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I find myself confused when comparing the lift generation amongst Thick and Thin Airfoils.

A paper to which I have added reference below claims that thin airfoils are better in generating lift because of which birds tend to have thin curved wings.

But an article from the NASA website, claims the opposite. And many other sources as well claim that thick airfoils produce greater lift.

Can someone please elucidate? Any help is appreciated,Thanks!

On the thin aerofoil, the amount of flow curvature below the wing is comparable to that above it and we might conclude that the overpressure on the underside is just as large as the suction on the upper surface— the two sides contribute almost equally to the lift. In the case of the thick aerofoil, however, there are regions of different senses of curvature below the lower surface. This suggests that there will be areas with suction as well as areas with overpressure. In this case, the lower surface does not contribute much resultant force and we can conclude that thin aerofoils are better at generating lift.

Babinsky, Holger. (2003). How do wings work?. Physics Education. 38. 497. 10.1088/0031-9120/38/6/001.

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Lift is mainly a result of AoA and camber. Thickness has a very small effect, so much so that some aerodynamic theories disregard it entirely. It mostly has an effect on drag and it should be relatively high for subsonic aircraft so that the airfoil can operate at a wide range of AoAs without stalling. It should also be high so that the moment of inertia of the cross sections is high and therefore less stress on structural components. And perhaps most obviously, it should be high so that the fuel tanks fit inside the wing.

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Babinsky, Holger (2003) are absolutely correct in pointing out that overpressure underneath the wing will contribute to lift.

However, this is not necessarily related to "thickness", which is more related to strength.

Scale is extremely important in aviation design: to support its own weight, scaling a sparrow up to a Piper Cub requires a wing that can support several thousand kg (don't forget manuvering G forces). This will no doubt require a proportionally thicker wing$^1$.

As mentioned in the above reference, curvature, or camber, determines lift at a given speed, wing area, Angle of Attack, aspect ratio, and air density.

At first glance, the thin wing would have the advantage of creating over pressure under the wing to enhance lift, but thicker wings in even the largest planes also have this trick up their sleeves by using ... slats and flaps for lower speed flight. The "thick" wing will also have curvature on its upper surface, which leads to another very important consideration: Reynolds number.

Reynolds Number = Velocity × Chord/Kinematic Viscosity

Kinematic viscosity for air is 1.46 × 10$^-5$, the units are meters and seconds

This will lead to a better understanding why larger, faster aircraft fly more efficiently using "top lift". A look at Reynolds number vs Lift/Drag ratios on Airfoiltools will show a marked increase in L/D ratios as Reynolds numbers rise from 10$^3$-10$^4$ typical of birds to 10$^6$-10$^7$ typical of aircraft.

Larger, faster aircraft can streamline the bottom of the wing, adding strength and reducing drag, by relying on more efficient "top lift". Here, the legend of the "thick wing" was born, exemplified by fighter designs of the Luftstreitkrafte and the Davis wing years hence. Thickness and curvature also become relevant as velocity approaches the trans-sonic and super-sonic realms (critical Mach number), where shockwave drag effects favor thinner wings with less camber.

Bird wings are generally too small and slow to take full advantage of the famed "Bernoulli" top lift effect. One may realize a diving hawk may cross into higher Reynolds numbers, but they solve this issue with ... variable geometry, by folding their wings!

enter image description here

$^1$ early aircraft builders supported their beloved thin
undercambered wings with cables, and by stacking the wings
(biplane), created very strong, light truss structures.
Emphasis on reducing drag would come later with higher speeds, enabled by more powerful motors.

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