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That sounds like the problem of explaining how magnetism works. Engineers and scientists understand very well how airfoils generate lift. It is not some kind of mystery like the article implies.

It is true that most of the popular simplified explanations are incorrect. Flat plate airfoils generate lift if they have positive angles of attack. Airplanes can fly upside down. At fractional mach numbers, pressure above and below the wings is essentially equal.

If you are not flying near the speed of light, Newton's laws apply. So, if you want simple explanation, the wing deflects air downwards and that pushes the airplane up. If you put your hand outside the car window at an angle, you will feel a force. Should be simple enough for 2nd graders.

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The article does specify that "nobody can explain how wings work", not that "nobody knows how wings work". It also tries to go into "but WHY do the Navier-Stokes equations work like this", which is just not how physics works.

But yeah, there is just not an explanation that is both simple and complete and journalists have a pretty rough time dealing with that.

The article doesn't imply it's a mystery, only that simple one-liner explanations are insufficient. The headline is reasonably clickbait-y.

The momentum theory of lift is simple, intuitive, but unfortunately incomplete (just as the differential pressure explanation). It's covered in the article.

> But taken by itself, the principle of action and reaction also fails to explain the lower pressure atop the wing, which exists in that region irrespective of whether the airfoil is cambered. It is only when an airplane lands and comes to a halt that the region of lower pressure atop the wing disappears, returns to ambient pressure, and becomes the same at both top and bottom. But as long as a plane is flying, that region of lower pressure is an inescapable element of aerodynamic lift, and it must be explained.

Also I want to address this:

> At fractional mach numbers, pressure above and below the wings is essentially equal.

Surely you mean density? Air pressure is certainly not the same above and below, as differential pressure integrated over the surface is equal to the lift force generated by the wing. So no, while the Newton's explanation is a great explanation for a second grade classroom, it is not complete.

> Surely you mean density?

The ideal gas law applies, at least nearly enough. So PV = nRT. By saying the density is equal between the top and bottom, you are also saying the pressure is equal. The air around the wing is having it's momentum changed, not it's pressure. At least, at sub mach speeds.

You're confusing static, dynamic and total pressures. Static pressure is the pressure of a fluid on a body when the body is at rest relative to the fluid. Dynamic pressure is the velocity created pressure. Total pressure is the sum of the two, and is what is used in the ideal gas law. To compute lift force static pressure is what is integrated around the wing surface. Total pressure remains constant in the fluid flow for low Mach numbers. Static pressure can and absolutely does change significantly as it accelerates through a streamline such as in low-speed aerodynamics. I understand the semantics on the different kinds of pressure can be confusing. But you should know that when aerodynamics refers to "pressure" as it applies to lift generation, they are referring to static pressure.

I should also mention that this pressure absolutely does change a lot over the flow field, and is commonly used to experimentally and mathematically quantify lift. The following is an image of the pressure distribution of a NACA 2412 airfoil at low speeds.

https://www.chegg.com/homework-help/questions-and-answers/n-...

Just to explain the chart a little bit, in aerodynamics, pressure is usually simplified to a Pressure Coefficient (CP) value. A CP of 0 is when static pressure equals atmosphere. A CP value of 1 occurs at the stagnation point (where velocity is 0, therefore static pressure equals total pressure). Note how this type of chart has an inverted y-axis (a common convention so that the wing upper surface is at the top). Notice how the static pressure on the lower surface is roughly atmospheric, while the upper surface pressure suction peak is high. In this case roughly equal in magnitude to the dynamic pressure. This is a typical pressure distribution for most airfoils, with the suction peak increasing in magnitude as angle of attack increases.

This plot can be obtained mathematically using some sort of potential flow scheme (see: XFOIL for 2D airfoils), or experimentally using pressure taps on a wind tunnel model. The area between the upper and lower surface curves is directly proportional to lift. The larger the difference between upper and lower surfaces, the more lift.

Google Bernoulli's equation, when you change the momentum of the flow, the pressure will change drastically (the energy has to come from somewhere).

> But taken by itself, the principle of action and reaction also fails to explain the lower pressure atop the wing

What? The pressure is lower on top of the wing and higher below because the air is being pushed downwards by the wing. I will happily explain this to any second-grade classrooms you find yourself having trouble with.

And how is that air moving from the upper surface to the lower surface of the wing? is it magically permeating the wing surface? Keep in mind that the vast majority of the pressure differential comes from upper surface suction rather than a pressure increase on the lower surface. At shallow angles of attack there is often little or no increase in pressure on the lower surface; nevertheless lift is produced. Your simplification does not adequately explain this, as addressed in the section of the article subtitled: "Turning on the Reciprocity of Lift"

> Nevertheless, there are at this point only a few outstanding matters that require explanation. Lift, as you will recall, is the result of the pressure differences between the top and bottom parts of an airfoil. We already have an acceptable explanation for what happens at the bottom part of an airfoil: the oncoming air pushes on the wing both vertically (producing lift) and horizontally (producing drag). The upward push exists in the form of higher pressure below the wing, and this higher pressure is a result of simple Newtonian action and reaction.

> Things are quite different at the top of the wing, however. A region of lower pressure exists there that is also part of the aerodynamic lifting force. But if neither Bernoulli’s principle nor Newton’s third law explains it, what does? We know from streamlines that the air above the wing adheres closely to the downward curvature of the airfoil. But why must the parcels of air moving across the wing’s top surface follow its downward curvature? Why can’t they separate from it and fly straight back?

"how is that air moving from the upper surface to the lower surface of the wing?"

What? Of course it isn't moving from above the wing to below - just that it's being compressed below the wing, and decompressed above it.

"Why can’t they separate from it and fly straight back?"

Because... they are parcels of gas, full of molecules flying in all directions at high speeds, bouncing off one another and things nearby, and if that parcel of air flies straight back it will find itself above a bit of space that contains nothing at all, and the molecules which are going in that direction will find they are able to do so unopposed (until they hit the wing) - so some of them will do so.

As a result, the mass of the gas will spread out into a larger volume, the number of molecules colliding with the surface of the wing per unit of time will drop (as they are more diffuse), and the pressure will drop.

This doesn't seem very mysterious.

This doesn't explain why a higher pressure on the lower surface should necessarily equal a lower pressure on the upper. I posted that quote to focus on the person I was addressing who stated that "pressure is lower on top of the wing and higher below because the air is being pushed downwards by the wing". The above commenter was stating that somehow the higher pressure on the lower surface somehow causes the lower pressure above. The quotation I posted refutes that point. Static pressure in a flow is not a conserved value. It does not have to come from anywhere. This can be easily demonstrated with an airfoil shape with a relatively flat bottom such as the NACA airfoil series. Static pressure on these airfoils' lower surfaces tends to roughly equal atmospheric. Yet the upper surface still creates suction. In the majority of airfoils there is way more suction than there is pressure increase on the lower surface. Why? This is not adequately explained by the above commenter's statement.

Also just a minor point of pedantry: wings don't compress air. At least not in low Mach number flows. The static pressure changes as a result of the relationship between pressure and velocity. Compression is when the total pressure (static + dynamic pressures) changes. Total pressure in a low-mach number flow remains constant.

Maybe there's a different word than 'compression' that means 'to cause an increase in pressure'. It seemed like the logical choice, but I'd love to know what other word is preferred.

Because I'm pretty sure wings cause an increase in air pressure.

I guess the idea of 'dynamic pressure' is 'pressure that is caused by colliding with air just because you're moving relative to it'. But surely in the moving reference frame of the wing, that looks, locally, quite a lot like compression...

I too would like another word, because I can tell you first hand that the confusion between total, static, and dynamic pressure is the source of many headaches amongst aerospace engineering students. It doesn't help that many textbooks often refer simply to "pressure" and expect the readers to intuit which they are referring to given the appropriate context.

A book will say:

"In low-speed aerodynamic flow, pressure is constant along a streamline"

and then one chapter later say

"Pressure changes with a change in velocity along a streamline"

The first references to total pressure while the second refers to static, but at first glance they seem contradictory.

However I would fully avoid the word "compression" since implies that we are squeezing more air into a fixed volume (a.k.a. an increase in density) which is NOT what is happening in a low-speed air flow. The definition of compression strictly applies to total pressure. Although most people don't learn this, since compression is often used in relation to stationary flows to begin with (such as in pressure vessels) where the dynamic pressure is 0, thus static pressure equals total pressure.

> But why must the parcels of air moving across the wing’s top surface follow its downward curvature? Why can’t they separate from it and fly straight back?

I’m sure smarter people than I wrote the article, but the way I explain it to myself is that it’s a manifestation of the same basic force or effect where the lower pressure area needs to be filled somehow. Like how the wind blows, cyclones form, etc., except in this case giving the wing lift somehow ends up being part of the most efficient “fill the void” solution.

Like how just behind a driving truck there’s an abrupt region of lower pressure; however, the air obviously doesn’t just keep on going straight forever but rushes in (incidentally, giving a boost to whomever happens to be tailgating). The gradual shape of the wing changes the scale of the effect, so that it happens constantly with tiny air ‘parcels’, each filling in the minuscule lower pressure region. (And, probably not unrelated to the fact that it’s intuitively unnatural for air to flow that way, lifting the wing a little apparently turns out to help even out that void most efficiently.)

It’s interesting to ponder for sure.

> I’m sure smarter people than I wrote the article

I doubt it. This daft idea that wings are hard to explain is kept alive by pop science writers because it's a reliable source of money for old rope, that's all.

The experts cited in the article are some of the most well-known researchers in the field of aerodynamics. John D. Anderson is the author of 7 reference textbooks, all of which are commonly used in the field. His research took him from the US Airforce Aerospace Research Laboratory to the becoming the Chief of the Hypersonics Group at the US Naval Naval Ordnance Laboratory. He was Chairman of the Department of Aerospace Engineering at the University of Maryland. He is a member of the National Academy of Engineering for aerospace engineering. His name is attached to enumerable scientific journals that I encourage you to search through if you think that an average Hacker News user knows more about aeronautics than him.

The pressures above and below the wing are absolutely not equal, even at idealized incompressible flow (zero Mach number).

Pressure distribution: https://www.researchgate.net/publication/262976779_Aerodynam...

Pressure contour plot: https://www.google.com/url?sa=i&url=https%3A%2F%2Fwww.ripubl...

> That sounds like the problem of explaining how magnetism works.

https://www.youtube.com/watch?v=36GT2zI8lVA

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