Posted with permission from Kitplanes Magazine.  Originally published in Kitplanes, May 1992.

Probably no question other than the danger of the downwind turn generates more debate in the aviation community than the source of lift on an airplane wing. Two fierce camps promote opposing views, each citing the work of an eminent scientist to support their argument. The first view, the Bernoulli theory, claims that the source of lift is due to higher velocity air flowing over the upper surface of the wing, creating a lower pressure on the upper surface that sucks the wing upward.

The opposing position, the Newtonian view, says that the wing, flying at a positive incline or angle of attack, deflects air downward. As a result, Newton’s Third Law—which states that for every force there is an equal and opposite force—predicts an upward force equal in magnitude to the force deflecting the air downward. This opposing reaction force is the lift force on the wing.

Now, using the wonders of computer-simulated time travel! KIT-PLANES brings you the first-ever Newton/Bernoulli debate. Today we may see this debate put to rest for good. Let us start by welcoming our distinguished guests.

KITPLANES: Our first guest, Sir Isaac Newton, was born in 1643. He was appointed to a chair in mathematics at Trinity College, Cambridge University, in 1667. He published his most famous work, or at least the work that is the subject of this debate, the Principia, in 1687. Sir Isaac died in 1727. Welcome to our debate, Sir Isaac.

Newton: Thank you, good sir. I say, this time travel simulation is certainly realistic. You and your office appear so real.

KITPLANES: Yes. I am surprised myself at how real our guests frequently appear.

Newton: Ah, but my good man, we are real. You are the simulation, are you not? At least that is how I believe they explained it to me when I agreed to participate in your debate.

KITPLANES: I guess, Sir Isaac, that it is a matter of viewpoint. Now for our second guest. Daniel Bernoulli was one of the second generation of Swiss mathematicians. He was born in 1700, in Groningen, the Netherlands. He was educated at the University of Bard and accepted an appointment as an instructor in mathematics at the University of St. Petersburg in 1725. He returned to Switzerland to accept a position at the University of Bard in 1732. While there he published his famous work on the motion of fluids, Hydra dynamica, in 1738. Welcome, Daniel Bernoulli.

Bernoulli: Thank you. And you must be Sir Isaac. You do look much like your paintings. You know, even though our lives overlapped, I never got to meet Sir Isaac in my lifetime. I did read your excellent works, however.

Newton: And I yours. Not in my lifetime, of course, but since then. So many books and essays to keep up with, but I did read Daniel’s work.

KITPLANES: Fine. Now, gentlemen, if we could get on with the debate. You have each been given copies of several current aerodynamics textbooks, and a statement of the issue we are trying to settle.

(The two scientists looked at each other sternly for a moment, then broke into broad grins, finally falling into loud laughter)

KITPLANES: Gentlemen, what is the problem? We have gone to great effort to bring you together today to explore this important issue.

Newton: But that is the problem, young man. It is not an important issue. It is really no issue at all. You will not find it discussed in any of these formal textbooks. I am of the impression that your professional aerodynamicists do not argue the issue. Only aviation enthusiasts, pilots and amateur designers seem interested in the question. We, Daniel and I, know that there is no real question.

KITPLANES: I—we——the readers, do not understand. Can you explain, Sir Isaac?

Newton: Of course. I have philosopher friends who debate whether a glass of wine is half full or half empty. It is both, is it not? Merely a matter of viewpoint?

KITPLANES: Yes, but...

Newton: Our laws describe the same situation. Well, not quite. One may better describe cause, the other, effect. But they both describe the same thing going on. In the words of some of your twentieth-century scientists, Bernoulli’s description accounts for the microscopic motion of the air, and the pressures over the wing surface. My law describes the next effect, the resulting force.

Bernoulli: Yes, exactly. I see no conflict either. In Isaac’s day there were no scientists interested in mechanical flight.  Only artisans, poets, and craftsmen thought about or tried to build flying machines. But in later years of my life, such scientists began to appear.

By the early years of the nineteenth  century, the study of aerodynamics began to interest many scientists and engineers. Many of the former were interested in it only to learn the laws of nature, for instance understanding the mystery of bird flight. The engineers, for the most part, wanted to invent the flying machine. It took them a century to do of course.

Newton: They made a mistake when they looked at only my theory. They did not realize that my laws only explained the large-scale effect, the result of airflow over the wing,  not precisely what caused the air to flow exactly as it did. Bernoulli’s principles were published by then but were ignored by the early flying-machine engineers. They correctly deduced that an inclined surface would deflect moving air downward, and that this would create an upforce.  But they overestimated the amount of the lift force, and also the increased resistance to the air, what you call drag.

Your scientists of today know that there is a region where my laws alone can predict fairly well the forces on a vehicle. This is at the fringes of space, where some low-orbiting satellites fly. You see, the flaw in these early thinkers was that my law easily predicts what happens when an air molecule strikes a wing. But the air molecules, at the altitudes that aircraft fly, bump into each other much more frequently than they do the wing.

Bernoulli: In theory, Newton’s law could explain the path of each molecule, whether it bounces off one of its peers—or off the wing. But the amount of computation would be staggering. Not even your best super-computers today can predict the path of each molecule.

Newton: Right. At the fringes of space, the molecules are so few and far between that they do not interact to any great degree. The body of a satellite comes along and bumps into each one individually.  Even when they recoil off the satellite, they bump into few of their own kind.

Now, within the normal air, on the other hand, the bumping into other molecules dominates their path. That is, they act as a continuous fluid. Bernoulli treated air as this continuous fluid and discovered ingenuous new ways to predict the flow near a wing’s surface. Once one can predict the direction of the average flow, the so-called downwash. then my laws of motion can predict the forces on the wing.

Yet if we do not want to do it this way, Bernoulli gave us a way to compute the force on a wing another way. His equations can predict, in theory, the pressure distribution around an airfoil. Because pressure is just the force of the air acting on a small surface area, if we sum up all the pressure forces, we can predict the force on the wing.

KITPLANES: You say, in theory. Can’t his laws be used in practice?

Bernoulli: In some cases, yes. Several great scientists of the twentieth century were able to use my equations to predict the flow and pressure about simple, streamlined shapes. Scientists like Eular, Kutta, Jankowski, and Prandtl provided sets of equations that estimate my Bernoulli forces for airplane-like shapes and at low angles to the airflow.

Unfortunately, my equations are so difficult to solve that, like using Newton’s methods, even your best supercomputers can only really compute the flow around clean, simple shapes.

KITPLANES: I thought that computational fluid dynamics was now in widespread use and designing complete airplanes.

Bernoulli: Well, in a way. If the flow around a similar shape is known, say from wind tunnel data, my equations can extend the knowledge and predict the flow around somewhat similar, but still different shapes. The better the computers get, the more they can model the flow around virtually arbitrary shapes.

KITPLANES: If the computers were powerful enough, could they also predict the flow using Newton’s laws and around a completely arbitrary shape?

Newton: Yes, in principle. But you would need orders of magnitude more computing power than using Bernoulli’s methods. On the other hand, my method is not quite as sensitive to the shape of the body. It is just so hard to compute the flow of all molecules reacting with any object.

Bernoulli: You can see this with some of the photos taken in your modern wind tunnels. In some tunnels they add streams of smoke in front of the section under test. You can see that pressures that build up in front of the wing effect flow a considerable distance ahead of the wing. At high angles of attack, the air sweeps upward before it gets to the leading edge of the wing.

This wind tunnel photo shows the streamlines made visible by injected smoke.  Note the leading edge of the wing affects the airflow even ahead of the wing.

Newton: Exactly! The force on the wing is produced not only by those molecules that hit the wing and are deflected, but by the molecules that bounce off these molecules, and then the molecules that hit the second set of molecules, and soon, ad infinitum.

For instance, look at a molecule that passes over the top of the leading edge of a flat-plate airfoil. Using the so-called free molecular flow, as exists in space, or that early flying machine engineers assumed worked In normal air, the molecule would continue on, and not be deflected downward. Only molecules that hit the bottom would be deflected. Yet we know that molecules that pass over the top are deflected. The smoke tunnels that Bernoulli mentioned clearly show that.

Nineteenth-century scientists imagined that air molecules would bounce off a surface like billiard balls.  In low earth orbit the occasional rare air molecules sometimes do behave like this.

Bernoulli: Yes. And only pressure can deflect those molecules. The air above them is at higher pressure. The air closer to the top surface of the wing is at lower pressure. Air molecules naturally want to flow from a region of higher pressure to a region of lower pressure.

So, molecules that flow over the top of a wing are deflected downward by the pressure patterns that develop around the wing. And my theory, at heart, is a way to predict those pressure patterns, knowing the properties of the fluid (air in this case), and the shape of the region.

And speaking of flat planes, we should put to rest here a simple explanation of how an airfoil works, that supposedly calls up my law. This ridiculous claim is that the top of an airfoil is curved, the bottom flat. Since the air has to travel a longer distance on a curved path, it must go faster to reach the trailing edge at the same time as the air on the bottom. If it goes faster, it will have a lower pressure, according to my law.

But, if this theory were correct, a flat wing or a symmetric airfoil could not generate lift. Thousands of model airplanes fly reasonably well with flat airfoils. And many jet aircraft and acrobatic planes fly excellently with symmetrical airfoils.

Air flows in curved paths around an airfoil.  Even a flat plate creates lift .  Streamlines come closer together in regions where air velocity is high, and are further apart where it is lower.

A cambered thin plate makes a fair airfoil, even though the distance from the leading to the trailing edge is virtually the same for the top and bottom surfaces.

Newton: Yes, good point. The reason the air over the top must go faster is that the airstream on top of the airfoil is on the outside of a curve. As any soldier knows who has marched in a column, the row of men on the outside of a turn have to take longer steps to keep up with those on the inside.

Bernoulli: Or, if you have ever played Crack the Whip on ice skates, you know that the outside person must and will go much faster than the inside. So it is the fact that the wing is deflecting, or turning, the air downward that causes the air on the top to have to go faster. And my law tells exactly how much the pressure is reduced when it goes faster.

KITPLANES: Didn’t you actually develop your theory primarily to predict the flow of water in pipes?

Bernoulli: Yes, that is a fact, It was basically a theory for hydraulic flow. I did feel that people could use it to understand flow around the hull of a ship, though. But, you see, I never actually met anyone trying to
build a flying machine. Still, air is a fluid, just like water, and I am delighted that scientists and engineers find my theory useful in predicting aerodynamic flow.

KITPLANES: One point still bothers me. I believe I remember reading that nineteenth-century scientists strongly believed that nature abhors a vacuum. Wouldn’t such a vacuum keep following a wing if the flow were as you two say the scientists of that period believed? Surely they could see the paradox involved if the flow went straight over the top of the wing, but was deflected by the bottom.

Newton, Of course. They realized the air behind the wing must flow back together to fill in the vacuum left by the passing wing. But they felt that what happened in the air behind the wing would not apply a force on the wing. The fact that the flow behind the wing would have to affect the angle of flow was felt to be irrelevant.

We know that even the downwash that the wing creates also comes to rest eventually somewhere behind the wing, but the lift force is still created. We can summarize lift according to my theory by saying that the wing deflects the air downward, creating a downwash. A force must have been placed on the air by the wing to get it moving downward.

According to my third law, that force on the air has an equal and opposite force, an upward force on
the wing: lift. But the problem is quantifying that force. An aircraft designer must know more than just that the wing creates lift. He must know how much lift. And it would be almost impossible, using my laws, to compute that force by looking at the motion of all the air molecules.

Bernoulli, Yes, but using the idea of a pressure field, we could compute how much downwash we had created. We can, however, after computing the pressure fields around the wing, use this pressure distribution to compute directly the lift force on the wing. We will get the same answer, either computing the lift force created by the pressure field, or using the pressure field to compute the acceleration of the downwash.

An airfoil creates a region of high pressure air below the wing, and a low pressure region above it.  The air leaving the wing has a downward flow- creating the Newtonian force- but it is the Bernoulli pressure field that creates the downwash.

So, indeed, the two views that are the source of so much argument are just different ways of looking at the sane phenomena.

KITPLANES: Ah, I see, now. So, there is no conflict after all. You are both reconciled. My thanks to you both, for putting to rest this important—or, if you insist, non-important question. I know I certainly have a better understanding of the source of lift on an airfoil, and I am sure our readers will also.

And now, good night, gentlemen, and thank you very much for being here.