# Which is more efficient, thickening an airfoil or adding a bottom-surface curve?

So if you were to take a standard airfoil and increase the thickness, you’d increase the lift (Bernoulli’s principle), but it would also increase the drag.

Now imagine you have the same airfoil, but instead add a curve to the bottom instead of making it thicker. Doing that would increase the lift also (Newtons 3rd law).

So to achieve say 5 pounds of lift extra, would it be more efficient (less drag) to make the wing thicker or add a curve to the bottom, similar to the curves seen in supercritical airfoils?

Edit : What is meant by “add a curve to the bottom”

• Not a bad question really. Much of airfoil design and performance depends on airspeed. Generally, if one wants more lift go faster, as lift is proportional to V$^2$. Wing design depends strongly on Reynolds number. Commented Apr 10 at 13:12

So if you were to take a standard airfoil and increase the thickness, you’d increase the lift

No, you don't. Lift is determined by camber and angle of attack. Both don't change with thickness, so lift also does not change. However, the thicker wing allows for more spar height, so a wing of the same area can be built lighter. This gives you less wing weight and more lift remains for carrying fuselage, fuel and payload.

Drag will also rise, dramatically so at transsonic and supersonic speed.

Now imagine you have the same airfoil, but instead add a curve to the bottom instead of making it thicker. Doing that would increase the lift also

Wrong again. Now you decrease camber, so the wing will create less lift at the same angle of attack and dynamic pressure. All what I said above also applies to this case.

New comment after the editing of the question:

The airfoil you show is by no means a standard wing airfoil. It looks more at home in a gas turbine. Such very highly cambered airfoils are not used in airplane wings precisely because they only work well in a very narrow angle of attack range. Generally, filling up the hollow bottom will widen that range and reduce drag at lower angles of attack. It also will make them look more like a standard airfoil (that would be older ones like the Gö 549 and the Clark Y, both of which were used to define the 4-digit NACA range). Still, it will result in a much too thick airfoil and will show separation over the full angle of attack range due to its excessive thickness. Drag will be horribly high.

• Oh okay, thanks. So I always thought adding a curved bottom to an airfoil would increase lift. Isn’t that how supercritical airfoils compensate for the flatter top? Commented Apr 10 at 15:16
• Also isn’t adding a curve to a supercritical airfoil what makes it have high rear loading? (See new edit to know what is meant by “adding a curve”) Commented Apr 10 at 15:36
• @Wyatt Don't add or subtract curves, but define a camber line and add an aerodynamic shape around it. Commented Apr 10 at 16:18
• Ah okay, yeah that edit made it more clear. So basically a higher cambered airfoil (like the one in the picture I edited in) will make more lift, but only at certain AoA ranges? (Last question because I don't want to keep asking tons of questions) Commented Apr 10 at 19:43
• @Wyatt Yes, right. Commented Apr 10 at 23:15

So if you were to take a standard airfoil and increase the thickness, you’d increase the lift.

This is true only till around 12% thickness, afterward the $$C_{l_{max}}$$ decreases with increasing thickness. This plot shows this behaviour quite clearly (source):

This would also increase thickness unless the shape of the bottom is concave (or unless you mean something else).

So to achieve say 5 pounds of lift extra, would it be more efficient (less drag) to make the wing thicker or add a curve to the bottom, similar to the curves seen in supercritical airfoils?

Increasing the thickness increases drag, mainly because the airfoil has a bigger surface and a bigger pressure recovery on the rear part (and a bigger divergence drag if used at transonic speeds). So if you can choose then it's better to trim the camber of the airfoil than increase its thickness.

• Note, this is a chart for CLmax, not for CL at fixed alpha. Perhaps that is what the OP was asking about, but the question was far from clear. Commented Apr 10 at 15:06
• @RobMcDonald I added a picture to maybe clear some confusion up. Commented Apr 10 at 15:31
• No, your figure adds nothing to the conversation. The curve of an airfoil is defined by the mean camber line. The thickness is measured from that. You don't just add thickness or curvature to the bottom or top. Thickness is added to the camber line - which is the middle and can be curved. Commented Apr 10 at 16:47
• The other potential confusion is whether you were asking about increasing lift at a fixed angle of attack -- say how much lift at three degrees. Or if you were asking about increasing the maximum lift possible that can be attained by a particular airfoil at any angle of attack. Peter and I are answering about lift at a fixed angle of attack. sophit is answering about maximum lift capability. Commented Apr 10 at 16:49
• I think @sophit is referring to coefficient of lift, which is fairly linear in the useful AoA range. Commented Apr 10 at 18:35

Don't cite Bernoulli's principle and Newton's 3rd law as causal in an aerodynamics discussion -- everything is far more complex and nuanced than that.

You can't add curvature to just the bottom.

You should learn about thin airfoil theory.

You were doing fine until you threw in "supercritical airfoils". Now we have to go over all 130 years of modern aviation. A bit much for one question but ...

Yes, adding undercamber will increase the lift coefficient. This is what we do with slats and flaps. Supercritical airfoils add a little undercamber in the back to help balance the center of pressure with the lift created by the top front portion of the wing. By design, most of the upper curvature, or camber, must be removed from the top of the wing to avoid a draggy supersonic shock wave from forming there.

Going back in time to the Davis airfoil, flying at less than Mach 0.5, designers took full advantage of upper curvature because it by far has a higher Lift/Drag ratio than lift produced by undercamber as long as the Reynolds number is high enough (> 500,000) to use it.

Designers of the Davis airfoil found that moving the area of maximum camber back a little delayed onset of drag producing turbulent flow (increasing span and shortening chord (higher Aspect Ratio) does the same).

"Laminar" wings, essentially turning a classic airfoil backwards, were tried. The stall characteristics proved difficult to manage but the idea can be seen in ... the hull of an Iowa class battleship! A sharp leading edge with very little camber will make the flow of the working fluid smoother along the surface, minimizing disruption of the boundary layer.

Further back in time, when airspeed was not high enough to take advantage of "top lift", undercambered wings were favored. Not surprisingly, early aviators modeled their wings based on birds.

In the second decade of the 1900's, designers found that thicker heavily cambered wings with convex bottoms were not only stronger ... but also had lower lift to drag ratios! (if they went fast enough).

Amazingly, some held on to the belief that thinner wings were better, and, when Mach effects became significant, they had their day.