Not-so-solid massive core wings: Lightening the core foam

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Vigilant1

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Billski has ardently (but patiently :) ) extolled the merits of solid wing cores many times (see here, many others), observing that they are often lighter and easier to build than a comparably-sized wing with sandwich skins, ribs, flanges, etc. I'm a believer.

And yet, because Weight is the Enemy (tm), and noting that the foam in a typical GA wing might weigh as much as the facings, I'm sure I'm not the first to wonder if we need all of it, or if there is extra (lazy!) foam that can be removed while maintaining the integrity of the wing.

If this is old territory, please just put me straight. I know I've seen the idea mentioned, but I don't recall that it was put out of its misery.

For consideration: Below is a drawing a NACA 2413 core of 48" cord (each square is 1"). The area is about 204in2. If the core is made of 2.1 lb/ft3 foam, then each linear foot of wing core span weighs 2.97 lbs.

1606099632116.png
If we cut the lightening cores shown below, the core weight is reduced by 36%. Each foot-span of foam core then weighs 1.9 lbs, a reduction of just over 1 lb per foot of span.
1606100135167.png
Considerations:
How to do the cutting: In a Peter Shipol video, his cores were in 4 foot (spanwise) sections. His wing core templates on either end had the wing profile (for hot-wiring, as normal) as well as the lightening channels. He heated a length of pipe (maybe EMT conduit?) with a torch and melted a hole from one end to the other of each lightening channel. Then he dropped his nichrome/stainless wire through the hole, hooked it to his transformer and bow, and cut out that channel. It wasn't high-precision work (like a wing outline), it was a one-person job and went fast. The video is here, see 1:20 through 2:05.

Will the foam be over-stressed? I couldn't locate detailed specs for DuPont (formerly Dow) Styrofoam Bouyancy Billet (the foam typically used for massive wing cores), but Billski has previously posted that it has a compressive strength of 70 psi. Another Dow XPS product (“Highload 60”) has a compressive strength of 60 psi and a listed compressive modulus of 2200 psi and a listed tensile strength of 85 psi. No tensile modulus was listed, but a similar XPS foam by BASF has a listed tensile modulus of 4.35ksi. So, I’ll use those numbers as rough stand-ins for the DuPont 70psi buoyancy foam.

Back-of-the-envelope in-flight loads: Our plane has a typical light-plane level flight wing loading of 15 lbs/ft2. If we are designing for 9G ultimate, that will be 135 lbs/ft2 of lift force. Let’s make the (overly simplistic?) assumption that this lift is produced entirely by reduced pressure on top of the wing and near-ambient pressure on the wing’s lower skin. So, if the inside of our wing/voids are at ambient pressure and the area outside the top skin of the wing is 135 lb/ft2 (about 1 psi) below ambient pressure (to produce the needed lift), then the foam core would primarily be in tension from the top laminate to the bottom laminate). If I’ve got that right . . .

Looking at the wing with the lightening channels, the cores are about 1.5” apart at the closest. There are 7 top-to-bottom “beams” from the nose to the flap hinge, and the sum of their thinnest portions is 30% of the wing chord (without the flap). If our total wing core top-to-bottom is under 1psi tension (again, oversimplified) , then the concentrated tension through these thin points is 3.3psi. This is well under the 85 psi tensile strength of the foam, and under this load the foam would be expected to elongate just .004” (this is a very conservative estimate, as I assumed the “thin” columns were 6” long. The thin portion is actually relatively short). If we envision the foam will instead be in compression, the loads are similarly quite low compared to the foam’s compressive strength and compressive modulus.

If we vacuum bag the wing during construction, the forces on the foam will be higher than the aerodynamic forces in flight. Assuming 20”Hg vacuum (about 10 psi), the thin column sections will be under about 33 psi of pressure, which is well under the foam’s 70 psi listed compressive strength (which is typically quoted at either 5% or 10% compression, depending on the standard used). If the foam’s compressive modulus is 2.2ksi, then a 6” column that is under a 33 psi load can be expected to compress by 0.09”. That ain’t zero, but it’s not a lot. And, again, the “thin” portions aren’t actually the whole 6” height of the wing at its highest point, but are a much shorter length. So actual compression would likely be much less.

Alright, that’s the suggestion in a (long) nutshell. Is cutting the lightening channels in the core likely to compromise the wing? Or is it too much trouble to save 27 lbs on a 25’ span wing? Thanks for any input and for any unvarnished corrections to my "logic" or my calculations

Mark
 

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Vigilant1

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So face skins are not required if strut braced for torsion?
?? Is this about the Shipol video? I'm not sure of his reasoning. But, his design has no flaps or ailerons, and it has two struts and two spars, so maybe that is part of the rationale (for better or worse).
Back on the subject-- any opinion about carving lightening channels in hot wired wired wing cores?
 
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stanislavz

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Ok. We have some internal communication on this with Vigilant1 . And for discussion you need opposition. Plus side - this solution is used on Europa ultralight aircraft:

1606121298196.png
And it is cover with two 30/-30 degree uni. Unknown gramature.

On my side - i would provide core lightening not span vise, but chord vise - a lot of hot wire cutted ribs, same as spacek sd1-minisport or same as legendary cri-cri. Or other European ultralights.

So - lets go to numbers - cri-cri 6mm 100kg.m3 pvc foam (~6 lb/ft3 foam ) spaced each 45/90mm. Magically heavy pvc foam translate to lower-than EPS range. ~13 / 6.5 kg/m3 (~0.8/0.4 lb/ft3 foam ) . Also - this spacing is ok to divide thin skin shear web to provide some buckling stability. 1/70 skin thickness / to stiffeners placing. 2.97 lbs per wings foot is going down to 0.4/0.2 lbs per foot..

Similar approach using XPS - could be viable, if xps ribs would be wound around with some fiberglass/ carbon fibre threads. Just to be safe on delamination side.

And this all is driven by air loads on minimal side, much more have to be done for wing twisting loads. Which was new to me.
 

sming

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I'm glad you are asking the question because I had the same reaction watching peter's video, "what if you laminate carbon fiber now?"
I hope somebody can answer !

Edit: thinking, because you are hotwiring wing section, we could vary the "lightening" along the span? Like full core at the root, to almost empty at the tip?
 
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Vigilant1

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I'm glad you are asking the question because I had the same reaction watching peter's video, "what if you laminate carbon fiber now?"
I hope somebody can answer !

Edit: thinking, because you are hotwiring wing section, we could vary the "lightening" along the span? Like full core at the root, to almost empty at the tip?
Peter's lightening cutouts are pretty aggressive with long, straight sections under the surfaces and as beams. And EPS of the most common kind (low density) is much weaker than the XPS we're yacking about. I suspect Peter's wing core would survive an open layup of CF just fine, but any attempt to vacuum bag it would be another matter. And so the skin would be relatively heavy with epoxy and not as strong as it could be.
Yes, I'd think it would be simple to vary the hole sizes spanwise.

Root or tip (but especially root), if the spar web is laid up directly on the core foam (Rutan style), it will be important to leave enough foam there to assure it adequately supports/stabilizes the web. Even a tiny misalignment under load is a big deal.
 

sming

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If we vacuum bag the wing during construction, the forces on the foam will be higher than the aerodynamic forces in flight.
What i like about this sentence, is it could be a simple practical rule/test. If it survive vacuum bag at xx psi, it will survive air loads with FOS x
 

Vigilant1

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What i like about this sentence, is it could be a simple practical rule/test. If it survive vacuum bag at xx psi, it will survive air loads with FOS x
It might work out that way. To know, we'd need a real engineer (or someone a lot more competent than I am) to characterize the air loads and the paths they take inside the wing.
 
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Vigilant1

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Ok. We have some internal communication on this with Vigilant1 . And for discussion you need opposition. Plus side - this solution is used on Europa ultralight aircraft:

View attachment 104519
And it is cover with two 30/-30 degree uni. Unknown gramature.
Groovy. I see that the foam beams go "up and down" rather than forming a truss as Peter's did. Peter's wing doesn't have a (significant) load-bearing skin, so the foam itself has to carry the air loads to the spars.
On my side - i would provide core lightening not span vise, but chord vise - a lot of hot wire cutted ribs, same as spacek sd1-minisport or same as legendary cri-cri. Or other European ultralights.

So - lets go to numbers - cri-cri 6mm 100kg.m3 pvc foam (~6 lb/ft3 foam ) spaced each 45/90mm. Magically heavy pvc foam translate to lower-than EPS range. ~13 / 6.5 kg/m3 (~0.8/0.4 lb/ft3 foam ) . Also - this spacing is ok to divide thin skin shear web to provide some buckling stability. 1/70 skin thickness / to stiffeners placing. 2.97 lbs per wings foot is going down to 0.4/0.2 lbs per foot..

Similar approach using XPS - could be viable, if xps ribs would be wound around with some fiberglass/ carbon fibre threads. Just to be safe on delamination side.

And this all is driven by air loads on minimal side, much more have to be done for wing twisting loads. Which was new to me.
That's another way to go--build up a "semi-monolithic" wing core of a thousand ribs. You won't catch me saying anything bad about the Cri-Cri, and when I helped remove and store an SD-1 wing I was really impressed by how light it was. Fantastic. The SD-1 takes great advantage of that 1mm plywood (very stiff for the weight thanks to its thickness). The plane's moderate speed and wing loading were well appreciated by Spacek and the wing is light and not overbuilt.

Maybe we should say "Weight is an Enemy." It would seem that in designing or building a plane there are lots of other enemies/challenges: expense, construction time, construction difficulty, etc. It's probable that, if we want to use foam to bridge the top and bottom wing skins, the Cri-Cri and SD-1 approach may provide a lighter core, and that's one important factor. A "core" weight of 0.4 lbs per foot of wingspan would be very good indeed.

What are advantages of the monolithic core with lightening channels?
- Continuous "rib" under every inch of skin surface. This allows use of less specialized adhesives, reduces stress risers, and may allow use of a lighter, less stiff skin. Just as XPS foam stabilizes the spar web against buckling, it also supports the skin against buckling when is taking compression/torsion loads from the wing. If we can avoid/protect against hangar rash and airshow idiots, perhaps this will allow use of a lighter skin (12 oz/sq yd CF? Less?). I don't know if CF with support every 4- 7 inches will be as buckle-resistant in compression, or as tolerant of bumps.
- A fast build. Once the cores are cut, the "ribs" are done and already in place.
- No complex tools needed. Templates and a hot wire cutter. The "thousand rib" approach is made >much< easier today by the wide availability of CNC equipment than can quickly produce the parts in high precision. But to those not wanting to undertake a new hobby (CNC manufacturing), it means that the bits need to be cut by someone else (or, he can get out the template and start cutting by hand. A lot.)
- "Wing skin mold? I already built it!" If we want a composite skin, we either need to build it on a male form (which maybe we just made, and it will be part of our plane) or we need to make a female mold for the skins. Making a female mold won't be an attractive option for many builders. We can't easily form a thin skin over a skeleton of ribs, but it is easy to do it over a solid plug.

I think choosing between a "built-up" wing of chordwise voids (Cri-Cri, SD-1) vs a monolithic ("semi-solid") core of spanwise voids may depend mostly on non-engineering factors. To a one-off homebulder who wants a composite wing skin, the solid core (with lightening channels! :) ) has a lot going for it even if it is a little heavier. If I'm in business and want to sell parts or kits, the "built-up" core has a lot of advantages: I can flat-ship the pre-cut ribs and the builder can cover them with sheet (AL or plywood) or I can sell hard-to-fabricate-at-home composite skins for them.

"How do you check those thousand ribs to assure they are aligned?"
"I pull a wire really tight across them and see if they are perfectly lined up."
"Hey, if you used that wire to cut the ribs in the first place, they'd be perfectly aligned from the start!"

I don't recall the thickness of the Cri-Cri skin, but .025" AL weighs .35 lbs per square foot. For each foot of span, our wing has about 8.5 sq ft of skin, so that aluminum skin would weigh 3 lbs. Oops, I think we just gave back the weight we saved with the thousand-rib built-up core. 3 lbs of AL skin plus 0.4 lbs for (many, thin) PVC ribs= 3.4 lbs per foot. On the other hand, with a solid core, if we could do the skin in 12 oz/sq yd CF and epoxy (because it is a continually supported by a core), then the skin weight would be 0.17 lb/ft2, and our total skin weight per foot of span would be 1.4 lbs. Add that to our 1.9 lb per foot "lightened" solid XPS core and we have 3.3 lbs per foot. So not a lot different from the Cri-Cri. But, it is apples to oranges.
 
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Vigilant1

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Obviously, it would be possible be more aggressive when cutting the lightening voids.
1606137644017.png
This wing has the same ratio of "minimum column width to surface" as the earlier on with ellipses, but (forward of the flap) only 55% of the foam remains. Maybe it would be fine, or possibly still too conservative. It would seem to me that cutting the foam into arches/ellipses would better resist deformation, but maybe it's not an issue. The Europa tail cut-away that Stanislav provided in Post 4 is pretty "blocky."
 

BBerson

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?? Is this about the Shipol video? I'm not sure of his reasoning. But, his design has no flaps or ailerons, and it has two struts and two spars, so maybe that is part of the rationale (for better or worse).
Back on the subject-- any opinion about carving lightening channels in hot wired wired wing cores?
Sure, Sripol is doing similar experiments.
Just saying your analysis seems to prove foam alone is ten times stronger than needed. So "weight is the enemy" always. Then why not use the lightest skin, if any?
So, you didn't say what type of wing you want. It appears two spar. So the skin weight would depend on type of wing (cantilever, strut braced). My Aeronca only had fabric skin and it had ailerons. And the fabric could absorb some wing twist. Is that bad?
I think you either choose a flex skin or a hard skin that is much heavier. So...that's my input.
 

mcrae0104

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V1, I think what you need to do is analyze a slice of the rib (say, an inch thick spanwise) as a beam to determine how large the lightening holes can be. First things first though. I'm assuming 1) a Rutan-style spar (UNI or graphite caps), 2) a similar rear spar that will be used to mount aileron hardware and transmit torsion back to a hard point on the fuselage, and 3) a composite skin that will carry torsion and contribute to resisting drag loads. Is that right?

So then you can draw a free body diagram of the nose block with the negative pressure all the way around the nose (remember it's negative all around, but more negative on top), a shear reaction at the spar, and fore/aft reactions in the skin to react the torsion (these would be fed through the nose skin into a shear flow along the upper and lower bond between skin and rib.

I know next to nothing about analysis of composite structures (you know the guys who do), but I would think that next you can analyze this part with regular old beam theory as a beam with a couple of holes through it.
 

stanislavz

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"How do you check those thousand ribs to assure they are aligned?"
"I pull a wire really tight across them and see if they are perfectly lined up."
"Hey, if you used that wire to cut the ribs in the first place, they'd be perfectly aligned from the start!"
Just answer this one now.

For build up composite wing, you mold is leftover from cutting core. And you may/want build it outside-inside - first done skin - Front D cell with top rear skin, D cell ribs, spar rear ribs and bottom rear skin. While all still in mold.
 

Vigilant1

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V1, I think what you need to do is analyze a slice of the rib (say, an inch thick spanwise) as a beam to determine how large the lightening holes can be. First things first though. I'm assuming 1) a Rutan-style spar (UNI or graphite caps), 2) a similar rear spar that will be used to mount aileron hardware and transmit torsion back to a hard point on the fuselage, and 3) a composite skin that will carry torsion and contribute to resisting drag loads. Is that right?
Yes, that's all correct.

So then you can draw a free body diagram of the nose block with the negative pressure all the way around the nose (remember it's negative all around, but more negative on top), a shear reaction at the spar, and fore/aft reactions in the skin to react the torsion (these would be fed through the nose skin into a shear flow along the upper and lower bond between skin and rib.
Oh, this is where it gets murky. Force vectors? For perspective, I've spent hours stewing over this kindergarten problem: If my foam sheet is in a vacuum bag (near perfect) and 14.5psi atmospheric pressure is pressing on top of the foam sheet and on the bottom of the foam sheet, is the foam being subjected to 29psi? Or, is it just 14.5? If I seal the bag to the inflexible table? If that's got me thrown, you can imagine the free body diagram I'd draw. More like Antonio Vargas than Isaac Newton.
More seriously, this is a good idea and a place for me to start.

I know next to nothing about analysis of composite structures (you know the guys who do), but I would think that next you can analyze this part with regular old beam theory as a beam with a couple of holes through it.
"Old beam theory" to you!
 
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Vigilant1

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Just answer this one now.

For build up composite wing, you mold is leftover from cutting core. And you may/want build it outside-inside - first done skin - Front D cell with top rear skin, D cell ribs, spar rear ribs and bottom rear skin. While all still in mold.
That could work. But it is a lot of fiddly bits, with tapes and flanges, etc. And eventually you have a blind closure of some kind to accomplish.
 

wsimpso1

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Well, first, Autoreply and I have commented on how classic massive cores are lighter than classic hollow (sandwich skin) at the modest chords we see in homebuilt airplanes. Autoreply has cited a doc where someone found the break even spot was around 2m, IIRC. Above that, you save weight by being hollow. Now, I emphasize that this is for skins with laminates on both sides, ribs, flanges, glues lines etc.

What is being proposed by Vigilant1 is to start with a massive core and then remove some of the core... Well, we know some can be removed safely. Rutan canards have historically removed a cylinder of foam spanwise for wing tip wiring and the rudder cable. It seems to survive a deletion of a 1" cylinder just fine, but that is what, a quarter pound in a Long Ez.

So, why is no one actually running some numbers? All this "theory" is pretty weak until you check on how much weight is removed and if the remaining structure will carry your flight and build loads. are you guys afraid of analysis? You can play "what if" and answer your own questions...

I must improve the thinking behind the analysis method. First, let's box in the thinking - we are dealing with a foam core and fiber-resin skins and spars. There are four main loads on the wing skins in flight plus one for construction:
  • Inflation - This one seems to be forgotten. In a 40 knot airplane it hardly matters, and in an airplane over 300 knots it pretty well defines skin structures. The air inside the cavities are stationary and thus the same as the atmosphere outside the plane. Outside the wings, the air is moving at some multiple of the airspeed of the airplane. TOWS Appendix I has this plotted for many symmetric forms at Cl=0 and at a one higher Cl for both surfaces. These velocity and thus pressure distributions apply when you add camber. You can estimate for any Cl. Using Bernoulli's Law, you can calculate the pressure outside and thus the pressure difference between inside and outside. Inflation effect is highest near the leading edge and diminishes as you go aft, and it goes with local V^2. Usually we then estimate stresses and deflections in constant thickness panels using Roark's Chapter 11, table 11.4. You have to do some interesting machinations of our asymmetric composite plate to use table 11.4, but it works. Doing the elliptical cutouts, well, that cries out for FEA. We can talk more about this if we want;
  • Lift - Once you have done the forces trying to pull the skins away from the wing, you can also get the lift. It is just the difference between the load pulling the top one up and the load pulling the bottom one down. The lift is transmitted through the sandwich of foam and laminate to the spars;
  • Bending - The combination of skin set and spar set make up the bending stiffness of the wing, and the wing curves upward under positive g. Near the root, the spar makes up most of the stiffness, with the skin pretty much going along for the ride. Out near the tip, a properly tailored spar's stiffness diminishes and wing skin usually dominates. The wing curves with the compressive strain (span wise) on one side and tensile strain (spanwise) on the other. Why emphasize spanwise? Well, the skins are in what ME's call plane stress. When we strain a plate in in one direction, at 90 degrees to that strain we get a significant strain of the opposite sense. So, the top skin gets compression spanwise and tension chordwise, while the bottom skin gets tension spanwise and compression chordwise;
  • Torsion - The combination of skin set and spar set make up the torsional stiffness of the wing, and the wing usually twists leading edge down under positive g. The skin pretty much defines the torsional stiffness with the spar more or less along for the ride. The wing twists with the shear strain on the skins.
  • Vacuum Bagging - This is like in flight inflation, except that you must carry the bag loads without the skin laminate helping and that the foam inside is in tension instead of compression. Oh, and this load is really big. 10 psi is 1440 lb/ft^2 which is about the dynamic pressure for 1100 fps. Hmm. Unless you are flying up into the transonic region, your skins won't be making this level of lead in flight.
Since we are probably talking the low speed end of the flight range, vacuum bag forces will probably be the BIG stressor on this structure.

Will the foam with cutouts stand the vacuum bagging? We EAA members can get SolidWorks for free, model up a wing profile with holes in it, extrude it to 10 feet, define the material with the specifics listed in the OP, apply an outside pressure of 10 psi and see what stresses and deflections it makes. If the foam's strength is exceeded, maybe you can investigate lower vacuum, or maybe vacuum bagging is simply out. But if the stresses in the foam are substantially below its strength, how much does it deflect into the cavities. You will probably have to fill and fair anyway, but that usually averages 0.015 to 0.030" thick or less than 0.09 lb/ft^2. If you have a bunch of filling to get the skin fair, you might be adding more weight by bagging than by doing open layups. All things you can check out with a SolidWorks model and a few simple calcs.

On to flight loads. The air is pulling out on the skins, and straining the panels to bulge outward. The wing is bending with axial strains both spanwise and chordwise in the panels. The wing is twisting with shear strains in the panels. And it does all of this at the same time. So all of these plane strain conditions must be superimposed and checked to see if they exceed the failure criteria for the asymmetric sandwich you are proposing.

You must stand the first three together and the last one by itself. We can do in plane loads and moments using composite plate theory.

What about me? Listen, I retired five years ago so I could do what I want, not what somebody else wants... I am building my airplane, trying to keep my wife happy, and other stuff that is important to me. If I spent my days doing your what-if's for you - and there are a bunch out there just begging for effort - my wife would be unhappy and my bird would never fly. You guys think this is so cool, do some analysis or some testing, or both.

It sounds like a great idea, and at small wing loadings and low speeds it can work. Peter Sripol is flying one. First, the solid core. It has proven to work just fine because even at the q's SpaceShipOne flew at, the forces pulling the skins away are less than the strength of the foam and the elastic deformations are tiny. Make a sandwich panel skin, with laminate on both sides of a core, and the neutral axis is somewhere near the middle of the sandwich, stiffnesses and strengths in bending go up by orders of magnitude. Bond the two skins together around the edges and it is way strong. Omit one laminate facing, and you can put in lots of foam before the neutral axis moves enough to start raising bending stiffness. And that is the problem - you lost a bunch of stiffness and strength... At the low end of the speed and wing loading regimes, this can work. But your skins have to stand your V-n envelope all the way to your Vdive. That means somebody better do the engineering and math. Unless...

An alternative of the "try it and see" school does present itself. If you have or can build a vacuum chamber and can connect outside pressure to inside tubes, you can perform a test series with test sections. There are tubes for applying atmospheric pressure inside vacuum bagged parts for fabrication. Run these inside the cutouts, so you can control inside pressure (run to outside air with a valve and gage) while the outside has vacuum that you also control. Do the designed experiment thing with large and small radii (cutouts) and large and small wall thickness (between cutout and laminate), throw in one case of mid wall and radius. Five permutations to build and test. Do each one twice, and you have some idea how much variability you will have as well as a good idea how much wall you will need and how small or large a radius you can stand for your flight envelope. Oh, I would put a scale in the back ground and another on the window so you can record your deflections as you ramp vacuum - deflection may stop you long before fractures do.

So what is holding your guys up? Come on, let's see some analysis and testing!

Billski
 

stanislavz

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So not a lot different from the Cri-Cri. But, it is apples to oranges.
Its all depends on your goal. As far as i got deeper into analysis, it looks like this for "standart wing load two seater"

Kitfox/Skyranger/Ikarus c42, vne 120 mph - rag and tube is totally ok, V strut is good for low weight. Cruise is in 90 mph range. Doing in full rigid wing on same weigth is only possible, because tube spar are not weight efficient, and skin is only dead weight. Strong D cell on the front with cf in necessary position and minimum of rear spar + single skin with some ribs each 4-10" is ok. If it sees only lift load, not torsion.

If you exchange one strut for massive D cell - it may have similar weight, but will be much better with three layered sandwitch on D cell. Or you want do divide it each skin*70 with local stiffeners. Standard solution for many eu aircraft with 150mph vne range. And still mtow < 450 kg. Again skin is mostly loaded in shear due to twisting. Not by airloads yet.

If gone into higher speed range - you need solid foam core or full sandwich construction.
 

stanislavz

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An alternative of the "try it and see" school does present itself. If you have or can build a vacuum chamber and can connect outside pressure to inside tubes, you can perform a test series with test sections. There are tubes for applying atmospheric pressure inside vacuum bagged parts for fabrication. Run these inside the cutouts, so you can control inside pressure (run to outside air with a valve and gage) while the outside has vacuum that you also control. Do the designed experiment thing with large and small radii (cutouts) and large and small wall thickness (between cutout and laminate), throw in one case of mid wall and radius. Five permutations to build and test. Do each one twice, and you have some idea how much variability you will have as well as a good idea how much wall you will need and how small or large a radius you can stand for your flight envelope. Oh, I would put a scale in the back ground and another on the window so you can record your deflections as you ramp vacuum - deflection may stop you long before fractures do.
In progress on this, on flat plate for beginning.
 
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