Ever since I started to be interested in science, the explanation that I’ve read about how planes stay in the air has been based on the Bernoulli principle: As the wing moves through the air, air flows around it, and the profile of the wing causes it to flow faster on the upper side than the lower side. This creates a pressure differential between the two sides, and that’s what pushes the wing up.
So far, so good. But lately I have repeatedly read an explanation (and in publications that I wouldn’t consider fringe) that relies on Newton’s third law: The shape of the wing, as it moves through the air, pushes the air that it hits downward, and this creates upward lift.
This explanation sounds plausible, but it is so radically different from the Bernoulli effect explanation summarised above that I almost feel I’m experiencing a Mandela effect here. Surely in the (more than a) century that humans have been flying with heavier-than-air machines, and all the research that is going into improving planes, the theory of flight is thoroughly understood. Can it really be that the view of what is happening in physical terms, or at least the way this is explained in popular science, has changed so drastically?
My understanding is that it is both the shape of the wing (and the Bernoulli effect) as well as the angle of attack of the wing, which pushes down on the surrounding air, and which by Newton’s third law pushes back to create the force referred to as lift.
It can’t solely be the shape of the wing, or no plane would be able fly inverted.
Actually, it’s a god question. Several years ago I saw a spate of articles going into how airplanes reallly fly, and professors being annoyed at the incorrect and lazy explanations for th processes, especially ones that misused the Bernoulli efect.
In private flight school in the 1980s the textbook presented the Bernoulli Effect. However, more recent discussions focused on the idea that the too-side air “doesn’t care” and has no incentive to flow faster. Further, some wings are symmetrical, so no difference in chord between top and bottom.
So my once rock-solid understanding is in crumbles.
Hold a sheet of paper in front of your mouth so that it droops down. Blow over the top of it, and you’ll see the paper rise. That is a simple demonstration of the Bernoulli principle.
I’ll post something more substantial later if I can. For now, this is the best book I’ve read which reconciles (or at least explains side by side) the Bernoulli and the Newtonian explanation of lift:
That’s true. It’s also about 95% irrelevant to how airplanes fly. As @Raza said, “Bernoulli effect” was the standard pedagogy until fairly recently.
Airplanes fly because the wing forces a mass of air downwards with sufficient F=ma that it offsets the gravitational force trying to make the airplane drop like a brick.
The vast majority of lift is the “barn door effect”. Hold the wing at an angle to the incoming air such that the incoming air “bounces off” the bottom side and is deflected downwards.
A secondary effect at lower speeds is Coanda effect. Air will tend to follow a convex curvature. With the result that a curved upper surface will impart a downward vector to the air departing the trailing edge. Trailing edge flaps get some of their effectiveness from this topside flow in addition to simply being big barn doors that force bottom-side air downwards.
Somewhere as a rounding error, Bernoulli gets a look in. But much more as a result of accelerating air upwards than any notion that topside and bottomside air have to meet back up exactly aligned at the trailing edge.
Consider that any upward acceleration of air is a direct subtraction from net lift. So the pressure drop is real and readily measurable even with primitive 1900s tech. But the contribution of the pressure drop to net lift is real small.
For reference, here’s a previous discussion about the Bernoulli effect and its relative irrelevance:
Also here, nominally about jet engines, but where I was educated about the fact that even the “barn door effect”, or a flap at the edge of a wing, is technically an airfoil – it doesn’t have to be the pedagogical Bernoulli-touting wing cross-section:
Indeed, it seems to me that early airplanes, with their thin flimsy fabric wings, exploited both of those effects, and not at all the Bernoulli effect because they didn’t have the cross-section profiles of modern wings.
It may be hard to explain to the layperson, but it’s well-understood by aerodynamicists. The lift equation sums it up fairly well, and includes all of the variables that contribute, along with the extent of their contribution:
L=Cl⋅(ρV^2)/2⋅A where:
CL = coefficient of lift - the complicated part. It is a function of flow conditions, wing geometry, and angle of attack, and can be mathematically determined for a range of geometries and simple flow conditions, but usually ends up being determined experimentally for a given lifting body.
ρ = air density
V = velocity
A = wing area.
density times the square of the velocity, and then divided in half, is the dynamic pressure and the Bernoulli equation part.
When I was arguing with someone deeply wedded to the Bernoulli explanation I asked what motive the top-side air had to accelerate so it wound up even with the bottom-side, shorter path air again. “Was it having an interrupted conversation?”
Most of the benefit of the “Bernoulli wing” or other convex profiles isn’t the raw lift force, which as stated in posts above is rather minimal. The benefit is in its lift response profile to different angles of attack. A symmetric “barndoor” wing is going to have a very steep lift response to angle of attack and induce turbulence and stall condition much more rapidly. A curved wing is going to maintain a shallower lift response over a greater AoA, and not collapse into a stall condition from the induced turbulence until much much later.
So when asked why, if Bernoulli lift effect is so minimal, do we use that wing shape so prevalently? The reason if for all of the other highly desirable dynamic flight profiles that it is excellent at.
It’s not “Bernoulli or Newton’s Laws”. Bernouli’s Law is Newton’s Law, as applied to fluids. At least, that’s what the real Bernouli’s Law is-- It has nothing to do with the nonsense about air moving faster over the top of a wing.
IIRC, when an airplane flies inverted, it is indeed naturally going to begin veering more and more downwards towards the Earth, and so it must continuously use its tail elevators “downwards” (down being up) in such a way that the airplane, while inverted, continues to go back up towards the sky in order to maintain level flight.
(Disclaimer: I have only ever flown real airplanes in level-upright flight. Flight simulators do not count.)
Use of the elevators on the tail of the plane is also how the plane changes its angle of attack. And any small effect of the elevators themselves (considered in isolation) is vastly outweighed by their effect on the overall angle of attack of the plane (and the main wing).
There is a similar phenomenon that occurs with submarines. There is a hydrodynamic force created by adjusting the stern planes. But the effect of the planes (considered in isolation) is vastly overwhelmed by the fact that the stern planes cause the entire hull of the submarine to be angled up or down.
Still confused. I trust this has been studied statistically in wind tunnels. Put a wing in a wind tunnel and attach it to a scale so that upward force can be measured. Hold wind speed constant. Vary angle of attack. Vary shape of wing: a flat plate would eliminate the “Wing curve effect”. (Use hidden weights to equalize weight of wing across different shapes.) Take dataset and estimate equation:
Force = constant + b1*(angle of attack) + b2*(bulge in wing)
I think the desired calculation is this:
b1*(mean(angle of attack))
-----------------------------------------------------
b1*(mean(angle of attack)) + b2*(mean(bulge in wing))
Yeah-yeah you don’t have to work with means. Yeah-yeah nonlinearities. Yeah-yeah Jensen’s inequality. I’m just trying to obtain a rough decomposition of lift forces between angle of attack and shape of wing. You could also plot a ratio similar to the above: I get that. You could also estimate the actual physics. I’m just trying to start with a rough picture.
An airplane, even a highly manueverable one, is indeed optimized for upright flight. As such the wing is installed at small upward angle to the fuselage. This is called the angle of incidence.
The purpose is to align the fuselage at the cruise condition with the relative wind for minimum fuselage drag, while also aligning the wing at an angle of attack relative to that relative wind that will produce the cruise lift requirement. So both the wing and fuselage work together to produce the needed lift with minimum drag. Typical angles of incidence are just a couple of degrees. It’s not much, but it adds up.
Now fly that same airplane upside down. If we assume for a moment that the wing is equally efficient upside down, we need to raise the nose enough to offset that built-in angle of incidence, and then the same amount again to provide the wing the same angle of attack it has in upright cruise.
For concreteness, let’s say the airplane has a 3 degree angle of incidence and can cruise with the fuselage dead level. To fly level inverted, they need to put the nose at a 6-degree up angle to provide the usual 3 degree angle of attack to the wing despite the -3 (from this POV) angle of incidence built into the wing / fuselage junction.
But wait, there’s more.
The wing on many airplanes, even aerobatic ones, is not equally efficient upright or inverted. The wing works better, IOW produces more lift for a given angle of attack, with a positive angle of attack than it does for the same negative angle of attack.
For this sort of wing, you need to further increase AOA when flying inverted. Going back to our example, in inverted flight you might need 3 degrees nose up fuselage to offset the now-inverted angle of incidence. Plus 3 more degrees, 6 total, to give the wing its usual 3 degree angle of attack for cruise lift. Plus a further 4 degrees to offset the relative inefficiency of the inverted wing versus the upright one. So now you’re driving along with the nose tilted 3+3+4 = 10 degrees up to generate the lift necessary to maintain a level flight path.