Theories Of Lift

A popular misconception is that the Wright brothers, in addition to all of their other achievements, invented the airfoil. They didn’t. Sir John Cayley, an English engineer who also first identified the four forces of flight—lift, drag, thrust and weight—developed the cambered airfoil through detailed experimentation. His three-part work, On Aerial Navigation, published in 1809 and 1810, is often cited as the first description of what we today call an airplane. Also today, we teach that the theories of Sir Isaac Newton (1642-1726) and Swiss mathematician Daniel Bernoulli (1700-1782) provide the detailed science that explains lift. They don’t, at least not fully.

The basic problem is that neither theory completely explains real-world observations. Bernoulli’s principle—that the faster air on top of the wing experiences reduced pressure—is correct but doesn’t explain why it’s correct. It also doesn’t explain inverted flight. That’s where Newton’s second and third laws (see the sidebar below for details) come into play. Taken together, Newton’s laws describe how we can fly inverted and how angle of attack works. But they don’t have the details we need from Bernoulli. Still, once we put Bernoulli and Newton in the same room, then sprinkle some Cayley throughout, we have a working idea of how to build and fly an airplane. But we still don’t know exactly why the air on top of the wing is at a lower pressure than the air underneath it.

We probably were told in ground school that the low-pressure area on top of the wing results from the air particles passing over it having to accelerate in relation to the air below the wing so that they both arrive at the trailing edge at the same time and rejoin. This is commonly known as the “longer path” or “equal transit time” theory.

But there’s no science that says the air particles have to arrive simultaneously. In fact, according to NASA’s Glenn Research Center, “The actual velocity over the top of an airfoil is much faster than that predicted by the ‘Longer Path’ theory and particles moving over the top arrive at the trailing edge before particles moving under the airfoil” (emphases added).

Yes, the wing’s curved upper surface establishes an area of lower-pressure air above it, but there’s no venturi effect because there’s no venturi. Bernoulli doesn’t really tell us why this happens, only that it does. Bernoulli also doesn’t explain how non-cambered wing designs—those lacking a curved upper surface, or nearly so—can generate lift, or how symmetrical airfoils, with identical cambers on the top and bottom, also create it. And we haven’t even gotten to inverted flight.

As NASA says, “We can…use Bernoulli’s equation to compute the pressure, and perform the pressure-area calculation and the answer we get does not agree with the lift that we measure for a given airfoil. The lift predicted by the ‘Equal Transit’ theory is much less than the observed lift, because the velocity is too low. The actual velocity over the top of an airfoil is much faster than that predicted…and particles moving over the top arrive at the trailing edge before particles moving under the airfoil.”

One way to explain inverted flight is Newton’s third law, that every action has an equal and opposite reaction. The simplest demonstration is to put your hand out the window of a moving automobile. By holding your hand horizontal relative to the oncoming air, there’s little resistance. Hold your hand perpendicular, however, and the moving air tends to push it rearward, toward the back of the car. You’ll need to flex your arm toward the front to keep it in place. If you hold your hand at, say, a 45-degree angle, it tends to want to move both rearward and upward at the same time. You need to flex your arm both forward and downward to counter the effect.

Your hand’s movement at the perpendicular and the 45-degree angle demonstrates Newton’s third law, regarding equal and opposite reactions: When the oncoming air meets your hand, it pushes up and/or aft. The same thing happens when a wing—or any other surface—is positioned at an angle not aligned with to the relative wind.

Thus, the inverted wing still generates lift by flying at an angle of attack greater than would be required when the cambered surface is the upper surface, thanks to Newton’s third law: as the air is pushed down by the wing, the Newtonian reaction also pushes up on the wing.

One thing to keep in mind when considering inverted flight is that a typical horizontal stabilizer is an airfoil. It’s mounted with the cambered surface facing down so its lift is directed opposite that of the wings as a counterbalance in favor of stability. So it’s not correct to say that lift only works in one direction. Presuming a cambered wing, the inverted airplane stays airborne more as a result of Newton’s third law than anything Bernoulli had to say.

Since lift is a force, Newton’s second law, which states that forces result from accelerating a mass, also figures prominently in our journey toward understanding it. The mass we’re concerned with is the air flowing past the airfoil as a fluid. As the air flows past the airfoil, some of it is deflected, or turned, which changes its velocity in magnitude, direction or both. At the leading edge, air is deflected upward and downward thanks to the airfoil’s shape. Also thanks to the airfoil, air is deflected downward as it passes beyond the trailing edge. Because of Newton’s third law involving equal and opposite reactions, the downward flow of air pushes the wing upward, creating lift.

One thing Newton’s laws regarding forces and reactions do not do, however, is explain why the relatively low-pressure air exists above the wing. Of course, neither does Bernoulli.

According to a February 2020 article by Scientific American (SA), aerodynamicists are aware of the gaps in theories of lift even as they apply ever-more advanced fluid dynamics computations. And they are moving toward what some might call a unified theory of lift.

One such aerodynamicist is Doug McLean, a former engineer at Boeing Commercial Airplanes and author of Understanding Aerodynamics: Arguing from the Real Physics. Part of McLean’s book is devoted to explaining lift and, as SA describes, he settled on four necessary components: “a downward turning of the airflow, an increase in the airflow’s speed, an area of low pressure and an area of high pressure.”

“They support each other in a reciprocal cause-and-effect relationship, and none would exist without the others,” his book is quoted by SA. “The pressure differences exert the lift force on the airfoil, while the downward turning of the flow and the changes in flow speed sustain the pressure differences.”

According to SA, McLean also came to realize his book “had not fully accounted for all the elements of aerodynamic lift, because he did not explain convincingly what causes the pressures on the wing to change from ambient.” McLean updated his text, recognizing that air is a fluid and that it interacts with a solid object. Fluid flows around objects are wildly variable in nature, requiring a separate discipline—fluid dynamics—and massive computing power to model the non-uniform behaviors.

Lift production has a broad impact on the air’s velocity and pressure as it comes in contact with the airfoil. There is a higher-pressure area below, a lower-pressure area above, and particles of air are accelerated and decelerated. Then, after the airfoil passes, velocity and pressure return to ambient. In other words, the science behind what actually happens when an airfoil generates lift is vastly more complicated than Bernoulli and Newton had tools to understand. Although the fluid dynamics field has made great advances, there are still minor details about lift production and the host of variables presented that elude the mathematicians.

For our purposes, few of those final details matter. What does matter is for us to understand that lift is produced by the complex interactions of a fluid (air) as it impacts solid objects (airfoils) or, if you prefer, vice versa. These interactions result in variable, dynamic combinations of pressure changes and downward-flowing air that produces lift.

Several pearls of wisdom disguised as witty sayings have stuck with me from a test-preparation course I took when studying for the commercial and flight instructor written exams. One of them, referencing Bernoulli, is, “The sky sucks.” Another is, “If you have enough power, you can fly a brick.” The latter also highlights that this discussion of lift presumes a constant angle of attack and steady airspeed. In the real world, these values rarely are constant for very long and in any case depend heavily on how much power is both available and applied. The sidebar "What About Power?" below touches on power’s relationship to lift generation, which is itself another topic.

There are many subtopics of lift generation that are not addressed by this article, perhaps most notably how pressure differentials are distributed above and below the wing, and how their centers may move. When the centers of pressure move, so must the airplane’s attitude change, and vice versa. In part and for a given wing, these pressure differentials depend on angle of attack and airspeed, and remain important topics for understanding lift.

The punchline to all this is fairly simple: Generating lift is a complicated, dynamic process that depends on a handful of physical laws regarding pressure and force. While those laws are well-understood, their application can leave us with gaps in our understanding that are difficult to fill without embracing the interactions they define, which are themselves dependent on those same physical laws.

Sir Isaac Newton first published what has become known as his laws of motion in 1687. Newtonian physics works well to explain the behavior of objects moving at well below relativistic speeds, so using it on a piston single shouldn’t present a problem.

A popular translation of Newton’s second law is, “The alteration of motion is ever proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed.” This is the basic principle of acceleration: the speed of an object depends on the force applied.

This law often is described with the phrase “equal and opposite reaction” when an object is acted upon by an outside force. Its translation reads, “To every action there is always opposed an equal reaction: or the mutual actions of two bodies upon each other are always equal, and directed to contrary parts.”

According to NASA, the “equal transit time” or “longer path” interpretation of Bernoulli’s principle states that “wings are designed with the upper surface longer than the lower surface, to generate higher velocities on the upper surface because the molecules of gas on the upper surface have to reach the trailing edge at the same time as the molecules on the lower surface.”

The error arises because, in reality, “the velocity on the upper surface of a lifting wing is much higher than the velocity which produces an equal transit time. If we know the correct velocity distribution, we can use Bernoulli’s equation to get the pressure, then use the pressure to determine the force. But the equal transit velocity is not the correct velocity.”

One of my least-favorite airplanes to witness—the AV-8B Harrier VTOL military aircraft, because it is loud—provides an extreme example of brick flying. Of course, a vertical Harrier takeoff involves no lift generation, only thrust exceeding the aircraft’s weight. Not until the Harrier’s wing is moving forward at what might be called a good clip is the downward vector from its single jet engine eliminated in favor of forward thrust.

To generate lift, we must have some form of energy, either kinetic (forward motion) or potential (altitude), or both in some combination. Regardless of which we use and in what proportion, the lift produced likely will change with the energy we apply to the task. In turn, control input also likely will be required to adjust the airplane’s attitude and compensate for increased lift from the wing and from the tail.

Unsurprisingly, materials published by the FAA don’t go into great detail on the relationships between Bernoulli’s principle and Newton’s laws. But they got the gist of it right. Consider the following excerpt from the FAA’s Pilot’s Handbook of Aeronautical Knowledge, FAA-H-8083-25B (PHAK):

“Applying Bernoulli’s Principle of Pressure, the increase in the speed of the air across the top of an airfoil produces a drop in pressure. This lowered pressure is a component of total lift. The pressure difference between the upper and lower surface of a wing alone does not account for the total lift force produced. 

“The downward backward flow from the top surface of an airfoil creates a downwash. This downwash meets the flow from the bottom of the airfoil at the trailing edge. Applying Newton’s third law, the reaction of this downward backward flow results in an upward forward force on the airfoil.”

This article originally appeared in the April 2020 issue of Aviation Safety magazine.

For more great content like this, subscribe to Aviation Safety!