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

[stanislavz]

After all that, lets remember that a really well done square foot of bond line made from slightly wet micro weighs about 1/8 pound.

Thanks for this info. I got more like 1/6 of pound per sq foot in other sources (about 800 grams per sq metre)

Would you compare fullfoam wing to Cri-cri like wing ? 1/4" foam ribs with spacing of 1.8" at we first half of the winf, double that on other one. And with 100kg/m3 pvc foam, you have only 0.8/0.4pcf of average foam density per span.. And 1/8 of original skin to foam bond area..

 

[stanislavz]

Come on Stan, you supplied the page from Roark's... OK, I will interpret the equations for everyone else.

Thanks. Then all else is clear. And rib spacing could be tailored to allow laminar flow.

Btw FEA shown nonsense on 24*24" panel.. Is this 1.02 psi unifirmly loaded on whole area ?


+- Similar deflection on 0.0102 Or 100 less..

 

[ragflyer]

Just to point out 1 lb/sq inch is towards the worst condition of flying at Va and full pull up (4G). I would not worry about deflection and laminar flow at that flight condition- it just needs to hold with out permanent damage. If anything you need a bit of drag to slow things down at this condition.

The pressure differential (and consequently skin deflection) at cruise condition and climb condition would be significantly lower (~0.07 lb/sq. inch) and this is where you would care about laminar flow.

 

[stanislavz]

Just to point out 1 lb/sq inch is towards the worst condition of flying at Va and full pull up (4G)

I am getting similar numbers too 0.006 N/mm2, for my loads, but just fea shows way off too much deflections. And this is not right. Will do panels with foam too.

 

[stanislavz]

Ran the numbers for on, two, and four plies of BIAX cloth and a 24" separation and 1.02 psi.

One ply of 18 oz BIAX gets 491 psi and 0.505" deflection in the center of the part - This is mighty thin and moving a lot;
Two plies gets 533 psi and 0.273" deflection - this is about the minimum in a sandwich panel, one ply on each side;
Four plies 629 psi and 0.162" deflection - Lots of cowlings and fairings with no cores at this level.

Rerun this on FEA - it shows nonsense, 600" deflection., Similar deflection was for 7" separation, not 24".. But for this case :

My standard Triax / 3/8" thick6 pcf divinycel foam / Biax, it sees 174 psi in the fiberglass skin, and 0.022" deflection at mid panel. Way understressed, and deflection will cooperate with laminar flow, but not with a lot of margin.

I am getting similar deflection.

 

[wsimpso1]

Just to point out 1 lb/sq inch is towards the worst condition of flying at Va and full pull up (4G). I would not worry about deflection and laminar flow at that flight condition- it just needs to hold with out permanent damage. If anything you need a bit of drag to slow things down at this condition.

The pressure differential (and consequently skin deflection) at cruise condition and climb condition would be significantly lower (~0.07 lb/sq. inch) and this is where you would care about laminar flow.

Yes, if this were a pull up at Va or Vd, I would not be too worried about deflection, but I would be designing to make sure the airplane stays together with a FOS of at least 2.0. A good reason to check deflections though is to make sure we are all getting similar results. If the results differ widely, one or more analysis has issues.

One worry over big skin deflection is poor stall behaviour, which is an issue in a Va pull, as you ARE going to approach max lift AOA in a Va pull. If weird skin bulges trip stalls or give asymmetric stalls, well, snap roll entries could get entered in the test record earlier than originally planned. Just one good reason to like small skin shape deflections...

Billski

 

[wsimpso1]

Rerun this on FEA - it shows nonsense, 600" deflection., Similar deflection was for 7" separation, not 24".. But for this case :
I am getting similar deflection.

Well, I have egg on my face. I went and looked at the equations because the answers did look too small in that part of the sheet. When I copied equations, I got them pulling from the wrong data set. Thanks for the catch, I fixed stuff to pull all numbers for plain glass laminate. My apologies for driving you down a blind alley Stanislavz. Really sorry...

1 Ply and a 24 x 48, I get stresses 20 times what can be allowed, deflection over 900 inches, clearly violating all small deflection assumptions, just like Stanislavz saw;
When I cut 1 Ply panel width to 3", I get a perhaps livable stress of 14205psi and deflection of 0.228";
2 Ply at 6", same perhaps livable 14205 psi, deflection of 0.456";
1 Ply at 2.4" that was requested, a perhaps livable 9091 psi and deflection of 0.093".

Now let's see if THAT makes any sense in the FEA. If Stanislavz is still willing to run them...

The reasons I say "perhaps livable" is because we have other stresses in wing skins too. There is doing a higher fidelity load case from v^2 outside, the stresses on the skins from bending- and pitching-moments, etc. Maybe that 14205 psi is OK, but I am skeptical, and will await better specified models specific to someone's airplane instead of my guesses and questionable assumptions of what was supposed to be educational runs. Really educational...

I am getting similar deflection.

I had the sandwich model and the foam with glass on one side pulling from within their own problems. When "somebody else thinks so too", perhaps we are both doing the math correctly. Good to hear.

A very embarrassed Billski

 

[Vigilant1]

One worry over big skin deflection is poor stall behaviour, which is an issue in a Va pull, as you ARE going to approach max lift AOA in a Va pull. If weird skin bulges trip stalls or give asymmetric stalls, well, snap roll entries could get entered in the test record earlier than originally planned. Just one good reason to like small skin shape deflections...

Another concern about large deflections is the impact on any unfaced foam inside, especially with regard to repeated large flexing. While we don't know the fatique properties of that foam, it is a good bet that more flexing is worse than less flexing.

 

[Vigilant1]

Electronic spreadsheets. Hard to believe they didn't even exist 40 years ago, until VisiCalc. Invention story here. It seems like such an obvious thing, in retrospect. But it was truly a big deal, and not at all an obvious development.
It's a shame that building a spreadsheet, one of the handiest skills for anyone, technical or not, wasn't taught in any school I attended. It should be a required skill for everyone, IMO. Maybe it is, today.

 

[ragflyer]

Billski, Just to verify are you using -alpha *q*b^4/(E*t^3) from Roark, where alpha is 0.0138 if a/b = 1?

 

[ragflyer]

One worry over big skin deflection is poor stall behaviour, which is an issue in a Va pull, as you ARE going to approach max lift AOA in a Va pull. If weird skin bulges trip stalls or give asymmetric stalls, well, snap roll entries could get entered in the test record earlier than originally planned. Just one good reason to like small skin shape deflections...

Billski

yes could be an issue and will depend on the sensitivity of the airfoil though it should be self limiting - less buldge when it stalls. You will find classic aluminum wings (even so called laminar sections) balloon significantly.

As for membrane stresses my sense (I am not totally sold) is that it is not an issue in the class of airplane we fly. For one I do not see this in any regulation relating to light airplanes. Secondly the phenomenon is very dynamic and nonlinear. If the skin starts bulging it alters the lift forces and some lift is lost/gained and the bulge reduces/increases. The equilibrium involves a balancing of aerodynamic and structural reactions (loosely like fluter). Also not sure how you are adapting the Roarkes formula to composites....the formula is an empirical fit to a numerical model. I would be very skeptical of the results.

 

[stanislavz]

Now let's see if THAT makes any sense in the FEA. If Stanislavz is still willing to run them...

Stanislav will. Same 18oz biax, loaded at 1.02 psi ? Laminas at 45/-45 or 0/90 ? And stanislav will make a bigger shhet of 31" radiused panel. On Fea it still looks better.

Limitation of single skin is shear load from wing torsion... As far as i was able to find by now. But for V struted wing - it is quite viable to take only air loads. Or we go to Cri-cri milions ribs approach.. Foam lightened to extremum and it works...

 

[stanislavz]

1 Ply and a 24 x 48, I get stresses 20 times what can be allowed, deflection over 900 inches, clearly violating all small deflection assumptions, just like Stanislavz saw;
When I cut 1 Ply panel width to 3", I get a perhaps livable stress of 14205psi and deflection of 0.228";
2 Ply at 6", same perhaps livable 14205 psi, deflection of 0.456";
1 Ply at 2.4" that was requested, a perhaps livable 9091 psi and deflection of 0.093".

1.02 psi on all surface, Vacuum infused fiberglass, 0.37mm thick (for hand lamination it shell be ~0.5mm) 3" width :


Deflection = 0.19" RF: 1.20

2 plies, spaced 6"



Similar again = 0.42" RF: 0.98

2.4" single ply :



0.072" RF: 2.35

So for single ply fiberglass, only last one can be seen viable for such high load.

With Carbon fibre, 450gsm, biax, 0/90 laminas, 0.48mm (0.02" same as bilion pvc ribs 2024 skin) thick: at 2.4" :



Deflection 0.0128" RF :10

At 4"

deflection 0.116" RF: 2.6

And for 3.6", same as in Cri-Cri


Deflection 0.074" And RF: 3.9

Final - same as last one, but laminas at 45/-45 degree


Rf:4.8, deflection 0.125"

My conclusion - it can be viable using CF. For FG - you need a trilion ribs And for 50/50 resin to fiber deflections will be lower..

Billski - could you analytically run an example with Radius plate ? R= 31", 16" arc length, loaded at 1.02 psi at front, and 0.6 psi at back.. On FEA, i am getting much better results than flat plate.

Cored at 24", uncored at 6" two plies.

 

[Vigilant1]

After the revisions, for the condition outlined in the OP (equivalent to a 1" thick bare-backed XPS under FG triax with a panel width of 6”) are we still at approx .001" expected deflection?

Stanislavz, what is the " Rf" term? Thanks.

Mark

 

[stanislavz]

Stanislavz, what is the " Rf" term

Reserve factor - how much you can load it further till destruction. You want it to be at least 2.0 for all structural parts.

 

[wsimpso1]

1.02 psi on all surface, Vacuum infused fiberglass, 0.37mm thick (for hand lamination it shell be ~0.5mm) 3" width :

View attachment 104941
Deflection = 0.19" RF: 1.20

2 plies, spaced 6"

View attachment 104943

Similar again = 0.42" RF: 0.98

2.4" single ply :

View attachment 104944

0.072" RF: 2.35

So for single ply fiberglass, only last one can be seen viable for such high load.

With Carbon fibre, 450gsm, biax, 0/90 laminas, 0.48mm (0.02" same as bilion pvc ribs 2024 skin) thick: at 2.4" :

View attachment 104945

Deflection 0.0128" RF :10

At 4"
View attachment 104946
deflection 0.116" RF: 2.6

And for 3.6", same as in Cri-Cri

View attachment 104947
Deflection 0.074" And RF: 3.9

Final - same as last one, but laminas at 45/-45 degree

View attachment 104948
Rf:4.8, deflection 0.125"

My conclusion - it can be viable using CF. For FG - you need a trilion ribs And for 50/50 resin to fiber deflections will be lower..

Billski - could you analytically run an example with Radius plate ? R= 31", 16" arc length, loaded at 1.02 psi at front, and 0.6 psi at back.. On FEA, i am getting much better results than flat plate.

Cored at 24", uncored at 6" two plies.

Cool stuff Stan!

The large rib count and its weight on uncored wing skins is largely why composite wing structures tend toward sandwich structures and few ribs. In the places where cores are not used (B787 fuselage) they obtained skin stiffness with stiffeners and frames. Biggest reasons given for the fuselage skin to be solid has been for ability to check for cracks without removing the interior. Boeing's conservative approach is probably in play there too...

A question on boundary conditions - are your edges fixed in both position and rotation or position only? Your earlier post seemed to show triple arrow heads... I used fixed position and rotation modeling from Roark's for my calcs.

My references do not have curved plates supported at edges. Roark's... While curved plates may appear to be a subset of shells of revolution, edge fixity is a demanding boundary condition - it greatly influences stresses and thus deflections in the curved plate. Does anyone have an analytical method and coefficients for curved plates under pressure so that we might validate Stanislavz's FEA work?

I do suspect that a validated flat plate FEA modelling method with fixed edges would give me the courage to go FEA with a wing skin shaped curve and tailored pressures, and believe the results for design work. Given the loads superimposed by inflation, bending, and torsion, I would be inclined to cover the wise composite designer's FOS of 2 by doubling the loadings and then checking failure criteria.

I look forward to the curved plate FEA.

Billski

 

[stanislavz]

A question on boundary conditions - are your edges fixed in both position and rotation or position only? Your earlier post seemed to show triple arrow heads... I used fixed position and rotation modeling from Roark's for my calcs.

In this sample - fixed from displacement and rotation.

I was curious, how FEA compares to analytical approach. Till now - i can really say it is in acceptable range. Yes, i will provide FEA results for curved surface. Could you suggest skin shear load from your bird case ? And if possible at 200 mph speed range too.

And milion ribs or sandwich structures - its all depends on ones builders wishes. For FG - only cored solution is viable. For CF i do provided some numbers on weight estimate to Vigilant (getting close to 7 oz (200gsm) CF + foam + 7 oz CF as minimum gauge possible), but in short, for pvc ribs same as in Cri-cri - 1 ply of CF at 16oz (450gsm) is similar as 2040 in 0.02" thickness, and ligher in total 2 plies of 16oz CF with half ribs amount - you still have same amount of foam for ribs with average density of 0.6...

7 oz (200gsm) CF + foam + 7 oz CF apporach have high penalty on extra glue for CF to foam bond.

 

[Vigilant1]

Does anyone have an analytical method and coefficients for curved plates under pressure so that we might validate Stanislavz's FEA work?

Caveman with unhelpful response wants to know: " Is it an "analytical method" if someone makes a 36" x 6" sheet of CF to approx the right curvature, bonds it to pine " ribs" cut with a band saw, turns it upside down and dumps sand or gravel inside until the desired loading is reached?" Measure deflection. It could even be varied as desired between nose and tail. In pea gravel (0.0644 lb/cu inch density), the pile inside would need to be about 16" high to equal 1psi.. Sand is easier to get (and get rid of), but is .059 lbs/cu inch, so would need to be piled slightly higher.

It is easier (for me, or probably anyone who has carried buckets of sand around) to appreciate the magnitude of that 1psi load when visualized in this way. The bonding of the skin to any foam ribs, and the tensile strength of the foam rib itself, would seem to be pretty important. Flanges and tapes could be needed, so more weight.

 

[stanislavz]

and dumps sand or gravel inside until the desired loading is reached?"

It is better than strings with weights. And i think the only viable approach to get not-constant surface load at home. For one skin

For xps backed - it is cheating, no skin/foam bond torturing. For it you need to have vacuum chamber.

 

[Vigilant1]

It is better than strings with weights. And i think the only viable approach to get not-constant surface load at home. For one skin

For xps backed - it is cheating, no skin/foam bond torturing. For it you need to have vacuum chamber.

I'm struggling with the details of that vacuum chamber. 1 psi isn't much, but I'm envisioning a mess of manometers, leaks at hard-to-seal junctions, etc. And if we want to have different pressures at different parts of the airfoil, things get even more complicated.
But if my airfoil is 4 inches wide and I want 1psi of "pull", I can get it with an 8 lb weight pulling on a 2" (chordwise) x 4" spanwise (width of sample) piece of skin. 1 gallon water jug, nylon cord, attach to a bit of something stiff that is roughly the shape of the airfoil underneath. Spray adhesive to stick 1" thick upholstery foam to the wing surface, stick the top of the upholstery foam to the stiff panel tied to the weight. The upholstery foam is only there to spread the load more smoothly over the wing skin, prevent unrealistic locally high loading on a few wing skin spots. Hang the weight over the smoothly rounded edge of the table (PVC pipe as edging?)
36 chordwise linear inches of wing surface = 18 hanging water jugs. Too much clutter? Wet sand has double the density, so use 1/2 gal jugs or half as many 1 gal jugs. Also, it will be less if if some areas are tested at lower loads (for most of our designs, it will be hard to get 1psi aft of the quarter chord point. Maybe a flap at 90 degrees and 180 mph could show positive pressures approaching that.)

Build a true wing section slice with a (dummy, pine) spar bolted to the table and we could even see how loads which are passed the whole distance of the wing chord affect skin deflections (together with our "inflation load") . And, then flaps...
Lots of fun. I'll start saving milk jugs.