Discussion in 'Wood Construction' started by mcrae0104, Aug 6, 2017.
Would that make it a wood chipper?
Well, I do not know how I fit in the reader's eyes for "reliable knowledge", but I will share what I know.
Weight? Each time you have a design, you can compute volume of wood and multiply by known wood densities. Glue is about 0.020” times the area of all the faying surfaces to get volume of adhesive (Epoxy densities are available from the makers). Glass cloth is specified by its weight per unit area. 1-1/2 oz fabric is 1-1/2 oz per square yard. Epoxy to attach glass is about the same weight as the cloth, and you will fair it with dry micro at around 4-5 pounds per gallon. Sorry, you have to estimate how thick your fairing job will go. Me, I plan to spray a coat of dark epoxy primer, and fair over that until the primer shows through. Most places that is only a few thousandths, but depending upon your joinery, you may need substantial fairing compound thickness.
Wing attachment? In cantilever wings made of wood or composite, I like overlapping spars. For wire braced wings, look to Steve Wittman’s Tailwind plans. Then scale per your specific strut loads.
Adhesive? West System is nearly magic with wood. Gougeon Proset can be post cured to gain another increment of heat tolerance.
Finishing? Wood plus 1.5 oz glass and epoxy, dry micro and fair to perfection for laminar flow. Go look at George’s website and the various Cozy builders' logs. Put the dry micro on once, take it off once, seal with five coats of wet epoxy wiped on and wiped off.
Now the topic of analyzing this thing came up to make sure it is sturdy before you build it. I am in favor of that approach. I just use the tools we mechanical engineers use to build structures. Bruhn and others may have refined the process, have more specific approximations, etc. I know the ME methods…
First and foremost, wood are composite materials, but very well known ones. The handbooks do provide reliable assistance on max stresses, Young’s Modulus, etc by species and by direction. Where to put the info from the handbooks?
If your fuselage skins are buckling, you have to go with semi-tension field theory and it gets more complicated. If your skins are not buckling, all of the wood in whatever section you are working with is in play, and contributes to EI and GJ of the section. You may have to back into E and G from the handbooks. Computation of I and J are relatively straight forward when assembled numerically in Excel over a section. Include the longerons and skin, but disregard the frames in calculating EI and GJ. I can help with details on all of this.
A rule of thumb used in many designs with a port is to place the material removed from the port back into the frame of the port. Yep, area of the doubler around the opening is equal to the area of the opening. Some folks go for a little more than that…
Now why put in the frames and for that matter the longerons? Well, the longerons and any other longitudinal stiffeners provide resistence to buckling. These frames and longerons also break the skin into panels of measurable width and length.
Start with computing the relative stiffness to longitudinal loads of the skins and longerons and other stiffnesses. The bending strain on the section is My/(sum of EI), so you can compute the strain at each longeron and at any place you want on skin. Take the strain times the modulus for the wood or plywood, and you have the axial stress. Is it in the safe range? Perform a similar computation for any torsion on the section using Tr/(sumof GJ) and compute shear strain, then shear stresses and check them too. When you have bending and torsion simultaneously, you get to review Mohr’s circle to combine the loads for each of the ply and longitudinal structures. Excel is your friend here.
This just combines to give you stresses due to tail loads, g loads on things attached to the section that produce moments, and the like. Another part of the puzzle is aerodynamic load. The inside has stationary or slow moving air, the outside has air going somewhat faster than the airspeed of the airplane. This produces air pressure that is attempting to inflate the airplane. At Pietenpol speeds, this hardly matters, but in a Falco at Vdive, yeah, it probably matters. I use chapter 11 of Roark’s. Yes, these are for flat plates. For wings, the curvature is small and the approximation is somewhat conservative. For the more highly curved fuselage skins, it is more conservative. Anyway, from these formulae you can estimate stresses and deflection of the skin between frames and longerons. These stresses will get added to those from tail loads, etc. Above. Keep orientation in mind…
Now all of this is assuming no buckling. How do we know that we are not buckling the skin? This is elastic stability, but we can make some simplifications that are also conservative.
Longerons can be checked using Euler’s methods – take apart the loads on the section per the EI of the section, EI of each of the contributors to the section and trust that the Bending load is distributed per the fraction of total EI that each element has. Yep, no buckling, the load gets distributed per the stiffness of the parts. Know the max compression on a longeron, the level of constraint at each frame, and the length of it between frames, then you can check if it will buckle. This is conservative, as the skin will help some too. Go to The airplane structures texts or theory of Elastic Stability to get closer. Anyway, if the longerons buckle, then they either need more of them, more section, or closer spacing of the frames.
Now we get to skin compression. If it is a simple flat panel, I computed for the thin way will be minimum and Euler works here too. Know the length, the constraint at the frames, the compression, EI of the panel (the thin way) and you can know if it will buckle… If the panel is tapered (conical) run the numbers on both ends and in the middle. If you have big membrane loads from the air, you might want to be pretty conservative here. Now if the panel between longerons and frames is curved, you have to draw a chord between the longerons, and compute the position of the neutral axis parallel to the chord line and then EI of the panel that way. You pick up quite a bit of EI from curvature. Now go to Euler’s rule and make sure it is secure from bending. You can Decrease frame spacing or thicken the skin, and remember that inflation loads are also trying to get you into buckling here.
So there you have it. You can sketch out a design, assign stations between frames, check the longerons and skin for buckling, compute air loads and stresses from that, add in stresses from bending and torsion, assemble the load cases at each position and load carrying element around the part with Mohr’s circle, and check that stresses are OK. I would get serious in Excel so that I have a generic elliptical section with longerons about where I would want them. Then you can put in major and minor axis radii, frame spacing, longeron dimensions, thickness and let it compute EI and GJ for the whole thing and for each of the elements. Then put in bending and torsion moments, and delta P, and let it tell you how we are doing on FOS and weight. I would do a downtown job on this, as you may run a lot of iterations. Depending upon FOS shown, you can play with skin thickness, longeron section and frame spacing. Heck, for the really serious, you can come up with a designed experiment matrix, and find the section specifics that minimize your weight at strength.
I know that I sometimes get the willies looking at how far apart reinforcements are and put them closer. Hell, my conservative efforts indicated three ribs in my outer wing panels. I needed more than that to contain fuel and mount the aileron control hardware. You might find yourself looking at a similarly flimsey looking design. Go do the laugh check - see what the other designers are using. If you and Dr Frati came to the same conclusions, maybe you are OK.
Always appreciate your input here. Thanks for sharing. Its a nice road map for the journey.
Billski, thank you so much for taking the time to type out such a thoughtful and helpful answer. You have no idea what a tremendous aid this is to me. You've given me plenty to digest for the next several months!
You are welcome. I hope that other readers on HBA can benefit from it too. Unfortunately, the analytical approach is kind of complex and technical.
Best place I know to review this is a mechanics of materials text under composite beams. They are talking rebar reinforcement of concrete in bending, and you work in relative stiffness. EA is axial stiffness, EI is bending stiffness, and GJ is torsional stiffness.
Of course, you could just copy a successful design with same performance and wing loading. I like to call that the monkey-see, monkey-do approach, but it works pretty well and is way easier, if laden with a big dose of uncertainty. I hate uncertainty... Much better to know that your FOS is adequate EVERYWHERE.
I had another point to bring up. Where you have a serious discontinuity, like at a door or canopy opening, run all of the numbers on both sides of the opening - once at the full fuselage just behind the opening, once at the aft end of the opening, once at the front of the opening, and then one just forward of the opening. This way you know how the structure covers the discontinuity. Typically, the fuselage will have to be beefed up through the door opening. When you do that, think hard about making the structure transition between being full and being partial. The loads have to make the transition...
OK, I referenced a LOT of design method in my big post, and I KNOW that not all of it will make sense, so if you want to get into specifics, this is where you ask for help too. While I won't do your math for you, I will help you guys. Discussion on how to do the analysis and where to find specific background is fair game. This stuff is not so much hard as it requires some attention and then understanding of how the math describes what is going on.
This French design has a plywood skinned laminar flow wing - http://gazaile2.free.fr/index.php. 1.2mm ply with a layer of 100gram/sq m glass cloth. Glass cloth is not structural, just their to protect the ply and make painting/fairing easier. The wing is high aspect with lots of foam ribs. I've just bought the plans.
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