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