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Now this seems to be the question of the ages, and various questions on this site regards it.

The often told description of lift is that it is due to air traveling faster over the wing than under it, creating pressure differences according to the Bernoulli equation.

This however, makes little sense to me and as I've read it is entirely false. Particularly interesting is this article where the author writes that

Those with this view must also believe that one can pinch with one finger and clap with one hand.

I had settled with the description that lift is caused by the downwash of air which imparts an equal but opposite force on the wing itself. As noted in the linked article, the downwash is attributed to the impact of air on the lower side of the wing constituting some, albeit little of the lift, and the air on top of the wing being curved downwards following the coanda effect.

Now, my confusion was re-initiated as I am currently reading "Aircraft Design: A Conceptual Approach" 6th edition, by Daniel P. Raymer - a highly regarded aerospace engineer.

In the 4th chapter on airfoil and wings, he writes:

An airfoil generates lift by changing the velocity of the air passing over and under itself. The airfoil angle of attack and/or camber causes the air over the top of the wing to travel faster than the air beneath the wing. Bernoulli's equation shows that the higher velocities produce lower pressures, so that the upper surface of the airfoil tends to be pulled upward by the lower-than-ambient-pressures while the lower surface of the airfoil tends to be pushed upward by the higher-than-ambient pressures.

Now I cannot imagine Raymer to have any misunderstanding on what causes lift, which makes me very curious about this statement.

The pressure difference found in calculations by using the Bernoulli equation and an equal transit time is much insufficient to lift an aircraft and windtunnel experiments show that the air on the top of the wing reaches the trailing edge much sooner than the air traveling below the wing.

Is it a simplification to avoid becoming too technical and into the "physics" for the average reader - or is something else going on? It is very difficult to become confident in what actually causes lift with a seemingly endless number of descriptions.

As a side note: on the bottom of the page in the book, this common dispute is mentioned and told that this view of lift is completely correct as is the Newtonian downwash description.

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  • $\begingroup$ Ultimately lift is the equal and opposite force generated by deflecting air downward. And consider a wing with a lower surface at an angle to the relative wind and a flat top surface exactly parallel with the relative wind. $\endgroup$
    – Jim
    Jul 7 at 22:08
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    $\begingroup$ Does this answer your question? How do wings generate lift? $\endgroup$ Jul 7 at 23:46
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    $\begingroup$ Recent (2020) write-up in the Scientific American "No One Can Explain Why Planes Stay in the Air", including references to the most relevant sources: scientificamerican.com/article/… $\endgroup$ Jul 8 at 10:45
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    $\begingroup$ Money. This is actually an aeronautical engineering joke I learned before transferring out of aeronautical engineering as a freshman 52 years ago and represents the only thing I took with me from that field. $\endgroup$ Jul 10 at 23:59
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    $\begingroup$ @Wasserwaage That article is a disgrace to Scientific American. It simply claims we could not explain Bernoulli's law when we actually can (conservation of energy). Being a private pilot himself, I guess the author simply listened too much to the "expert" opinion of other hobby pilots and their uneducated drivel. $\endgroup$ Jul 12 at 5:18

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Just because someone has access to an editor and a webpage does not mean that they understand the topic they write about.

Short answer: Raymer and Bernoulli are right. The finger-pinching / hand-clapping comparison is silly.

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. Spreading happens in flow direction - the packet is distorted and stretched lengthwise, but contracts in the direction orthogonally to the flow. This contraction, by the way, is necessary so the air can move out of the way of the wing. The thickness of the wing alone already causes this acceleration and stretching on both sides of a symmetric airfoil at zero angle of attack. With increasing angle of attack and/or airfoil camber, the flow around the wing becomes asymmetric and more acceleration will happen on the suction side of the wing.

Once there, the air molecules will "see" that the wing below them curves away from their path of travel, and if that path would remain unchanged, a vacuum between the wing and our packet of air would form. Reluctantly (because it has mass and, therefore, inertia), the packet will change course and follow the wing's contour. This requires even lower pressure, to make the molecules overcome their inertia and change 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. You see, as Bernoulli found out, faster air has less static pressure and the speed difference between both sides creates a pressure difference. Integrate dover the wing surface this is lift.

Note that 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.

With the changed direction of air flow the air is leaving the wing at an angle compared to its initial direction. This change of direction imparts a momentum on the air which, according to Newton's third law, needs an opposite force, which is lift. You see, lift can be explained in different ways and all of them describe in the end the same process.

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  • $\begingroup$ I submit that the classic Bernoulli experiment with a glass u tube simply shows moving fluid acts as a vacuum pump, much the same way as a sink top aspirator. This actually agrees with the Coanda effect. The only reason the moving stream has lower pressure is that where it is going has even lower pressure. Otherwise the air would not be moving. The moving fluid drags some of the static fluid (air) along with it. With wings, energy for this "pump" is provided by ... thrust! $\endgroup$ Jul 8 at 13:41
  • $\begingroup$ There's a few things here I don't understand. First as you say, the air accelerates towards a low pressure area on top of the wing. It appears from your explanation, that this "initial" low pressure is not due to the vacuum forming by following the curvature of the wing. The acceleration causes pressure to lower, and more air is drawn in. But what exactly causes this low pressure to begin with? Perhaps due to the wing thickness if I understand correctly? $\endgroup$
    – Erik
    Jul 8 at 22:24
  • $\begingroup$ @Erik There is only one low pressure area. It is caused both by thickness and by the surface curving away from the initial flow direction. In subsonic flow all transitions are gradual, so the low pressure makes itself felt already ahead of the wing, but there is no "initial" low pressure. $\endgroup$ Jul 9 at 20:24
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Both Bernouilli and Newton indeed happen in subsonic airflow over wing profiles, but Newton provides a much better picture:

  • Bernouilli describes incompressible flow, yet wings still provide lift in high subsonic and supersonic circumstances.
  • A flat plate still provides lift when at an angle of attack other than zero, despite Bernouilli not being present.

enter image description here

In the flat plate case there is higher pressure at the bottom (at AoA > 0) and lower on top - due to the sharp nose the air cannot follow the surface immediately, yet there is still some underpressure in that region.

My choice: Newton.

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  • $\begingroup$ Several places I've read, as well as the article I linked tell states that the static pressure term in the Bernoulli equation disappears for unconfined flows such as the flow over a wing because it assumes the atmospheric value for pressure. How can Bernoulli be applied in this case? Is it truly applicable to this case, or does it only provide means to calculate the pressure from the change in velocity from an energy point of view? $\endgroup$
    – Erik
    Jul 7 at 22:48
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    $\begingroup$ It's indeed a source of confusion. The static pressure at infinity is the atmospheric pressure indeed, not the local static pressure. Bernoulli needs to be considered in a stream tube. I reckon Bernoulli provides a means of explanation for starter pilots, that's it. Too many inconsistencies and invalidating circumstances. $\endgroup$
    – Koyovis
    Jul 8 at 0:34
  • $\begingroup$ Why should Bernoulli not "be present" on flat plates or with compressible flow? It does cover all those cases, too. $\endgroup$ Jul 8 at 12:53
  • $\begingroup$ @PeterKämpf If I recall correctly, Bernoulli is derived based on energy. So when the flow picks up speed and dynamic pressure, the static pressure should drop due to conservation of energy. It would seem intuitive that the surrounding atmospheric pressure would "violate" this and add the extra energy to the flow, keeping the static pressure constant. Even locally. Now it seems I am misunderstanding something regarding this that I don't understand. Does the local conditions "win" over the atmospheric pressure in the short timeframe the air takes to travel the length of the wing? $\endgroup$
    – Erik
    Jul 8 at 21:57
  • $\begingroup$ @Erik well, if you're traveling at 30 m/s with a 1.3 m wing, "transit time" is a fraction of a second, not enough time for the deflected airstream to return completely to the wing surface. Local conditions "win". An easy to see fluid example is at the transom of a boat. When it is slow, the water "sticks" to it, but once the boat speeds up, it separates, and the shape of the fluid flow wake is no longer determined by the shape of the transom, but by the fluid "chasing" the low pressure area behind the boat, forming the classic "V". $\endgroup$ Jul 8 at 23:23
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Welcome to the club. What happens on the bottom of the wing is fairly straight-forward action reaction, also seen with water skis or sticking your hand out the window of a moving car.

The "top lift" is a little tougher to explain and actually only happens under certain conditions pertaining to Reynolds number. Top lift is desirable because it comes with very little drag expense. Effects of Reynolds number with various airfoils can be studied at www.airfoiltools.com.

Just remember, the wing hits the air, but is explained in a relative sense as an "airstream" (also true in wind tunnels). Coanda may be a better explanation of top lift than Bernoulli. Using the "airstream" model, consider that air molecules have mass, and if the flow is fast enough, their momentum cannot quite follow the curve of the wing, causing pressure to drop near the upper wing surface. This is Coanda!. A little like a bunch of race cars approaching a turn. There will be a void of cars near the inside of the turn.

Remember, that "vacuum bubble" on top is only possible with adequate chord and airspeed, and will collapse (with massive increase in drag) if proper Angle of Attack is not maintained. This is the "stall" that early aviators, in their slow, light aircraft, experienced.

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  • $\begingroup$ Interesting description where the air momentum cannot follow the curvature of the upper surface. As you say, Coanda is when the vacuum is created from the air not being able to follow the curvature. How come then, that water flowing from a faucet will follow an included glass below it? Are there different effects taking place? $\endgroup$
    – Erik
    Jul 7 at 21:32
  • $\begingroup$ Water molecules have a much stronger attraction to each other than air molecules. This is one reason why water is a liquid at ambient Temps, while N2 and O2 are gasses. And water is also attracted to glass. Also try water at 100 km/hour. (Reynolds). $\endgroup$ Jul 7 at 21:34
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Air hits the wing. Air hits every square inch of the surface of the aircraft. And it is hitting every square inch of the surface all the time, even when the aircraft is not moving, when there is no relative wind. Air molecules are always moving (Brownian Motion). And because they are always moving, they are always hitting the surface of the aircraft. Every time an air molecule hits and bounces off the surface of the airframe, there is an exchange of momentum (a.k.a. a FORCE) and this force is applied to the surface, perpendicular to (or Normal) to the surface. The total aerodynamic force on the airframe is just the vectorial sum of all these forces caused by all the molecules hitting and bouncing off the airframe.

Lift, is just the component of this total aerodynamic force that lies normal (or perpendicular) to the flight path of the aircraft through the air. Why is the distribution of Lift uneven? because the momentum exchanged when an air molecule hits the wing is dependent on the velocity of the air molecule and the angle at which it is moving locally relative to that surface.

Drag is just the component that lies parallel to the flight path.

An air molecule hitting the very back tip of a ICBM reentering the atmosphere at Mach 20 is still pushing the missile forward.... But the air molecule at the front of the ICBM is hitting the nose with a much greater velocity - More velocity, bigger momentum change, greater force.

All the other explanations are just aggregate simplifications used to make calculations and help explain complex side effects of aerodynamic forces on specific airfoil shapes, (or observations of aggregate effects like wingtip vortices, or downwash, etc. etc. etc., which are necessary to conform to principles of conservation of Energy or Momentum ). The Bernoulli explanation is especially silly. How then do Symmetrical airfoils create lift? Golly, How do aircraft generate negative Lift and fly upside down? The increase in speed on the top of the wing is a side effect of the lift, not the cause.

NOTE. I use the word "hitting" with some literary license. The molecules never actually "hit" anything, they just get close enough for the electromagnetic forces exerted by their electron clouds to repel one another.

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  • $\begingroup$ Symmetric airfoils generate lift with a non-zero angle of attack. This can be very nicely seen for example in the CL vs alpha graphs here: airfoiltools.com/airfoil/details?airfoil=naca0015-il. Additionally, your explanation with air molecules can be very nicely extrapolated to arrive at Bernoullis principle. Your explanation is therefore the same as explaining it with that principle... $\endgroup$
    – U_flow
    Jul 8 at 20:17
  • $\begingroup$ If by "Explaining", you mean to attribute causality, then no, you cannot so extrapolate. correlation is NOT the same as causation. Almost every heroin addict drank milk as a child... And extrapolation or derivation is also different from attributing causality. There are many, many aggregate properties of fluids that must be as they are because of Conservation of Energy, Momentum, and/or principles of Symmetry, but that does not justify using them to explain or attribute one as the cause of the other. $\endgroup$ Jul 8 at 22:41
  • $\begingroup$ Re "The Bernoulli explanation is especially silly. How then do Symmetrical airfoils create lift?" -- no, when you look at the flow around a symmetrical airfoil flying at positive angle-of-attack, you can see how differences in flow velocity are created, leading to differences in pressure. $\endgroup$ Jul 9 at 14:14
  • $\begingroup$ Re " they just get close enough for the electromagnetic forces exerted by their electron clouds to repel one another."-- this answer might benefit from some discussion of the "boundary layer"-- the unimpaired free-stream flow is surely not "hitting" the wing (or getting close enough for molecules to be repelled by electromagnetic forces exerted by electron clouds) $\endgroup$ Jul 9 at 14:16
  • $\begingroup$ Perhaps, but the "free-stream flow" has nothing to do with lift. It is as you said never in contact with the aircraft. How can it exert a force on something it never comes in contact with. All these "explanations" are, as I said, only observations about many-times removed indirect consequences of energy and/or momentum conservation effects. $\endgroup$ Jul 10 at 12:50

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