Do you have a number for the pressure difference

between the inside and outside of a wing?

Just curious ,it must be a fraction of one psi, and vary with construction and airifoil.

.5 psi=72 lbs ft which might be a design consideration in its own right.

Push me for data? I just ran some numbers so we have data.

- TOWS page 371, for NACA 65sub2 A015 foil. This page plots v/V for all foils with this thickness distribution. Top surface with the wing making Cl = 0.22, shows (v/V)^2 = 1.53 from about 5% to 45% of chord;
- Making up a suitable example, let's put this wing at 150 knots, which is 254 ft/s. Multiply that by the square root of 1.53, and local velocity is 314 ft/s over what should be the laminar portion of the wing;
- Let's also say the wing panel between rivet lines is 12" on a side and 0.040" thick;
- Applying that to Bernoulli's Principal, deltaP = 1/2*rho*v^2. Using rho for standard temperature and pressure at seal level of 0.002378 slugs/ft^2, I get 117 lb/ft^2 or about 0.82 psi. This pressure is pulling the panel away from the wing everywhere from 5%c to 45%c;
- Then I went to Roark's formulas for stress and strain to get max deflection at the center of a square plate supported at the edges. Formulae are the same for simply supported and fixed edges, but coefficients are smaller for deflection with fixed edges, which will be closer to reality if the skin continues beyond the supported edge and into another panel;
- Deflection in the center of the 12" square panel 0.040" thick with fixed edges is 0.35";
- Deflection of the same panel with 0.080" thickness with fixed edges is 0.042";
- Deflection of the same panel with 0.125" thickness with fixed edges is 0.011" - finally getting there;

- You can achieve similar reductions in deflections by making the panels smaller - more ribs and false spars and a lot more build complexity and rivet lines;
- If you have about 100 square feet of wing skin that you will thicken your wing from 0.040 to 0.125" to get laminar flow, you will add 134 pounds to the airplane - is that worth it for the drag reduction you got?

Now if somehow you manage to get 0.82 psi of suction on the inside of the wing at that speed and Cl, you will have an undistorted skin from 5% to 45%. Unfortunately, the wing will have lower Cl as you go out the span, requiring less pressure further out to balance the drop in pressure of the wing - that could be interesting (in a bad way) to manage. And I only selected the Cl where the (v/V)^2 is flat over the laminar region. At lower Cl, the (v/V)^2 starts lower and increases as you go aft. At higher Cl the peak (v/V)^2 is close to the leading edge and drops off the whole way aft, so matching the pressure differences as you go chordwise could get interesting too.

So you would have to adjust the pressure curves applied to the inside of the wing with airspeed, Cl, chordwise position, and spanwise position. I am not sure how you can actually get a vacuum source with that much volume capability from around the airplane (what with the way metal wings leak air), much less adjust it panel by panel.

This is why I said I do not believe you can get there at reasonable weight with thick skins, and why I am skeptical of folks telling us you can balance that pressure with strategically picked vents for the wing...

If you want extensive laminar flow at reasonable weights, you really need skins with much higher bending stiffness - composites with cored skins do the job nicely and at low weights. Composites over massive cores will do it too.

And yes, this becomes a design issue all by itself. As the airspeed goes up, the stresses in the skins and ribs go up too, with the square of airspeed. At my Vdive of 268 knots, I have had to do some design work and then build a stout bird. The beefup for faster airplanes is usually OK, as wing torsional and bending stiffness also have to go up to keep ahead of flutter.

Billski