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I have read about the lift of airfoils a lot recently and just want a few things cleared up.

  1. When incoming airflow hits a typical cambered airfoil and diverges into “top” and “bottom” air flows, why does the top have a low pressure and the bottom a high pressure?

    My thoughts: From what I've read on this site and online, the top airflow creates a sort of “vacuum”, and by Bernoulli's theorem & the Coanda Effect, a lower pressure region relative to atmospheric is created just above it. However, why doesn't the bottom air flow also create a vacuum similarly? Since the bottom airflow also has a velocity >0, won't it create a vacuum underneath the airfoil rather than a High pressure region?

  2. Why is bottom airflow slower than top airflow?

    My thoughts: I don't know. I know that the “equal transit theorem” is inaccurate and incorrect.

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It has everything to do with geometry.

(for a complete story, here's a good link)

The answer is really that it's a bit complicated because there's many ways to cause the effect, for varying aircraft. The low pressure is typically caused by the curvature of the wing. The top of the wing is more often more convexly curved than the bottom -- that's why the pressure isn't symmetric . This effect can also be caused by modifying the angle of attack. In general, we find the long haul aircraft (such as 747s) gain as much lift as they can from the curvature of the wing because getting lift through angle of attack means you pay a cost in drag. Drag is the enemy of long-haul planes. Acrobatic planes, on the other hand, tend to have roughly symmetrical wings because they want to be able to fly upside down. They generate almost all of their lift via varying their angle of attack. At higher angles of attack, the top of the wing becomes a "leeward" side, where air has to be pulled from above in order to fill in the shadow (of sorts) behind the wing.

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To get to the bottom of it, it might help to look at airflow at a molecular level:

Every air molecule is in a dynamic equilibrium between inertial, pressure and viscous effects:

  • Inertial means that the mass of the particle wants to travel on as before and needs force to be convinced otherwise.
  • Pressure means that air particles oscillate all the time and bounce into other air particles. The more bouncing, the more force they exert on their surroundings.
  • Viscosity means that air molecules, because of this oscillation, tend to assume the speed and direction of their neighbors.

Flow over the upper side of the wing

Now to the airflow: When a wing approaches at subsonic speed, the low pressure area over its upper surface will suck in air ahead of it. See it this way: Above and downstream of a packet of air we have less bouncing of molecules (= less pressure), and now the undiminished bouncing of the air below and upstream of that packet will push its air molecules upwards and towards that wing. The packet of air will rise and accelerate towards the wing and be sucked into that low pressure area. Due to the acceleration, the packet will be stretched lengthwise and its pressure drops in sync with it picking up speed - at least at subsonic speed. Spreading happens in flow direction - the packet is distorted and stretched lengthwise, but contracts in the direction orthogonally to the flow. Once there, it will "see" that the wing below it curves away from its path of travel, and if that path would remain unchanged, a vacuum between the wing and our packet of air would form. Reluctantly, the packet will change course and follow the wing's contour. This requires even lower pressure, to make the molecules change their direction. This fast-flowing, low-pressure air will in turn suck in new air ahead and below of it, will go on to decelerate and regain its old pressure over the rear half of the wing, and will flow off with its new flow direction.

Airfoil in wind tunnel with smoke trails indicating flow

Approaching the speed of sound, this stretching is accompanied by a thinning of the air - density decreases as speed increases. The streamtube will contract less, so more air needs to move away to make space for the approaching aircraft. At the speed of sound, the thinning from acceleration is exactly balanced by the expansion of the stream tube from the drop in density, and the aircraft cannot squeeze through as easily as before - this is the sound barrier. At supersonic speed this expansion becomes dominant, and luckily is accompanied by an increase in density when the flow slows down. Now the air in the streamtube decelerates and contracts from the increase in density, again allowing the aircraft to squeeze through. Therefore, supersonic lift is no longer caused by camber and curvature, but by the aircraft's inclination toward its direction of movement which causes a pressure increase on the lower side of the wing.

Back to subsonic flight: Here, lift can only happen if the upper contour of the wing will slope downwards and away from the initial path of the air flowing around the wing's leading edge. This could either be camber or angle of attack - both will have the same effect. Since camber allows for a gradual change of the contour, it is more efficient than angle of attack.

Flow over the lower side of the wing

A packet of air which ends up below the wing will experience less uplift and acceleration, and in the convex part of highly cambered airfoils it will experience a compression. It also has to change its flow path, because the cambered and/or inclined wing will push the air below it downwards, creating more pressure and more bouncing from above for our packet below the wing. When both packets arrive at the trailing edge, they will have picked up some downward speed.

Behind the wing, both packets will continue along their downward path for a while due to inertia and push other air below them down and sideways. Above them, this air, having been pushed sideways before, will now fill the space above our two packets. Macroscopically, this looks like two big vortices. But the air in these vortices cannot act on the wing anymore, so it will not affect drag or lift. See here for more on that effect, including pretty pictures.

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The top actually has a varied contour pressure, in front starting from the edge of the wing up to part of the front leading edge it has even positive pressure because of wing drag, but over most of the rest of the area of the back of the wing it has negative pressure because the flow of air is bent down.

Many new theories about lift do not assume the Bernoulli principle as the main reason for lift, because it can not explain why the planes can fly upside down. They consider a complex mix of factors such as conservation of mass in the boundary layer, bending of the flow, and Bernoulli effect. However, it is important the boundary layer doesn't separate from the back of the wing causing stall.

Generally, the idea is the fact that both top and bottom of the wing bend the stream of the air boundary layer, they change the momentum of the air downward, and cause pressure deference on top and bottom and as per Newton, the cause an equal and opposite force, lift, on the wing.

The other component of lift is the tilted flux of the air over the top of the airfoil leaves a semi vacuum zone trailing above it which optimally could be a very strong force considering the theoretical limit of 1-atmosphere pressure on the back of the wing.

The real dynamics of lift are very complex and the factor CL, coefficient of lift which has to do with the airfoil profile and its aspect ratio, camber and chord length and some other properties is mostly determined in wind tunnels.

There are some incorrect explanations in even scientific or professional literature about lift, (I am a private pilot), and some correct but complex theories. Here is a link to Wikipedia page on lift, which is trying to explain the wrong and correct theories.

Lift force

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  • $\begingroup$ I read this section of the Wikipedia article, "When a fluid follows a curved path, there is a pressure gradient perpendicular to the flow direction with higher pressure on the outside of the curve and lower pressure on the inside.[59] This direct relationship between curved streamlines and pressure differences, sometimes called the streamline curvature theorem..." From what i understand from this, both top and bottom airflows along the curves of the aerofoil follow a curved path and therefore should have higher pressures above the curve? Why is this not the case then? $\endgroup$
    – user2935073
    Commented May 6, 2019 at 6:24
  • $\begingroup$ @user2935073, it may be kind of centripetal force that tries to peel off the boundary layer from the back of the wing. yes that could be one component but it looses its effects in fast speeds near or above the speed of sound. one factor that predominantly applies is bending the flow of stream. $\endgroup$
    – kamran
    Commented May 6, 2019 at 6:36
  • $\begingroup$ this is too much to process right now. just gonna hope it doesn't turn up in my final the day after. fingers crossed. $\endgroup$
    – user2935073
    Commented May 6, 2019 at 8:07
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For the layman:

Visualize the typical wing with the front (Left) slightly raised:

like this: '\' but only slightly.

More like this ' - .

It is moving left " <---. "

The air moves past wing to the right 'air --> ' - . wing

Look at the bottom. It is moving toward the air. It pushes on the air just like you push on the water in a pool when you try to run. You can feel the pressure you cause by pushing when moving toward the water. Same with the wing.

So, there is a little more pressure under the wing.

Above the wing, the air follows the curve. (BTW, this is NOT Coanda. It is a little similar, but it is not truly Coanda). Don't worry about why we just know it follows the curve path over the wing. Also, it is the PATH of the air that is important, not simply the wing's shape. CURVED FLOW PATH.

This air is going around a curve just like you on a playground merry-go-round. You try to go straight but are pulled in a curve, so YOU are pulling away from the center of the curve.

On the wing, the air tries to pull away from this curved path which lowers the pressure at the surface.

[ NO Bernoulli. Fast air does not cause pressure to decrease. The fact is that higher pressure behind that air pushes it faster, so THAT is why it is moving faster when it gets to the low pressure - pressure behind is pushing it faster.]

SO, there is a little less pressure at the upper surface.

That's lift... a pressure difference top to bottom: More under pushing up than what's pushing down from above. The result is a 'net' upward push.

In addition, The pressures created BY the relative MOTION (of wing and air) ALSO cause all the other air movement around the wing as it passes by. I won't go into detail here, but see my references below.

It is those same pressures that also push a bunch of air down which satisfies Newton's Third Law that other people like to say "caused" lift.

Summary:

  • Movement, pushes air around, causing pressure changes.

  • Fortunately, these changes push the wing up AND some air down.

  • Done.

Please, Lemme' know if this helps.

Some other answers address some of this but are pretty complicated. - - Regards, Steve

P.S. Bernoulli does not teach us that fast-moving air has lower pressure. This is bad science repeated by way too many people.

Here are my full explanations:

https://www.quora.com/profile/Steve-Noskowicz/Understanding-Bernoullis-Principle

https://www.quora.com/profile/Steve-Noskowicz/Understanding-Lift

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