How complete is our understanding of lift?

Question

I'm currently studying for my PPL and one of the accepted textbooks contains the following disclaimer at the end of the Principles of Flight section on lift:

It is important to note that the forgoing explanation of lift, and its reliance on Bernoulli's theorem, is very much the 'classical' theory of lift production and the one on which the exam questions are usually based. There are differences of opinion amongst scientists on the subject....[snip]

The same book previously also describes the venturi theory which NASA discredits.

Additionally, one of my previous CFI's told me that during a previous successful job interview he had been asked to explain lift and had merely responded with "Which theory would you like me to cover?"

On the contrary - we must have an excellent understand of some components because of the way we're able to design and build such stable (and unstable when we want) aircraft. Plus, I see some absolutely incredible mathematics described on this website which seek to accurately answer complex questions.

So, my question isn't how is lift generated -it's how complete is our understanding? Which bits are still in dispute, and which bits are fully accepted?

For those interested the book in question is

"AFE - The Private Pilots Licence Course - PPL4

Principles of Flight, Aircraft General Knowledge, Flight Performance and Planning"

ISBN: 978-1-874783-23-7 https://www.afeonline.com/shop/private-pilot-s-licence-course-ppl-4-principles-of-flight-airc.h

Answer 1

Short answer: Yes, our understanding of lift is complete, but solving the equations for some practical cases needs more resources than what is technically sensible.

Lift is a matter of definition

First of all, lift is only one part of the aerodynamic forces. It is the component normal to the direction of airflow. Since the aircraft will distort the local flow around itself, this direction is taken ideally at an infinite distance where the air is undisturbed.

The other component is, of course, drag. It is defined as the part of the aerodynamic forces parallel to the direction of airflow.

The aerodynamic forces are the sum of all local pressures, which act orthogonally on the local surface of the airplane, and the shear forces, which act parallel to the local surface.

When aerodynamics was researched first, electric fields were new and exciting, and the same equations which help to calculate electromagnetic forces could be used to calculate aerodynamic forces. Therefore, abstract concepts like sources or sinks were used to explain aerodynamics. This made it not easier to understand, and many authors tried to find simpler explanations. Unfortunately, they were mostly too simple and not correct, but the next generation of authors would mostly copy what had been written before, so the wrong concepts were still bandied about.

To get to the bottom of it, it might help to look at lift 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.

All three contributions are well understood, and with the Navier-Stokes equations they can be completely mathematically expressed. What is still improving is our ability to solve these equations, and in turbulent flow the characteristic length required to capture all effects is so small that it is practically impossible to solve those equations fully with finite time and resources.

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. 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 (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.

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.

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.

Lift can be explained in several, equivalent ways

Following the picture of a pressure field outlined above, lift is the difference of pressure between upper and lower surface of the wing. The molecules will bounce against the wing skin more at the lower side than at the upper side, and the difference is lift.

Or you look at the macroscopic picture: A certain mass of air has been accelerated downwards by the wing, and this required a force to act on that air. This force is what keeps the aircraft up in the air: Lift.

If you look at the wing as a black box and only pay attention to the impulse of the inflowing and outflowing air, the wing will change the impulse by adding a downward component. The reaction force of this impulse change is lift.

Either way, you will arrive at the same result. By the way: Most of the directional change happens in the forward part of the airfoil, not at the trailing edge!

Supersonic flow

When the aircraft moves faster than pressure changes propagate through air, the changes in pressure are no longer smooth, but sudden. The aircraft will push the air molecules aside, producing a compression shock. Behind the shock front pressure, temperature and density are higher than ahead of it, and the increase is proportional to the local change in flow direction. The incremental pressure change $\delta p$ due to the aircraft hitting air with an incremental angle of $\delta\vartheta$, expressed in terms of the undisturbed flow with the index $\infty$, is proportional to the change in the streamlines: $$\delta p = -\frac{\rho_{\infty}\cdot v^2_{\infty}}{\sqrt{Ma^2_{\infty} - 1}}\cdot\delta\vartheta$$

Gas pressure on a molecular level is the number and severity of particle collisions. The air molecules experience more collisions on the downstream side of the shock, since air pressure is higher there. The average direction of the additional collisions is indeed orthogonal to the shock, because it is the boundary between blissfully unaware molecules at ambient pressure ahead of the shock and their bruised brethren downstream which have just crossed that boundary. Once a molecule has passed the shock, the collisions are coming again equally from all sides and its speed does not change any more.

If the surface curves away from the local flow direction, the air produces an expansion fan which re-sets the old pressure and density values when the air flows again in its original direction.

Pure supersonic lift is only a matter of the angle of incidence, and any local curvature of the wing will not change overall lift (but increase drag). Now the total aerodynamic force is normal to the wing, and drag will become proportional to the angle of incidence. In hypersonic flow you will get good results with the venerable impact theory first formulated by Isaac Newton.

Separated flow

This happens when the air molecules are no longer able to follow the contour of the aircraft. Instead, you get a chaotic, oscillating flow pattern which is very hard to compute exactly. This is really the only part of aerodynamics which cannot be predicted precisely, even though the effects are well understood. Separated flow will produce lift, too, but less than attached flow. In delta wings, this separation is produced on purpose to create what is called vortex lift.

Answer 2

From this paper:

The principle of equal transit times holds only for a wing with zero lift. [!!]

[...]

The air passes over the wing and is bent down. Newton’s first law says that them [sic] must be a force on the air to bend it down (the action). Newton’s third law says that there must be an equal and opposite force (up) on the wing (the reaction). To generate lift a wing must divert lots of air down.

[...]

So how does a thin wing divert so much air? When the air is bent around the top of the wing, it pulls on the air above it accelerating that air downward. Otherwise there would be voids in the air above the wing. Air is pulled from above. This pulling causes the pressure to become lower above the wing. It is the acceleration of the air above the wing in the downward direction that gives lift.

We (those of us reading this) can conlude the following about our (humanity's in general) understanding of lift:

• We certainly understand it well enough to design aircraft, and there may be overlap with this knowledge in other areas, such as maybe wind-powered generator design.
• Many believe we have a fairly complete understanding of lift.

The second bullet is not at all in impune the excellent (and challenging!) work done through history in fluid dynamics, aeronautical physics, and aeronautical engineering. It is merely to allow for the possibility of future paradigm shifts in our understanding of those topics, even if those shifts do not affect common design practice or practical discussions of lift. A historical example of that last point would be General Relativity as a paradigm shift in our understanding of gravity, while Newtonian gravitational theory was still used for the moon program and is still widely taught and used for situations not requiring extreme precision.

In addition to links in Frederico's comment, see also: https://physics.stackexchange.com/questions/290/what-really-allows-airplanes-to-fly

Edit:

This NASA page discusses the controversy of "Bernoulli versus Newton" and concludes that both explanations of lift are "correct" and that there is even more to it. The Euler Equations and the Navier-Stokes Equations are mentioned. This page in the same series on NASA's site suggest that lift is fairly well understood by experts, but is poorly explained in the majority of popular sources:

There are many explanations for the generation of lift found in encyclopedias, in basic physics textbooks, and on Web sites. Unfortunately, many of the explanations are misleading and incorrect. Theories on the generation of lift have become a source of great controversy and a topic for heated arguments. To help you understand lift and its origins, a series of pages will describe the various theories and how some of the popular theories fail.

Lift occurs when a moving flow of gas is turned by a solid object. The flow is turned in one direction, and the lift is generated in the opposite direction, according to Newton's Third Law of action and reaction. Because air is a gas and the molecules are free to move about, any solid surface can deflect a flow. For an aircraft wing, both the upper and lower surfaces contribute to the flow turning. Neglecting the upper surface's part in turning the flow leads to an incorrect theory of lift.

Answer 3

The problem here is that "correlation does not imply causation". Neither Bernouilli's principle nor Newton's laws of motion explain lift. Both of them give valid methods of calculating the lift force from the air flow pattern around the wing, but neither of them explain why the flow pattern is what it is.

Ideas like "equal transit time" at least try to give a reason "why," but experiments which visualize the flow pattern with smoke demonstrate that is just wrong.

The best "one-word explanation" of what causes lift is the viscosity of the air. Viscosity is the reason why there can't be any discontinuities in the overall flow pattern*. In particular, the air velocities on either side of the relatively sharp trailing edge of the wing have to be the same, otherwise the effect of viscosity at that point would propagate upstream through the air (at the speed of sound) and change the global flow pattern.

If there were no viscosity, no wing of any shape would produce any lift, or any drag force.

*Let's limit this discussion to subsonic flows. Introducing shock waves into the airflow makes a "hand-waving" non-mathematical discussion more complicated, but it doesn't invalidate the essential point I'm trying to make.

Answer 4

How complete is our understanding?

• Complete enough to design and fly a number of complex aircraft of varying sizes, shapes and applications.
• Complete enough to extract power using it.

On a basic level, lift is the force generated as solid body 'turns' fluid while satisfying the conservation laws. The issue is not that we don't know what lift is, but there is no consensus about how to explain it. Most of the 'theories' of lift are just models try to explain the same thing based on the points of view of the people involved.

The way the pilot views the lift is different from that of an engineer or a mathematician. For the pilot, the lift is a force that keeps the aircraft in the air (and proportional to $\rho V^{2} S$ and angle of attack, at-least till stall), while a mathematician can say that lift 'follows naturally' by solving Navier-Stokes Equation (whether it can realistically solved or not is another matter) for some conditions. Of course, this is of no practical use to either the engineer or the pilot. Both can claim (rightfully) that they are correct, while a physicist can object that NS assumes that the fluid is a continuum, while it is not the case in realty.

This is the reason for so many theories of lift. As the fluid flow is extremely complex, some simplification is done in each theory (like omitting viscosity in the Euler or potential flow theory). Based on the simplification, the theory is either useful in some (or most) of the situations or is outright wrong.

Which bits are still in dispute, and which bits are fully accepted?

Almost all 'theories' of lift accept that lift is a force and its requirements. As far as engineering goes, the issue is which bits of are necessary for the problem in hand.

For example, the potential flow theory can predict the lift as long as we are not approaching stall. After that all bets are off. There is no point in arguing about a result from a theory after using it in a situation for which it was not designed for in the first place.

This is the reason for arguments about lift. Some theories are developed to describe a particular situation (for example inviscid flow) and then applied in general, which obviously leads to confusion and dispute.

As far as engineering is considered we have enough understanding of lift to create the flying machines we need though not as much as to explain everything that happens with accuracy.

Answer 5

Many physical phenemona do not reduce down to an elementary algebraic equation.

Aerodynamics -- including the generation of lift -- is very well understood. It has also been validated through experiment (many wind tunnel tests and flight tests) where the theory and experiment are in very close agreement. In fact, we have several approaches to the development of the aerodynamic equations -- depending on the assumptions and simplifications we wish to make.

Engineers have a very good understanding of how these levels of theory compare and which are better / worse at predicting reality in different situations.

The issue at hand is that the fundamental theory of aerodynamics does not boil down to a simple equation with immediately obvious physical interpretation.

Everything in aerodynamics can be explained in terms of (and rigorously derived from):

1. Conservation of mass
2. Conservation of momentum
3. Conservation of energy
4. Gas equation of state
5. Some other gas relations like the dependence of viscosity on temperature

These five things are intuitive, observable, testable, etc. There are multiple ways to get from these five things to aerodynamics....

Unfortunately, they are not simple algebraic equations. Instead, they are a coupled system of nonlinear partial differential equations (1-3) (with some algebraic equations thrown in (4,5)).

The 'modern' way uses the least mathematical abstraction. It is called CFD (computational fluid dynamics). In CFD, we divide the domain of interest into a large number of tiny elements. We initialize all of the elements to an initial guess (that is wrong). We then solve the above equations on every element, applying appropriate boundary conditions. This makes a small correction to the properties at every element. We then do it again, and again, and again....

CFD is a very brute force approach with very little mathematical abstraction. After millions and millions of calculations, if we're lucky, the properties in all of the elements stops changing (there is theory on how this should happen too). We then say that the solution is converged. We can then sum pressures and shear to get lift and drag, we can produce beautiful images of the flow, etc. We have 'solved' the flow.

Although CFD is very powerful, it is not very satisfying in terms of intuition (which is what you're after).

There are other ways to attack aerodynamics (and the calculation of lift). You mentioned Bernoulli's equation -- Bernoulli's equation is most frequently derived from the conservation of energy, but it also can be derived from the conservation of momentum.

Potential flow theory (which most pre-CFD low-speed aerodynamics theory was based on) is usually derived from the conservation of mass -- but can also be derived from the conservation of momentum.

Potential flow theory allows aerodynamic calculation with much less brute force than CFD -- but instead, it adopts a great deal of mathematical abstraction. Complex variables (imaginary numbers), a potential function, sources, sinks, and vortices (mathematical singularities), superposition of elementary solutions, etc.

All of this can be rigorously derived from the fundamental equations -- and all of it has been validated through comparison to experiment. And more than 100 years of successful application to the design of aircraft. Engineers have deep understanding of their applicability and limits.

Unfortunately, although all of this is true, it does not mean that it can be explained in one or two sentences without heaps of math.

Any simple explanation of lift is wrong.

Any rigorous and correct explanation of lift is going to get messy.

Answer 6

TL;DR: we can very precisely model aerodynamic forces at the micro level; we can reasonably predict behavior at the macro level by aggregating micro-level models (CFD). We don't have a universally-applicable story for why the macro level behavior is what it is.

Fuller explanation:

At the risk of being a bit pedantic, I'm going to back up a couple of steps of abstraction in order to provide a more-complete picture.

The overall aerodynamic force on a body is decomposed into vectors normal to the direction of travel and parallel to the direction of travel, which are labeled 'lift' and 'drag' respectively; they are not distinct forces in & of themselves. Aerodynamic force itself is often decomposed at a different scale into pressure & friction; for the most part, friction only contributes to the 'drag' component while pressure contributes to both the 'lift' & 'drag' components.

Trying to tell a stylized story about why the integrated pressure & friction across the entire body result in a particular net force is challenging at best, since it is affected by the idiosyncrasies of each body; various models (such as Venturi, downwash, & circulation) really just provide designers & analysts with rough rules of thumb within particular flight regimes.

This last point is more important than it appears. As soon as you enter transonic flight (a mix of subsonic & supersonic flow at the surface of the body), drag increases precipitously (standing shocks creating adverse pressure gradients). Passing through to fully-supersonic flight you find yet another set of behaviors (because the leading shock radically alters the pressure distribution on the body). Don't even get me started on hypersonic flow (where the temperature change across the shocks is enough to decompose the N2 & O2 from the air itself).

Edit Peter Kampf's answer covered most of the same topics as mine, with pictures, so I'll just add this for completeness:

Answer 7

Scientifically speaking, lift is perfectly understood. Lift is merely the vertical component of force generated by a body moving through a fluid. And we know perfectly well how to calculate forces on a body moving through a fluid since the Navier-Stokes equations was published in 1822. That is to say, we know the physics of it and it has to do with the viscosity of fluids (in the case of aircraft, air).

But using the Navier-Stokes equations to design a wing is like trying to use Quantum-Electrodynamics (QED) to cook the perfect steak. Since gravity isn't involved in the perfectionness of steak, all you need to formulate a perfect steak is QED.

The Navier-Stokes equations calculate forces on a single point on the wing. Therefore you have to repeat the calculations over the whole wing to calculate lift. Over the last 190+ years mathematicians and engineers have formulated simpler algorithms to calculate the result of the Navier-Stokes equations and over the last 30 or so years we've used computers to calculate lift. However, you can see how this doesn't tell you the ideal shape to generate the aerodynamic characteristics you want. You can also see how this doesn't explain "lift" in terms a human can understand. It's all just large arrays of numbers.

Is it possible to explain lift in terms a human can understand? Maybe. We've certainly given names to how certain shapes generate certain output when subjected to the Navier-Stokes equations. Names such as "Coanda effect" and "Bernoulli Principle" etc. In the end, nature/physics doesn't care what name we give to our interpretation of the result of the Navier-Stokes equations - if calculating the equations result in a vertical force vector upwards you have lift. Maybe, like quantum physics, we'll never get a complete intuitive understanding of what lift is. But we certainly have the complete theory to explain it.

---

Additional note: Apart from not being helpful in helping us formulate a theory of wing design, the Navier-Stokes equations are also problematic because it's computationally expensive. For example, it's often not practical to use the Navier-Stokes equations to simulate turbulence (even though it's possible in theory). So we often take shortcuts for certain forms of simulations using other simpler but less perfect equations.

Answer 8

Lift is generated because air molecules are bouncing into and rebounding from the airfoil, on both top and bottom surfaces. It is the difference in the amount of momentum transferred in these collisions that creates lift. It is, (obviously), only the velocity of the air molecules that is normal (perpendicular) to the airfoil, that produces lift.

The Bernoulli principal is true, because the TOTAL average momentum of any air molecule in incompressible (subsonic) flow is a constant. Therefore, if the velocity of the air parallel with the airfoil increases, the normal component of the velocity must decrease to keep the total constant.

So, if the air is moving faster, the normal component must be slower, and it's pressure (against the airfoil) must be lower.

So, the longer distance to travel argument is only bogus if you try to assume that it can only be generated by a asymmetrical airfoil. Other things can change the travel distance (and resultant velocity) of the air across the airfoil as well. If a symmetrical airfoil is inclined to the relative wind, then as the air flows across the airfoil on the side where the airfoil bends away from the flow, the air must travel a longer distance (to fill in the gap created by the inclination) than air flowing across the surface on the other side, where the surface is inclined into the relative wind, and must either compress (in supersonic flow) or move away from (change direction away) the airfoil (in subsonic flow).

This is because in subsonic, (incompressible), flow, the air cannot make an instantaneous change in direction when it gets to the leading edge of the airfoil. If the Angle of Attack (AOA) was 10 degrees, the air does not make an instantaneous 10 degree change in direction. From the point of the leading edge away from the airfoil, the change in direction, and the resultant pressure, gradually changes as you move further away. the result is that the flow of the air is following a curved path, and travelling a longer distance, on this side of the airfoil, than it is on the other side, even for a symmetrical airfoil.

Answer 9

The principles of aerodynamics and fluid dynamics are what you would call "well understood."

The ambiguity is around what so-called "lift" is, which can be a nebulous concept. For example, if you drop a piece of paper it will drift slowly to the ground, essentially a form of gliding; this same air resistance is the basic force keeping a plane aloft. Would you consider this "lift"? Once you get into these arguments about semantics, things get vague.

To prove my point, in 2020 Scientific American actually published an article entitled "No One Can Explain Why Planes Stay in the Air".

Just as one example of the craziness, the FAA test, the same one you are taking, requires you to know the "four forces of flight" in which the so-called "lift" is the force that keeps the aircraft aloft. The only problem is that you can compute lift by equations that are in every book on aerodynamics and if you actually do this (like I did) you will find that the force generated is nowhere near enough to keep a plane in the sky. If "lift" were the force keeping a plane up, it would fall like a rock, so the FAA guidelines are simply completely wrong. It's just a huge semantic hairball that is not going to go away anytime soon.

The worst part of it is that EVERY pilot (or wannabe pilot) I have ever known thinks they know exactly what "lift" is and, even worse, their beliefs generally fall into one of 5 or 6 different categories with contradictory principles. This leads to huge arguments whenever the subject comes up. After 15 years of this, I just try to stay out of it, other than to tell the beginners not to make the same mistake (like I am telling you now).