Fuzzy Aerodynamics

A week or so ago in an aircraft owner’s forum, the exact thing I was concerned about happened, i.e., a pilot trying to explain how an airplane creates lift to a newer pilot started talking about “the downforce” under the wing that pushes an airplane up into the air (you know, because that’s how the reaction force…referred to in Newton’s Third Law is created…and the airplane reacts by going up!). I’d think it was funny but AOPA’s current iteration of “Essential Aerodynamics” also says that a wing pushes down on the air, creating a misperception that will probably take a decade to clear up. It’s not that Newton’s Laws are not involved; they are. The popular misunderstanding of what that means is fostered by the incorrect idea that somehow only Newton’s laws apply and Bernoulli’s laws are somehow incorrect and is all pure nonsense. So, I’m going to give you a technical explanation of why and do it without going into a lot of math. (I’m going to assume you’re not too dumb to follow what I’m saying, unlike some other folks who say we don’t need to teach aerodynamics like engineers do it because we’re not designing airplanes and then screw the whole thing. If you’re new to this controversy of befuddlement and want to get completely spun up, see the blog entitled “When Simpler Becomes Dumb”, another entitled “Only One Form of Lift”, go through AOPA’s “Essential Aerodynamics” presentation, and come back here. Otherwise, just read on; I’ll explain it in enough detail where you can grasp the core issue.)

The text we used in my aerospace engineering classes discussing aircraft performance was “Airplane Aerodynamics” by Dommasch, Sherby, and Connoly. Section 2:4 “Development of the Bernoulli Equation” explains how,by analyzing a small packet of air as it moves using Newton’s Second Law (F=ma) (Spoiler alert: Newton’s Third Law is not involved here) and assuming no mechanical or thermodynamic losses (conservation of momentum and conservation of energy),one derives Bernoulli’s equation. For incompressible flow (a good assumption for flows less than 200 knots or 230 mph), Bernoulli’s equation is:

p+(D(V2))/2=constant

where p=Pressure, D = air density, and V2=velocity of the airstream squared. P is the “static pressure” term and “D(V2)/2” is the “dynamic pressure” term. So, as the velocity of the airflow increases, the dynamic pressure (pressure in the direction of the airstream flow) increases and the static pressure (pressure of the mass of air and measured perpendicular to the flow) decreases.

Section 4.3 of that text is entitled “Development of the Lift, Drag, and Moment Equation”. It starts out with this: “…the only forces that can act on an object moving through a fluid are those produced by friction (shearing stress in a fluid) or those produced by pressure. Except for when minimum drag is considered, the pressure forces are by far the most important and completely responsible for the production of lift”. (NOTE: I know the reference to “minimum drag” creates a question; I’m researching that and will post an answer here once I have it.) It then goes on to discuss the generation of the force equations associated with deflecting a small packet of air using Newton’s Second Law (F=ma) to calculate the force produced. After showing you the answer, it states: “An airfoil..produces lift by changing the momentum of a given stream tube of air and is capable of producing a force greater than that predicted by the use of simple energy solutions.” In other words, an airfoil produces more force than can be attributed to this simple calculation (F=ma) alone.

So, the blind use of Newton’s second law doesn’t account for the total amount of force generated by an airfoil (or a wing). Notice, too, this analytical approach uses a “microscopic” viewpoint to derive the equations, a common practice when starting at the bottom of an engineering or scientific analysis. How can you figure out what the lift is practically? By stepping back and examining the pressure distributions around the airfoil and calculating the forces they generate. This is easily done, which is why it’s routinely used. (This is using Bernoulli’s principle, folks.)

Have we disregarded Newton’s laws? Not at all! And in doing so, we have generated Bernoulli’s principle, which gives us a more practical and easier to understand approach to working with many aerodynamic problems. Not only does its use make engineering solutions easier, but using Bernoulli’s principle makes for an accurate and easier to understand explanation for the layman. How Newton’s laws apply to aerodynamics is not intuitive; and as we’ve already discussed, often leads to misperceptions, especially when understanding of the subject is incomplete. It’s easy to jump to incorrect conclusions based on what we are familiar with, and most people seem to latch onto Newton’s Third Law, which we see in common thrust/acceleration relationships. Because of that, it jumps into the forefront of thought much more than Newton’s first (i.e., an object at rest tends to stay at rest or continue moving until acted on by an outside force) or second (F=ma).

There’s a more important reason to talk about Bernoulli’s principles when teaching aerodynamics to pilots. When I use Bernoulli’s to explain what’s happening with lift, I not only stick to a technically accurate explanation; but I continue to make a linkage back to airflow around the wing, which for a pilot is the critical thing to control. It’s easy to see the case surrounding controlling the angle of attack to keep from disrupting the airflow controlling the lift. If you try to explain how a wing works using Newton’s Third Law, you will probably think the wing creates a downward jet of air as our wayward pilot did. It does in the form of downwash around a wing but its primary effect on lift is to create induced drag by canting the lift vector rearward and decrease the effective lift the wing produces; to use Newton’s Law second and third laws to find the lift you have to calculate the TOTAL change in momentum of the flow field around the aircraft (and not all of that is going to be in the vertical plane). Want to teach that in your pilot information classes? Better be ready for calculus and lots and lots of work!) If you have a pilot thinking he can create more lift by increasing the wing’s “upward” reaction, you also just created the potential for having a pilot INCREASE back pressure when he encounters a stall to increase the downward force of the “jet” or create “impact lift” (if you teach that concept, too). Poo-poo that possibility if you want; but you can never predict how someone with the wrong idea will react or when you plant the wrong information on their head. I believe it’s a very bad idea to teach anything that is technically incorrect or that can be easily misconstrued into a bad result.

So, the next time you hear that only Newton’s laws apply to aerodynamics and Bernoulli’s don’t, hopefully you’ll understand there’s no way that can be true. Explain that Bernoulli’s equations COME FROM an analysis of the behavior of an airstream using Newton’s laws (Newton’s second, mainly), and you CAN’T DISCOUNT ONE WITHOUT DISCOUNTING THE OTHER. In fact, trying to make the case that “only” Newton’s laws apply can only be correctly understood by PERFORMING a very in depth technical analysis as I have discussed; and that makes understanding the subject harder, not easier. As Einstein said: “Make things as simple as possible. not simpler.”

Because when you take it past that point, you make it wrong.