the strut fitting on the fuselage (the other end of the angled lift strut) I realized a "rotational moment". I think this is simply because the center of lift of the wing is aft of the point at which this lift is applied to the fuselage, that being the forward lift strut fitting near the bottom longeron generally below the front spar. So far I have dealt only with compression and tension on columns so the moment was a new encounter for me, but one I anticipate I will get a better understanding of when I look at all the up and down forces on the fuselage.
Here is an example. This is hard to explain effectively, but I think the light has been getting brighter at your end. Let me try another approach.

A fabric covered wing has two long slender spars that have ribs connecting them together, and all of these elements are pretty soft in torsion, so the two spars do not particularly move together, and twist from end to end is pretty easy to get until you connect the lift struts. Put a skin around the front of the wing, making a D-tube and now the front spar is torsionally stiffer, but the aft one and the connections between them is still soft, so the spars can easily not be parallel.

Lift originating as locally lowered pressure outside the skins everywhere is reacted to the ribs and then the spars. The difference between suction on the bottom and suction on the top is lift, and it is calculated at 1/4c from Cl and S and q and spanwise lift distribution. The chordwise distribution of just lift between the forward and aft spar is simply lever rules with load in at 1/4c. In the simplest system, one spar is at 1/4c and carries all of the lift. Nothing more fancy than that. Then pitching moment is calculated using Cm, S, c, and q.

Moment absent lift (which is what we are doing) is two forces in the opposite direction some distance apart. the magnitude of the moment is F*L where F is the force and L is the distance between the two instances. Since the only thing picking up this load is the two spars, the distance between them is L, and one force is down at one spar, the other is up at the other spar. Nothing more complicated than that.

Oh, and fore-aft loads (drag and anti-drag) is occurring too, but since drag is much smaller, it is too easily neglected. Once you can get low alpha stuff figured out, you can do high alpha and add in the forward component of lift that is substantial.

These loads start at the tip and accumulate as you go toward the root. Since we simply hinge the outer panel at the cabanes, we hang a downward force on the wing at the strut mount. It pulls down equal to all the bending moment calculated from all of the lift applied to that spar about the hinge line at the cabanes divided by the distance from cabanes to the lift strut. Since the strut can not connect to anything straight down, we use an angled strut. The direction of the strut tells us the proportions of vertical and lateral and longitudenal forces, and since we know the vertical, we can figure the lateral and longitudenal forces. Put the strut right underneath the spar it carries and fly it at low alpha, and the longitudenal component is small. Slide the mount forward or aft and you can see where you are generating longitudenal forces in the strut.

The difference between total lift on a spar and the strut vertical force is the force that has to be reacted at the root. There is no bending moment in the spar at the hinge at the cabanes. Lightest spar possible is designed by placing the strut so the positive moment at the strut mount is equal to the largest negative moment between strut and cabane mounts. This minimizes the maximum moment in the spar, so you design the spar for one place and use it spanwise. You can tailor the spar, but most do this only outboard of the strut mount. That takes care of lift and pitching moment finding their way to struts and hinges.

Drag and anti-drag remain. The forward component of lift can be around 25% of lift, distributed along the span like lift is, but pointed forward. then subtract local drag. This force times the arm from cabane hinges and summed up over the span is trying to rotate the wing forward around the combined centers of the hinges at the cabances. It is resisted internally by the diagonal bracing found in fabric covered wings, usually wires plus a compression rib where each wire intersects a spar. Without the wires or some other form of bracing, the wing will easily wrack out of square. The wing is now stiff and strong against wracking, and the moment generated by drag and anti-drag is reacted at the cabane hinges, with equal forces out and
in and calculated in a way that should now be familiar.

One last load on the cabane hinges - the actual sum of drag and antidrag for the outer panel is a longitudinal load on the cabane hinges. The lift struts do little for you on this - the root fittings usually do the work. Exactly how it is split is tough to figure as it is usually indeterminate. Now if one cabane is triangulated (stiff) and the other is a simple column (quite soft), all of the longitudinal load will go in the triangulated one. If they are equally stiff and perfectly fitted, the load might be split 50-50. and so on.

So now we have a way to calculate loads from lift and pitching moment, know how they find their way into the spars, then to either lift struts or cabane struts. If these struts are angled we use the tiniest bit of trig to work out components in various directions in proportion to the directions of the struts and the loads. We also know how to work out the drag and anti-drag loads and how they get reacted.

That's a good point I had wondered about. The "pre-load" or "tensioning" of the wires (that seems it need not be a lot more than taking out the slack as they will get plenty tight when "worked") are added to the loads created by flight.
I know a little about the amount of preload in the wires. They are pretty darned tight between the wings of biplanes and on the tail of my wife's Rans S-6. Diagonal bracing wires inside the wing of fabric covered wings use a specified torque or number of turns after they snug up. From everything else I have done in my world, the usual case is to put in more preload than the system will see in use - this reduces variation in load on those threaded fasteners to small levels and thus prevents fatigue. Let it load up and then unload frequently, and well, threads grow cracks and break (fatigue).

After calculating drag and anti/drag forces on the cabanes and adding these loads to the loads from lift I expect the final (are there more?) loads to consider are the lateral loads (that will cover all 3 axes) which I believe are created by asymmetrical lift. This is where I expect the "diagonal element" will be quantified. The pietenpol uses x cables in front of and behind the front seat. Basically x bracing both pairs of cabanes laterally. My Hatz uses what it calls "roll wires" that cross laterally but instead of crossing "right in front of your face" they cross from the firewall to top longeron fitting up and over to the opposite tip wing fwd spar to cabane fitting. So yes, they run not only left and right, but also slant fore and aft. I suspect running them this way will impose higher loads in them (that whole cosine thing) but intend to calculate them in both arrangements as I'd prefer to run them like in my Hatz, a bit further out in front of the pilot's face.
These cross bracings keep the fuselage cross section square. Without them asymmetric landing or flying forces will distort the fuselage. Steel tube versions will have a diagonal tube in these frames.

Finally my other question about dual load paths was just in regards to design in general when a single force is reacted by two separate structures. For example an object with a downward force, say a bowling ball in earth's gravity, could be set on top of a column and supported by the compression of that column. It could also be suspended from the ceiling by a cable. In either case the column or cable would have to be able to support the gravitational force from the mass of the ball. OR - you could do both, the column and the cable. In such a case do you engineer it so each has to be able to carry only half of the force of the ball? My "guess" is that this is not a good idea because of one of the structures is "stiffer" than the others (or if the cable was not tensioned properly) the member that was supposed to carry half of the force is unexpectedly carrying more or all of the weight.
These are indeterminate. The loads in each element depend upon relative stiffnesses and how much preload is put in the system. It is a whole topic unto itself, and is a good reason to use things like FEA to model it.

In a similar airplane related example: My Hatz has parallel flying wires acting as the primary lift strut to the top wing. They run about 3 inches apart from each other. I have often considered that if they were unequally tensioned that one would carry much more than half of the load of that wing, and maybe all of it and it may or may not be designed to "act alone". So I wondered if in mechanical design there was some "rule of thumb" for "redundant load paths" where each one should be able to carry, say, 70% of the total load. If each had to be designed to carry the total load it seems there is little reason to install both structures or "pieces" unless you think one may get "shot out" such as in a combat aircraft.
Redundant structures is one reason to to that. Another is simply that wires can be draggy things, and round wires very draggy things, but two wires in close tandem are much lower drag than either by itself. So use about the same number of pounds of hardware but greatly reduce the drag by splitting them in two. Reviewing processes, I bet they are carefully tightened to about the same load. In bearings and other applications of paired, tripled, etc parts, there are rules given on what fraction of the total must be assumed to be carried by any one piece...

Billski

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