Just about every pilot would agree that studying certain aspects of flight can be a time-consuming mental workout. Any attempt to master complex aviation subjects can be frustrating, if not impossible, when pilots are given conflicting or incorrect data. One topic in particular, how lift is generated, tends to muster a tremendous amount of heartache among aviators and aerodynamicists alike. In fact, if you look at five different aviation references, you’re likely to find five different explanations about how lift comes to be. Even worse, some sources advocate a specific theory, while rejecting the premises favored in others. Groundschools, instructors and mainstream pilots have a tendency to unquestioningly embrace what’s written in certain texts, each of which is quick to defend its theory. This shouldn’t be much of a surprise, as it’s said that “arguing with a pilot is like wrestling a pig in mud—after a while you begin to think they like it.”
The primary conflict about how lift is created centers on two white-wig-wearing historical figures—Sir Isaac Newton (1642-1727) and Dr. Daniel Bernoulli (1700-1782). Those who prefer Newton’s ideas (i.e., Newtonian lift) believe that air is forced downward behind the wing. Simultaneously, the wing is forced upward with the famous “equal and opposite reaction” described in Newton’s third law. Then there are those who favor Bernoulli’s celebrated principle that as airflow accelerates, the static pressure within the airflow drops. We all know that the air flows faster over the top of the wing than the bottom. Bernoulli’s equation therefore concludes that the wing gets “sucked” upward by the reduced pressure.
All right, so you’re tired of the guys at the hangar making fun of you for preferring one theory over another. Off you go to prove them wrong. You pull out the classic Stick and Rudder by Wolfgang Langewiesche and quickly find the statement “forget Bernoulli’s theorem.” Still unsatisfied, you reach for Aerodynamics for Naval Aviators. There you find nothing but Bernoulli and something called “circulation.” You find much of the same while inspecting Aerodynamics for Engineers by John Bertin and the more readable Illustrated Guide to Aerodynamics by Skip Smith. In fact, Newton isn’t even mentioned during the lift discussion in the latter book. To add more fuel to the fire, prestigious academic institutions seem to favor one theory over another. Portions of Harvard’s and Princeton’s Websites discuss Bernoulli as though his ideas are the only ones available.
Don’t feel sorry for Newton just yet—he has his group of supporters. The recently published Understanding Flight by David Anderson and Scott Eberhardt dedicates two pages to Bernoulli, mostly about how his theory doesn’t appropriately describe lift, followed by nearly 200 pages about Newton. The Pilot’s Handbook of Aeronautical Knowledge and Jeppesen’s Private Pilot Manual mention that both Newton and Bernoulli have to be considered to accurately define lift (frustratingly, though, an earlier edition of Jepp’s Instrument/Commercial Manual leaves Newton out of the picture entirely). Nonetheless, even among those who prefer Newton, there’s some disparity. Cranfield University, one of the U.K.’s leading aeronautical institutions, offers the suggestion that, contrary to popular belief, the wing pushes upward, providing the Newtonian action, while “the reaction to this would be for the wing to push the air down,” thus producing the requisite lift.
When I asked Dr. Sheila Widnall, professor of Aeronautics and Astronautics and Engineering Systems at MIT, about this argument, she responded, “It’s scary to think there might be controversy about this issue. This is the basis of all subsonic aircraft design.” Indeed, it is scary. Pilots at all levels are receiving conflicting information about how their favorite toys stay in the air. Equate this to some doctors thinking the heart works one way, while others believe it works in an opposing manner. Yikes!
If you’ve been standing on a soapbox supporting one theory over another, there’s no need to hide your face the next time you pass the flight-school water cooler. The truth is that, among the Newton-Bernoulli disputers, neither party is wrong. According to Dr. Jean-Jacques Chattot, professor of Mechanical and Aeronautical Engineering and director of the Center for Computational Fluid Dynamics at the University of California-Davis, the descriptions of lift advocated by Newton and Bernoulli “are actually the same thing, just from two different perspectives.” How is this possible? Take another look at the dates when Newton and Bernoulli lived.
Newton presented his laws in a publication released in 1687 (good luck reading the original as it was in Latin). Bernoulli was an avid science and mathematics scholar who followed the works of Newton. Not surprisingly, Bernoulli’s equation is actually derived from Newton’s laws. Bernoulli and Newton each correctly describe lift, but use divergent methods.
According to NASA, lift can be calculated by “adding up the pressure variation” as found by Bernoulli’s equation to “[determine] the aerodynamic force on the body.” At the same time, one could verify the value of lift by adding together the “net turning of the gas flow...from Newton’s third law of motion, a turning action of the flow will result in a reaction [aerodynamic force].” Indeed, according to Aerodynamics for Naval Aviators, to get the airflow necessary to produce Newtonian lift, an airfoil must be “able to create circulation in the airstream and develop the lifting pressure distribution on the surface,” which, of course, is described by Bernoulli.
But if both Newton and Bernoulli are correct, how did so many pilots get so off track? Well, you can pin some of the blame on educators and writers for their attempts to take something that’s rather complex (it is aeronautical engineering, after all) and spin it into something comprehensible to laypersons who aren’t calculus experts. As lift is watered down from the pocket-protector level to that of the average pilot, some things get lost or skewed in the translation. Thankfully, Newton’s laws are fairly straightforward and less confusing.
Conversely, poor Bernoulli’s concept tends to be butchered on a regular basis. Something that’s expounded in many aviation classrooms is the idea of “equal transit time,” which is an analysis of what occurs if two air molecules travel across a wing, one going over the top while the other slides along the bottom. The particle cruising over the curved upper portion of the wing has to travel farther, thus it must move faster to rendezvous with the particle from the bottom of the wing. This contention further states that the two air molecules must simultaneously rejoin one another at the trailing edge of the wing. But nothing could be further from the truth. According to significant wind-tunnel data (see Aerodynamics for Naval Aviators, www.av8n.com/how/htm/airfoils.html and www.allstar.fiu.edu/aero/airflylvl3.htm), the air molecules never meet again because the air over the top of the wing accelerates much faster than most people think.
Another common butchering of Bernoulli’s principle is the concept that a wing is a half of a Venturi tube. It’s true that Bernoulli’s equation accurately describes the pressure fluctuations that occur within a Venturi. However, no matter how you slice it, a wing simply isn’t a half of a Venturi! There’s always a tremendous amount of focus on the upper portion of the wing, but the lower surface also contributes to lift. Depending on the angle of attack, portions of the lower surface of the wing may also generate negative pressures. That, however, is hardly mentioned in most discussions of Bernoulli. Lift only occurs if there’s a positive net pressure difference between the bottom and top of the wing (commonly referred to as “high pressure on the bottom, low pressure on the top”).
Another widely held misconception about Bernoulli asserts that “fast-moving air results in low pressure.” Yet this isn’t always the case. Think about how fast air passes by the static port on the side of the fuselage. Why does it still give accurate static information as you accelerate down the runway? The reasons are somewhat complicated. Bernoulli’s equation requires you to compare “apples to apples and oranges to oranges.” The equation is actually an analysis of the total energy within a particular airflow. Therefore the total energy of air at rest (apples) isn’t equal to that within a 100-knot airflow (oranges). Actually, if you’re cruising at 100 knots, low pressure will only occur at locations where air is accelerated to a velocity higher than that of free stream flow (100 knots).
Now you’re probably thinking, “Great, they’re both right—there’s even more to learn!” Don’t get bent out of shape. Since both concepts are true, you can pick the one with which you’re most comfortable. Bernoulli’s theory tends to be harder to understand and is favored by mathematicians and engineers. Newton’s is palatable to pilots because it’s more intuitive. Regardless of which philosophy you prefer, the important conclusion is that you realize there’s more than one correct way to explain lift.