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

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#### Sockmonkey

##### Well-Known Member
You can try just about anything.... please tell us why you would run different densities in different parts of the foil. Oh, epoxy will absolutely stop the hot wire saw.
I guess they'd have to be cut to shape before gluing then. The different densities would be to save weight without creating voids.

#### stanislavz

##### Well-Known Member
HBA Supporter
Cutting limbs is hardly necessary... Are you saying you want to model just the fiberglass laminate with no foam support? This thread is about the foam and taking some of it out...
Thanks ! No, just was kidding. We had a lot of internal discussion with Vigilant - and my proposition, was to remove foam chordvise - aka milion ribs. And it is used in eu - especially france. And in some glider with metal skin wing..

#### stanislavz

##### Well-Known Member
HBA Supporter
Ran the numbers for on, two, and four plies of BIAX cloth and a 24" separation and 1.02 psi.
But on milion ribs, you need denser ribs. For same comparision - it shell be separated 2" or 4" at max.

On fair comparision we are able to use same amount of foam as in sandwitch construction as in 4" spaced ribs

#### stanislavz

##### Well-Known Member
HBA Supporter
One ply of 18 oz BIAX gets 491 psi and 0.505" deflection in the center of the part - This is mighty thin an moving a lot;
And for 2.4" it will be 1/10000 of this 0.505" ?

#### Vigilant1

##### Well-Known Member
I could not stand the uncertainty any longer, cracked open Roark's to get us some numbers on these sorts of things.

First, I established a local dynamic pressure of 1.02 psi pulling on the skins, and used a uniform pressure model. I postulated a 48" chord, 7.2" thick, and started with uniform thickness skin panel 12" by 48".
Thanks for your indulgence. Just so I understand, is the 12" x 48" panel fixed at all edges, or just on the 48" long edges? And who knew Mr Roark even owned a calculator?

My standard Triax / 3/8" thick6 pcf divinycel foam / Biax, it sees 195 174 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.
Regarding the bolded portion, could you please briefly expand on that? Our aero load is 1.03 PSI over the panel, is the 195 174 psi a tensile load carried to the (fixed) panel edges through the approx .03" thick triax (so 195 psi x .03" thick = 5.85 lbs per linear inch of boundary)? Or, is the 195 174 psi the stress between the top FG skin and the inner skin? Or (probably) something else?

[with 6" panel width] Blue foam core dropped to 1.1" thick with stress of 31 psi and deflection of 0.001.

Then I went to a 4" width, and only needed 7/8" foam thickness to get stresses down.

So, no matter how small you make the panels with removed cores, the foam removed is not going to be huge.
This seems like not such bad news for the "foam borer" idea. I agree that carving out every bit of foam between "normally spaced" ribs (aside from an inch backing the skin) is probably not in the cards at these forces and desired deflection limits (though the KR apparently does okay with it, maybe no laminar flow concerns there).

Isn't a -1psi (144 lbs per square foot) outward load on the skin quite a bit? As I understand things, at typical GA airspeeds and wing loadings we'd only see (negative) pressures like that near the leading edge and only during an aggressive pull-up. I hope this example is right: At 150 KTS (sea level) dynamic pressure ("q") = 0.53 psi. So, that's the (max) positive pressure we'd be getting (at the stagnation point of the airfoil, assuming incompressible flow). For negative pressure: If we pull and attain an 8 degree AoA at that speed, a NACA 4412 airfoil will achieve a pressure coefficient of -1.0 to -1.7 from about the LE to the 1/4 chord point*, so that would get us to -0.53 to -0.9 psi over that limited area, but we wouldn't reach -1 psi. TOWS says we'd get a Cl of about 1.1 at that AoA, or about 84 lbs of lift per sq ft of wing. That's a lot for most GA aircraft that are typically designed for <15psf wing loadings at MTOW and 1G. The Cl would be a tad less with a real 3D wing, but it's still a lot.

But, leaving that aside, let's go with -1 psi. Per your calculations (again--thanks!), if our panel width is 6" and our (bare) foam is 1.1" thick under the skins, the deflections (with FG triax skins) are expected to be .001".

Here's diagram from Post 11 with some fairly aggressive holes. The grid is 1". The skins are about 1" thick and none of the spans reach the 6" span for which you did the calculations-- a .001" deflection sounds pretty good (though it would a spanwise here ). Between the LE and the rear spar, 45% of the foam has been removed. The removed foam weighs 1.2lb per foot of span (30 lbs off the empty weight if our span is 25').

Removing the foam is more trouble than leaving it in place. But if we can save the weight, keep the skin smooth enough to retain laminar flow, and do it while retaining a safe wing structure, I think it might be attractive to some designer/builders. Heck, at the $26/lb we pay to save weight with a lithium battery, 30 lbs is worth almost$800. That'll pay for most of the wing foam!

The big question (and not an assignment for anyone): When removing this foam, is skin deflection under air load the only concern? With 1" foam under the skin laminate supported by skin-to-skin 70 PSI XPS foam every 6", is there any risk of skin buckling due to compression loads on the skin? I've heard frequently (and believe) that these loads on the foam are very small as long as the skin is kept in plane, but when it is under deflection due to air loads the skin isn't in plane.

And then there's the KR . . . .

Mark

*NACA Report 563, pgs 2, 15

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#### wsimpso1

##### Super Moderator
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Log Member
And for 2.4" it will be 1/10000 of this 0.505" ?
I do not understand...

Are you asking for deflection of a massive core under the aero loads? If yes, Massive core deflection at any spot along the chord is estimated by a standard relationship:

Y = PL/E where
P is 1.02 pounds;
L is one half the depth of the foil (the top pulls up, the bottom pulls down, there is no movement at the midline) so 3.6";
E is somewhere around 4500 psi.

y is around 0.0008"

#### wsimpso1

##### Super Moderator
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Log Member
Thanks for your indulgence. Just so I understand, is the 12" x 48" panel fixed at all edges, or just on the 48" long edges?
I used fixed edges - zero displacement or rotation. This is what you would have with a long continuous skin that bridges across the main spar, the drag spar, and ribs, and is solidly attached to each. I also used uniform pressure over the entire panel. If you want high fidelity, you need to use one model for fixed edges and uniform pressure superimposed on another model with fixed edges and pressure uniformly decreasing.

Regarding the bolded portion, could you please briefly expand on that?
We have a sandwich with 0.022 thick ply of Triax, a 0.375 PVC foam core, and a 0.018 thick ply of BIAX. Each has its own E and they all contribute to bending stiffness in the fore-aft direction. At the center of the long edges of the panel, we know the maximum stress occurs in the panel, and the panel is being bent. The stress at the skin outer surface is established. This is the stress in the glass. The core deflects in bending along with the skins, but the strain at 174 psi in the glass is really tiny. E in that direction on the TRIAX is 1.1E6, strain is 195/1.1E6 = 0.000158. Foam is a tiny bit closer to the neutral axis, and bending strain goes with the distance to neutral axis, so strain in the foam is about 0.000142. E foam is 4500, stress in the foam is about 0.000158*4500 = 0.71 psi. No big deal, as long as the glass skins are OK, the foam is fine. The other way to know the foam is fine within a sandwich is that failure strains in glass run 1 to 2%, failure strains in the foams run 5-8%. As long as they are straining together and the glass is OK, the foam has all sorts of margin.

Our aero load is 1.03 PSI over the panel, is the 195 psi a tensile load carried to the (fixed) panel edges through the approx .03" thick triax (so 195 psi x .03" thick = 5.85 lbs per linear inch of boundary)? Or, is the 195 psi the stress between the top FG skin and the inner skin? Or (probably) something else?
Nope see above. Tensile and compressive strain carrying the bending load are at the worst place in the sandwich.

This seems like not such bad news for the "foam borer" idea. I agree that carving out every bit of foam between "normally spaced" ribs (aside from an inch backing the skin) is probably not in the cards at these forces and desired deflection limits (though the KR apparently does okay with it, maybe no laminar flow concerns there).
NOT bad news? I think it sure sounds like bad news. I put only part of the load from 120 knots on the panels, and the foam with glass on only one side needs to be 1.65 inches thick on a 7.2 inch thick wing. That let's you take 4 inches out at the thickest part of the wing, and less as you go forward. If your ship has a higher Vdive and you get the rest of the stressors on there, stresses in the foam forward may not allow much or any removal. Aft, where the pressures get smaller, maybe you can remove more. I had to reduce the fore-aft distance of free panel to 4" to get the foam under the fiberglass to under 1" thick. Unless the bird you are contemplating has either lower q than I modeled or pretty narrow panels, it is looking like you may not be able to remove much of the core.

Isn't a -1psi (144 lbs per square foot) outward load on the skin quite a bit?
Open TOWS to Appendix 1, any airfoil, lets try page 358, the NACA 64(2)A015. At x = 0.1, (v/V)^2 for a foil at Cl = 0 is 1.3, and for Cl 0.21 it is 1.55. to get max g at Vd, you probably need Cl = 0.8, and that works out to (v/V)^2 of 2.25. Go up to Cl =1.6 for Va, and (v/V)^2 is 3.2. I got generous and just used 3.0 and V=120 knots. Q is 147 lb/ft^2 for Va of 120 knots and max Cl. You could run your Vd at say 160 knots and (v/V)^2 of 0.8, it is 197 lb/ft^2.

As I understand things, at typical GA airspeeds and wing loadings we'd only see (negative) pressures like that near the leading edge and only during an aggressive pull-up. I hope this example is right: At 150 KTS (sea level) "q" = 0.53 psi. So, that's the (max) positive pressure we'd be getting (at the stagnation point of the airfoil, assuming incompressible flow). For negative pressure: If we pull and attain an 8 degree AoA at that speed, a NACA 4412 airfoil will achieve a pressure coefficient of -1.0 to -1.7 from about the LE to the 1/4 chord point*, so that would get us to -0.53 to -0.9 psi over that limited area, but we wouldn't reach -1 psi. TOWS says we'd get a Cl of about 1.1 at that AoA, or about 84 lbs of lift per sq ft of wing. That's a lot for most GA aircraft that are typically designed for <15psf wing loadings at MTOW and 1G.
Look at TOWS appendix 1. Suction everywhere except the first few percent around the stagnation point.

But, leaving that aside, let's go with -1 psi. Per your calcs (again--thanks!), if our panel width is 6" and our (bare) foam is 1.1" thick under the skins, the deflections (with FG triax skins) are expected to be .001".

Here's diagram from Post 11 with some fairly aggressive holes. The grid is 1". The skins are about 1" thick and none of the spans reach 6." Between the LE and the rear spar, 45% of the foam has been removed. The removed foam weighs 1.2lb per foot of span (30 lbs off the empty weight if our span is 25').

Removing the foam is more trouble than leaving it in place. But if we can save the weight, keep the skin smooth enough to retain laminar flow, and do it while retaining a safe wing structure, I think it might be attractive to some designer/builders.

The big question (and not an assignment for anyone): When removing this foam, is skin deflection under air load the only concern? With 1" foam under the skin laminate supported by skin-to-skin 70 PSI XPS foam every 6", is there any risk of skin buckling due to compression loads on the skin? I've heard frequently (and believe) that these loads on the foam are very small as long as the skin is kept in plane, but when it is under deflection due to air loads the skin isn't in plane.
Oh, it can work. Skin deflection does not seem to be as big an issue as I thought it might. Foam stresses on the inside surfaces look to be the driver for how much foam has to be left in. Then there is the issue of fatigue of this exposed surface foam. We have not even gotten into that yet. Then if 1.02 psi can threaten the foam, imagine someone slipping on the wing and driving a hand down, making 50 times that pressure over a few square inches. First there is a strange crunch, then a thump as we see the fiberglass skin oilcanning back to shape with cracked paint, then the sounds of a grown man sobbing. How likely this is will come out of your testing...

And then there's the KR . . . .
KR's used polyurethane foam - IIRC, it has higher strength and higher stiffness than EPS foam, so better margins.

It can work, it is just a matter of designing it to stand the foreseeable abuse and then staying within that level of loading. Which could be less impact tolerant than the skin systems we are used to.

Billski

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#### Vigilant1

##### Well-Known Member
Thanks, Billski. I appreciate the work.

Fatigue of the inner foam surface: I suppose cyclic load testing would be the way to answer that, unless manufacturers have the data or there's a "natural experiment" out there somewhere with long-term foam flexing at these same strain levels.
Environmental effects on exposed foam: You mentioned vermin. UV shouldn't be a factor. Maybe, long term, other oxidative agents (ozone, etc).

Who thought this was a good idea? I'm not entirely dissuaded yet.

The key, apparently, is moderate loadings, moderate unsupported spans . . .and moderate expectations.

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#### ragflyer

##### Well-Known Member
The key, apparently, is moderate loadings, moderate unsupported spans . . .and moderate expectations.
or use a high E skin like carbon fiber. This limits deflection and hence reducing the stress on the underlying foam allowing you to remove more of it.

#### stanislavz

##### Well-Known Member
HBA Supporter
Are you asking for deflection of a massive core under the aero loads? If yes, Massive core deflection at any spot along the chord is estimated by a standard relationship:
Hi. No, i am just trying to find single skin deflection with 10 times denser support.

If all else is same - making support 10 denser, will give 10^4 less deflection ?

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#### Vigilant1

##### Well-Known Member
or use a high E skin like carbon fiber. This limits deflection and hence reducing the stress on the underlying foam allowing you to remove more of it.
My own interest would primarily be in using CF skins, especially as the price has come down. As thin as I'd like them to be, though, maybe stiffness wouldn't vary much from the thicker FG laminate Billski calculated, but I'm not sure. We need a "weighs very little, absorbs little epoxy, doesn't rot or warp, will bend around a leading edge" 1mm thick interlaminate core..something that sells for about 25 cents psf, just to guild the lilly.

I am very appreciative of the calculations as they are, though. I'm pretty confident I won't find a handy web-based Roarke Panel Deflection Calculator online somewhere, which is a pity.

#### wsimpso1

##### Super Moderator
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Hmmm, you know how when you have analyzed something, and then go to explain what you did to someone, you sometimes catch an error in your algebra or your execution. Well, I am embarrassed to admit it, but I did, fixed my Excel file, and have edited post 193 and 207. Post 197 was correct. Things still look less sturdy than I would feel good about, but it is not my bird.

Now to questions

Hi. No, i am just trying to find single skin deflection with 10 times denser support.
...
If all else is same - making support 10 denser, will give 10^4 less deflection ?
What is "10 times denser support"? You will have to describe how you get better support for that to have meaning. E*t^3/12 is bending stiffness of the plate section made of a homogenous material. Go to composites and we can sum up EI for the sandwich. you can see that it is sensitive to the third power of thickness, but only the first power of Young's Modulus.

Looking at sigmamax and remembering that this math is simplified for homogenous panels, we have a coefficient, pressure on the panel, short side length squared and divide thickness squared. Bending absolutely dominates this situation, and the shear stress in the panel has been neglected. You can put that in later and compute the entire stress state if you want. I/r = S = (t^3/12)/(t/2) = t^2/6. So t^2 = 6*S = 12*I/t. If we back out to a more general composite plate theory, then compute an equivalent I/r or S for the panel, then we can calculate stresses. While it looks like E of the components is not included, it is in the calculation of equivalent S or I/r. In the OP's case of glass on one side of foam, the inside surface is foam and sees substantial stresses. In my calcs, that is where we appear limited and drives us to pretty thick foam without even considering all of the loads for this case. S and I are terms used for computing stresses, and the thickness of the foam contributes, so they might be "support".

Looking at ymax and remembering that this math is simplified for homogenous panels, we have a coefficient, pressure on the panel, short side length to the fourth power and divide by Young's modulus and thickness squared. If we back out to a more general composite plate theory, then compute an equivalent EI for the panel, then we can calculate stresses. In the OP's case of glass on one side of foam, we appear to be pretty good shape on deflection than I had expected. EI is bending resistance of beams and plates, and the thickness of foam contributes, so this term might be "support".

I hope this long answer clarified the situation.

Billski

#### stanislavz

##### Well-Known Member
HBA Supporter
Hmmm, you know how when you have analyzed something, and then go to explain what you did to someone, you sometimes catch an error in your algebra or your execution. Well, I am embarrassed to admit it, but I did, fixed my Excel file, and have edited post 193 and 207. Post 197 was correct. Things still look less sturdy than I would feel good about, but it is not my bird.

Now to questions

What is "10 times denser support"? You will have to describe how you get better support for that to have meaning. E*t^3/12 is bending stiffness of the plate section made of a homogenous material. Go to composites and we can sum up EI for the sandwich. you can see that it is sensitive to the third power of thickness, but only the first power of Young's Modulus.

Looking at sigmamax and remembering that this math is simplified for homogenous panels, we have a coefficient, pressure on the panel, short side length squared and divide thickness squared. Bending absolutely dominates this situation, and the shear stress in the panel has been neglected. You can put that in later and compute the entire stress state if you want. I/r = S = (t^3/12)/(t/2) = t^2/6. So t^2 = 6*S = 12*I/t. If we back out to a more general composite plate theory, then compute an equivalent I/r or S for the panel, then we can calculate stresses. While it looks like E of the components is not included, it is in the calculation of equivalent S or I/r. In the OP's case of glass on one side of foam, the inside surface is foam and sees substantial stresses. In my calcs, that is where we appear limited and drives us to pretty thick foam without even considering all of the loads for this case. S and I are terms used for computing stresses, and the thickness of the foam contributes, so they might be "support".

Looking at ymax and remembering that this math is simplified for homogenous panels, we have a coefficient, pressure on the panel, short side length to the fourth power and divide by Young's modulus and thickness squared. If we back out to a more general composite plate theory, then compute an equivalent EI for the panel, then we can calculate stresses. In the OP's case of glass on one side of foam, we appear to be pretty good shape on deflection than I had expected. EI is bending resistance of beams and plates, and the thickness of foam contributes, so this term might be "support".

I hope this long answer clarified the situation.

Billski
Can you provide deflection for supports spaced 2.4" inch same load, same lamina.

10 time denser 2.4 in place of 24 inch.

#### Vigilant1

##### Well-Known Member
KR's used polyurethane foam - IIRC, it has higher strength and higher stiffness than EPS foam, so better margins.
I bought some PU foam for a home project awhile back, it is nice and hard. Good R-value and easy to work with. The price was right-- \$10 for 2" x48" x 48" panels taken off an industrial flat roof, very good condition. Seems like an attractive material for forming with saws, files, and abrasives, but I've also heard of issues with friability at the foam/laminate interface (similar to the Last-a-foam issue/debate). I'm sure there are various types of PU foam, perhaps with different plasticizers and resilience properties, so maybe some brands/types are more suitable than others.

Hmmm, you know how when you have analyzed something, and then go to explain what you did to someone, you sometimes catch an error in your algebra or your execution . . fixed my Excel file, and have edited post 193 and 207.
Thanks for the fix/edit. I revised the portions of your posts that I quoted.

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#### Tiger Tim

##### Well-Known Member
How about building wings like the deHavilland Technical School's TK.4 light racing plane. It was built by students back during the 1930s. Wings were made of huge balls wood blocks. Vertical holes removed some balsa to lighten the structure, then the entire wing was wrapped in plywood. Only one was built and it crashed a few months later.
Could this technique be updated with modern foam and composites?
I believe only the control surfaces of the TK.4 were balsa cores sheeted in thin plywood. The majority of the wing was a couple box spars and two(?) diagonally-planked skin layers, similar to the Comet and Mosquito. I bet the de Havilland Don and Albatross used similar structures though I’m not certain.

EDIT: Found the cutaway I was thinking of. It’s an elegant little thing the way it’s put together and it ought to make a fun little hot rod nowadays.

#### Riggerrob

##### Well-Known Member
Dear Tiger Tim,
Thanks for finding that cutaway drawing of the deHavillland T.K. It shows balsa-cored control surfaces with cylindrical lightening holes like I suggested. deHavilland students glued balsa ribs into the vertical and horizontal stabilizers. It also appears to have solid balsa wood stiffening the slot and wing leading edge.
When we look at the fuselage construction, we wonder if Ken Rand peeked at T.K. 4 drawings before building his first foam and fibreglass airplane ... or did Mr. Taylor look at T.K. 4 before designing his Taylor Monoplane and Titch which inspired Ken Rand?

#### blane.c

##### Well-Known Member
HBA Supporter
Dear Tiger Tim,
Thanks for finding that cutaway drawing of the deHavillland T.K. It shows balsa-cored control surfaces with cylindrical lightening holes like I suggested. deHavilland students glued balsa ribs into the vertical and horizontal stabilizers. It also appears to have solid balsa wood stiffening the slot and wing leading edge.
When we look at the fuselage construction, we wonder if Ken Rand peeked at T.K. 4 drawings before building his first foam and fibreglass airplane ... or did Mr. Taylor look at T.K. 4 before designing his Taylor Monoplane and Titch which inspired Ken Rand?

I think the direction of the lightening holes is very enlightening.

#### stanislavz

##### Well-Known Member
HBA Supporter
I think the direction of the lightening holes is very enlightening.
But only for aft part of wing it have too much of span wise distorsions for any laminar flow.

#### wsimpso1

##### Super Moderator
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Log Member
The different densities would be to save weight without creating voids.
It would have to be lighter than 1.9 lb/ft^3;
It would have to be about as strong and tough as our 1.9 lb/ft^3 foam;
It would have to be silicone free, so that all bonding will stay bonded;
It would have to be readily cut with a hot wire saw;
It would have to not make deadly fumes when hot wire cut;
It would have to bond using epoxy;
It would have to be commercially available.

Right now, the only commercially available foam that we know hotwires safely is polystyrene. The others either cut nicely but can kill you, or do not cut. Some do not cut well and can kill you. That narrows the field. Polystyrene lighter than 1.9 pcf exist at a bout 1.6 pcf as white popcorn foam, but they are crumbly, soft, etc. Think coffee cup foam, but more fragile. I use the stuff for tooling.

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. A 2" thick piece of standard foam weighs 0.32 pounds/ft^2. For a 2" thick piece of lighter foam to weigh the same including the glue line, it would have to be 0.19 pounds/ft^2 or 1.15 lb/ft^3. That is to weigh the same. So to go lighter, it would really have to be 1.1 pcf or lighter. If anyone finds any of this frozen smoke, please let us all know the brand name and suppliers we can get it from. If someone can get me a sample and it survives being mailed to me, I will build one of my standard laminates on it and send it to V1 for his tests.

Billski

#### wsimpso1

##### Super Moderator
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Log Member
Can you provide deflection for supports spaced 2.4" inch same load, same lamina.

10 time denser 2.4 in place of 24 inch.
Come on Stan, you supplied the page from Roark's... OK, I will interpret the equations for everyone else.

Rib spacing 1/10th of before. "b" is rib spacing in the equations. I will make the assumption that "a" - the chordwise size of the panel - is more than twice b. Stress goes with b^2, deflection with b^4. So, chopping b to 1/10 of what it was and keeping the skin foam thickness between ribs WILL decrease stress by 1/100 and decrease deflection by 1/10,000. Since the original deflection was 0.009, dividing that by 10,000 will be way less than 0.001". Good luck ever measuring it.

If you skip the foam between ribs, and only have 2 plies of BIAX, the skin will bulge 0.273" with panels 24" wide. That may violate the "small deflections" assumptions in doing the calcs. Anyway, chop b to 2.4 and deflection is below 0.001". I suspect you will not need to go quite that small on your rib spacings.

Have fun.

Billski