The mysteries of aerodynamic lift
scientificamerican.com
scientificamerican.com
As far as I understand it, the fundamental reason airfoils in boats and places work the way they do requires viscosity. Without that, the math falls apart and the ship doesn't move. It is not enough to treat air as a bunch of tiny billiard balls bouncing off the bottom of the wing (the Newton's third law argument). Likewise, you can't pretend the air above and below the wing are each confined to their own perfectly frictionless tubes with different velocities (the Bernoulli argument), since the air moving over the wing is part of a continuous whole extending out arbitrarily far.
In order to explain how fabric-thin sails are able to generate lift, how planes with curved wings can fly upside down, and how the ground effect comes into play, you have to treat the surrounding fluid as a continuous medium with viscosity. That's how the math works. Unfortunately, we don't seem to have a good intuition for how that feels so it's hard to treat that as a satisfactory explanation.
Really? Can you elaborate?
And of course here comes that:
https://newatlas.com/wind-powered-car-world-record/11346/
"March 29, 2009 With a wind speed of just 30mph (48kmh), British engineer Richard Jenkins has set a new land speed record for a wind-powered vehicle at blistering 126.1mph. "
Or you can just think of it like squirting toothpaste.
The wind pressure on the sail and the water pressure on the keel form the two "objects" being pushed together and the sailboat "squirts" out the side.
Edit: The angle between the sail and the keel is like the angle on the triangle. The keel really was a great invention.
It's two concurrent visualizations of the same force.
The pressure that the air above the wing applies to the top of the wing is lower than the pressure that the air below the wing applies to the bottom of the wing. The net force is upwards.
There are two kinds of sailboats. There's the big square sailed ones which always have to move downwind. Then there are the triangular sailed ones, which can move in any direction except for right into the wind. (Maybe a 30 degree on each side dead zone).
The square sailed boats can't move faster than the wind, as they just rely on the air pushing on the sail to move with the wind.
That's also how the triangular sailed boats move when moving directly downwind. They too can't outrun the wind.
However, when moving sideways to the wind, the wind passes over the sail, which looks like a wing sticking out of the water. Like a wing, there's a "lift" force generated, although it's not up but sideways. The boats also have a fin sticking into the water, which prevents the boat from slipping directly along with that "lift" force, and instead move forward.
Actually, that's not true. Square rigged "pirate-style" ships are more efficient when sailing downwind compared to fore-and-aft style sailboats, but they can still sail just fine close-hauled (into the wind) or on a reach (perpendicular). There are some efficiency pros and cons to both styles, but they all have the same aerodynamic capabilities.
The main reasons square-rigged ships fell out of fashion, as far as I know, are mostly logistically. Square-rigged sails make sense when you have a really big ship. A single huge fore-and-aft sail would be too hard to handle. Square-rigged ships break that sail area down into a larger number of smaller individually manageable pieces.
But larger vessels are almost all powered now. For a smaller sailing vessel, it's easier to manage the simpler Bermuda sail plan, and its more efficient. I think maybe square-rigged ships have an efficiency advantage when going straight downwind, but most sailboats simply carry a spinnaker to cover that case.
(Caveat: I'm not a sailor, I've just read some textbooks.)
They typically (or maybe always?) have "staysails", which run fore-and-aft between the masts, which works mostly like the main triangular sail you think of with a simple sailboat (with the exception that, as far as I know, these staysails aren't on a boom that can change its angle relative to the ship). These are able to take the wind at an angle but still generate forward thrust.
The "yards", the sections that hold the square sails perpendicular to the ship, are also able to rotate between perpendicular and nearly-parallel to the ship, which lets them take advantage of a wide range of wind directions.
(I'm also not much of a sailor, I've just sailed some tiny single-sail boats, but I've learned a lot while reading through the Aubrey-Maturin series and from playing the game Naval Action)
This isn't quite right, as split fore and aft rigs existed that solved this problem. I suspect it is more that power replaced sail for crossing oceans and square sails make little sense for coastal work so they had already switched to fore and aft rigs (with a few notable exceptions, such as Humberkeels in the north of England).
True, but it gets more complicated than that. For fast long-distance commercial travel they were replaced by the steam and later diesel propulsion, which both a) were faster and b) required less crew (so were logistically superior).
On the other hand, where sailing is still used (and that's mainly sport and leisure) the square rig is still here, only in an evolved form: the spinnaker. But whenever the speed is not the primary factor, fore-and-aft rigs (primarily Bermuda) is preferred because it requires far less crew. And then again, when the goal is to have plenty of crew -- like in some navy office training -- classical square rig is still highly merited [1].
I think that only really applies when the sails were set from aloft. I'm familiar with square-rigged cargo vessels of around 60ft in the UK that were crewed by 2.
Some numbers from Wikipedia:
In 1902, the Preussen, famously huge square rigged ship launched with a crew complement of 45-49 while the contemporary Thomas W. Lawson, schooner rigged and even bigger, got by with 16-18.
https://en.wikipedia.org/wiki/Preussen_(ship) https://en.wikipedia.org/wiki/Thomas_W._Lawson_(ship)
The boat starts moving forward. But, because the wind is perpendicular to the boat, even when its moving the wind is still coming in at the same velocity, so it's still producing thrust. If you can get the boat efficient enough, it can harness enough of that wind energy to reach a velocity along the sailboat's line of motion higher than the velocity of the wind relative to the ground.
Note that boats can only do this when sailing at least somewhat offcenter from the wind direction. When sailing directly downwind, the faster the boat goes, the slower the wind is relative to the boat, leeching away thrust.
The motive force on that vehicle is a gear and chain between the prop and the wheels. And prop blades are set at an angle to the wind.
Consider a boat on a beam reach, where the wind over the water is at 90 degrees to its track. If the boat is travelling at wind speed, the apparent wind over the deck is at 45 degrees to the bow.
The useful angle of attack for airfoils goes up to about 15 degrees, so let us assume that the sails are set to this. Therefore, the chord of the sail is at 30 degrees to the boat's track, its lift is at 60 degrees to its track, and so half the total lift is in the direction of motion [1]. So long as this exceeds the total drag of the boat, from the water and the air, then it will continue to accelerate.
[1] To simplify (and to go faster!) assume a multihull sailboat, hydrofoil, or a dinghy with its crew hiked out so that is not heeling appreciably, as when a boat is heeled, a component of its sails' lift is directed downwards.
\\ wing is to wind as seed is to fingers \\
Anyway, absolutely flat wings generate lift as long as the angle of attack is non zero. But, by changing the wings shape they get more efficient. The reasons for that are complex differential equations that don’t really have simple plain English explanations, which is why people do so much testing and simulation. Aka simple 2d diagrams don’t result in: https://en.wikipedia.org/wiki/Wingtip_device
What’s even more confusing is most wing diagrams put the center line in the wrong location. If you take a symmetrical tear drop shape with zero angle of attack the bottom will be sloped up at the same angle the top slopes down. Thus if you instead lay that teardrop so the bottom is flat that represents a positive angle of attack. Granted, wings generally don’t have a symmetric shape, but similar principles apply.
Why not? You have a flat plate with high pressure below and low pressure above. Air escapes around the end of the plate at the wingtip from the high pressure to the low pressure area, reducing net force. So you put some sort of barrier to impede the flow - a wingtip device.
The purpose of an airfoil, in this approximation, is giving the pulled air a longer, gentler acceleration compared to the short peak of acceleration a flat wing would require at the same angle of attack. You won't be able to calculate optimal airfoils with this model, or even a winglet, but it's good enough for many of the usual little riddles like symmetric airfoils, inverted flying etc.
The thing is, both sides of a wing are defined by some nonlinear polynomials, and aft edges are sharp. Machinists don’t/can’t use such surfaces for any reference purposes so centerline can’t be there.
https://aviation.stackexchange.com/questions/7560/what-are-t...
Angle of attack is a separate issue.
To be clear I am not saying how the wing is mounted arbitrary, just what angle is written down in the documentation. Chose a different centerline and that angle changes even as the aircraft stays the same.
Bernoulli's principle is often misunderstood. The principle itself doesn't say anything as to why different speed effects are observed around airfoils. It only states that within a steady state of fluid flow, increases in speed are associated with a drop in static pressure or a decrease in potential energy. That's it.
Again, as to why air flows faster over on one side of an airfoil, or similarly a sail isn't explained by the principle. However we can measure the airflow around airfoils and see that it is flowing faster over one side. Hence, we can accurately model forces exhibited on a wing using Bernoulli's principle under the appropriate conditions...
When the sail has no thickness the outer flow cannot go faster and still be a valid Bernoulli effect, because the outer and inner paths have the same distance.
That being said, there might still be another similar principle at work, though technically speaking it should not be called Bernoulli.
If you trace a line on the wing cross section between the stagnation point and the trailing edge you will see the upper surface restricts/squeezes the flow more than the lower surface. So with a constant flow rate, the upper velocity will be higher even without equal transit.
Now that I read about it more, it looks like Bernoulli's principle is just conservation of energy - and as you say, there are no other requirements.
I believe the key fact is instead that the outer flow is forced into a curve, even though the straight path is technically free (no sail to stop it), because a vacuum (low pressure zone, anyone?) would be generated between the outer flow and the sail.
Hence, the sail needs no thickness to generate its lift, but only to separate the inner and outer flow.
Moreover, due to the viscosity of air, the area of influence of the sails goes well past the immediate layer of outer flow, but rather the layers of outer air closest to the sail have a similar "sail" effect, to a lesser degree, to adjacent layers of air.
That's the very simplified version of a simplified explanation used in aviation teaching materials :)
There is no viscosity in solar wind, yet the solar sail is expected to work.
EDIT: s/solar wind/solar radiation/
momentum has nothing to do with energy and vice versa.
For example, energy can be stored (transformed into different forms, short or long term) and released later, momentum cannot.
o_O In a mechanical system Ek = p^2/(2m), where p is momentum. Please clarify if you meant something else.
> energy can be stored ..., momentum cannot.
Have you ever seen a yo-yo?
It just happens that in one particular manifestation of the energy, the kinetic energy, can also be expressed with a squared momentum in the formula - but does not mean that momentum "is" energy by any interpretation.
As I said before momentum and energy are completely different concepts altogether - energy can be stored and transformed. Momentum cannot be stored nor can you transform a linear momentum into another kind of momentum.
If not convinced, consider for a moment (pun intended) that momentum is a vector and it conserves (in each dimension) as a vector! - whereas energy is a scalar and conserves as a scalar.
I beg your pardon?
> does not mean that momentum "is" energy by any interpretation
I never said that. You literally said "momentum has nothing to do with energy", and I gave you one example where they are directly related.
> can you transform a linear momentum into another kind of momentum
Yes, you can. This is exactly why I mentioned yo-yo.
> momentum is a vector and ... energy is a scalar and conserves as a scalar.
That's a good point, it's 100% correct and I'm not arguing with that. But I insist that saying that they are unrelated is still wrong.
Let's go back for a second to where we started. My claim was (and still is) that the only source of aerodynamic lift is the kinetic energy of the air molecules acting on the airfoil. There is just nothing else, after all. This is not conceptually different from how [solar] sail works. Now, in this specific case, the energy of particles acting on the air/solar foil is directly related to their momenta.
So, what are we actually arguing about?
Not sure what could be unclear there at all. Nuclear energy can be turned into any other energy and vice versa. As long as something has mass it has energy - whether or not we can readily transform that is beside the point.
Your recurring yo-yo example only demonstrates that you don't understand the physical phenomena in the first place. The linear momentum is conserved when the yo-yo pulls on your hand and through that your body, you are either pushing or pulling on Earth via gravitational force, the Earth wobbles opposite of the yo-yo (albeit infinitesimally, thankfully). That's the conservation of the momentum.
The rotational energy of the yo-yo has nothing to do with the linear momentum, that rotation comes from the chemical energy of your muscles that have first lifted, pulled or tossed the yo-yo. With that, you have transformed chemical energy stored in your muscles into the rotational energy of the yo-yo. Momentum has nothing to do with energy. Just because both exist and both get conserved. It is quite profound actually that they are not related at all.
As for this discussion we were talking about you conflating momentum with energy, a common misconception actually, your reticence of even remotely entertaining the idea that you did indeed misuse these concepts diverted into a lengthy discussion that slowly drifted away from the actual points to flawed analogies and yo-yos - also not surprising and a common predicament
Why am I still replying? Because it demonstrates why it is so hard to discuss flying (the very point of the original post) the majority of participants conflate and misuse scientific concepts - then go onto lengthy roundabouts to avoid owning up to these mistakes.
As of the yo-yo, let's remove the muscle power and the wobbling earth out of the picture and consider a it a closed system.
We've got a fully wound-up yo-yo, not rotating. It has a certain amount of potential energy. When you release it, its potential energy starts transforming into kinetic energy of linear motion and of rotation. This kinetic energy can be measured at any moment via observing the linear and rotational momenta of the yo-yo, which are the functions of its mass and torque, and the both velocities. Speaking of which, there is no other way of measuring the energy of this system. As it reaches the end of the line, and starts winding up again, its potential energy is zero, its kinetic energy is at its maximum, and its linear momentum changes the direction to upwards.
I'm telling you this to demonstrate that I understand the difference and your main objection is not exactly applicable here.
And, of course, momentum and kinetic and potential energy are intimately related in such a system. I don't understand how one could deny that.
> Momentum has nothing to do with energy
That's what I meant. Kinetic energy is a function of momentum and you are insisting it is not!
Perhaps we are being confused by each other's different ways of using the word Energy. When I use it (in the mechanical context), I mean strictly kinetic energy or potential energy, but nothing else. I've been taught to use it that way and was quite harshly slapped on the wrist (verbally) for failing to stick to it (that is, for magical thinking).
You seem to be using it in a broader sense (e.g. "nuclear energy". I don't know what nuclear energy is -- it s what multiplied by what, specifically?).
The third law of Newton's mechanics tells us that for the plane to get an up force to counteract the gravity, the air must receive and equal amount of down force. Therefore what planes must be doing is deflect air masses down. A plane must be applying a downward force to air masses, with total force value of "mass * g", i.e. supply "mass * g * 1second" worth of downward momentum per second. As simple as that.
Assuming the plane/helicopter didn't accelerate up or down and assuming there's no wind.
You can't postulate that something flies as part of an explanation why it can fly...
There are some invariants to the world, I can infer information from those invariants.
Just like if I weigh a bottle in the morning, and it shows 3kg, the. I weigh it in the evening, it shows 2kg - I'll know that net 1kg has left the bottle. Doesn't mean I know how.
https://sciencing.com/calculate-lift-rotor-blades-7680704.ht...
A fluid is governed by fundamentally different physics than a bunch of particles, so just because a bunch of particles hitting an inclined plane also would generate lift does not explain why air hitting the same plane does.
For example, in the particle analog, the upper surface of the wing is totally immaterial. You could make it look however you want without affecting the generated lift. In reality, the amount of lift generated is much more sensitive to what happens on the upper surface than on the bottom.
The angle of attack is important in kickstarting and keeping running various phenomena that ultimately result in pressure differential between both sides of the lifting body (be it wing or other shape).
You really can't "just" explain lift simply.
For a general solution to that question, you need to solve the appropriate Navier-Stokes equations, which take into account both the inertia and the viscosity of the air, and are also explained by Newton (up to the point where Newton does not explain the origin of viscosity.) Once you have the velocity field, you can, if and only if the velocity is low enough that the air behaves as an incompressible fluid, calculate the pressure on the wing using Bernoulli.
One significant issue is that if you do this without taking into account friction at the surface of the wing, and the boundary layer that results, you will find that there is no lift at all! Your solution will show the air that passes under the wing turning around the trailing edge, and flowing forward for some distance over the upper surface. In practice, the presence of a boundary layer causes the flow to separate at the trailing edge (if not before).
Modelling at this level of detail is computationally very costly, and the Kutta–Joukowski theorem can be used instead, for a wide range of practical airfoil profiles.
So yes, it is complicated, once you go beyond the barest hand-waving.
https://en.wikipedia.org/wiki/Kutta%E2%80%93Joukowski_theoremYou need bernoulli to explain why the flow field is changed beyond just the area in contact with the flow. This induces the measured pressure differential, explaining part of lift along with the reaction effects of deflected flow for momentum conservation (NS, Newton's 2nd law). It's simply not _enough_ to say that it's purely angle-of-attack or geometry, and it's definitely not enough to say it's just pressure difference caused by Bernoulli, it's _both at once_.
>One significant issue is that if you do this without taking into account friction at the surface of the wing, and the boundary layer that results, you will find that there is no lift at all! Your solution will show the air that passes under the wing turning around the trailing edge, and flowing forward for some distance over the upper surface. In practice, the presence of a boundary layer causes the flow to separate at the trailing edge (if not before).
Not really true for 2d inviscid flows, a very useful approximation -- you need to enforce the K-J condition IIRC (which includes viscosity in a sense)
In short: fluid dynamics is complex, and you need more than just newton's laws to explain it thoroughly (newton's laws don't explain conservation of mass either...)
I may have made one mistake in that the the separation at a sharp trailing edge may be inevitable simply because of the high acceleration that would be needed to go around it, together with the impossibility of negative absolute pressures, but in more general cases, such as the flow around a sphere, the effect of the boundary layer in triggering separation is important - as it is when we consider a stall, for that matter. The Kutta condition is merely a way of putting trailing-edge separation into Kutta–Joukowski. It is not a law of nature, it is a rule of thumb that makes K-J a realistic and useful model.
Conservation of mass? well, you need that, but who doubts it? You mentioned conservation of energy, and I simply pointed out that you do not need it as an additional constraint, whether or not you are using Bernoulli.
> It's simply not _enough_ to say that it's purely angle-of-attack or geometry, and it's definitely not enough to say it's just pressure difference caused by Bernoulli, it's _both at once_.
Given a situation where Bernoulli is applicable (steady-state flow and inignificant compressibility effects), if you were to measure the airflow velocity and pressure fields around the wing, you would find both that they conform to Bernoulli, and that the pressure summed over the whole wing would account for the entirety of its lift.
Alternatively, if you were to calculate the rate of change of momentum of the entire airflow affected by the wing, you would find that this also accounts for the entirety of its lift. This works even in those cases where Bernoulli is not applicable.
So we have two different approaches to calculating the lift, and summing them would give the wrong answer.
Both approaches can themselves be explained in more fundamental terms, and in both cases, it comes down to Newtonian mechanics.
Neither approach allows us to calculate what the airflow looks like and how the presence of the wing shapes it, so neither approach offers a complete explanation. For that, we need Navier-Stokes, which is also reducible to Newtonian mechanics.
What's wrong with many attempted explanations of lift, by either principle, is that they don't get the details right: they try to simplify the issues to the point where they are simply wrong.
Only for incompressible flow is it a consequence of Newton's second law (NS)
See https://en.wikipedia.org/wiki/Bernoulli%27s_principle#Deriva... -- the broader (applies to compressible flow too) derivation is via conservation of energy and mass
Glad we agree!
In this case, you say simply that 'oh it's the equal and opposite reaction', and that seems theoretically possible. But then you do the experiment, and all of a sudden, you see not only a force due to the third law, but also a pressure differential. Based on the laws of pressure, a high pressure beneath the wing and a lower pressure on top must also exert a force. These pressure laws are as fundamental (and are actually simply a consequence of the third law, since pressure is just a statistical approximation of the third law applied to invisible microscopic particles).
Thus, while almost certainly true the third law does contribute, it's also true that it is not a full explanation. The third law could explain lift, but it does not explain why the pressure differential would exist, and thus cannot account for the extra lift due to that.
The third law would additionally predict that the pressure on top should be greater than that on the bottom. This is an easy experiment to do. Get a piston in a closed cylinder (the piston does not need to partition the cylinder). Place two pressure gauges on each side. Now pull the piston up. The side being compressed has higher pressure. This suggests that, if a flat board moves towards a side of a closed system, that side of the system ought to experience higher pressure. But it doesn't in the case of wings, so that's weird
There is no "extra lift" due to the pressure differential. The pressure differential IS the net force that changes the motion of the air. You can't change the motion of the air without a pressure differential, and you can't have a pressure differential without changing the motion of the air.
> although bernoulli's theorem is largely correct ... the theorem alone does not explain why this is so or why the higher velocity atop the wing brings lower pressure along with it
this blurb is accompanied by an upside down plane with the caption "doesnt explain why planes can fly inverted". this is a "tide goes in, tide goes out, cant explain that" statement [1]. im speechless. some planes can fly upside down, and some cant. its not a mystery we discover through trial and error - theyre designed that way by people who use bernoulli's equations, et al.
equations are not explanations. calling a theorem partially correct because you dont know why it works is totally unrelated. either the theorem accurately represents and predicts reality, or it doesnt. no equation says why itself works, thats nonsense talk.
The article goes on to discuss two accounts that have been given historically, and outlines why they are insufficient. A plane flying upside down is a perfectly fine refutation to the naive Bernoulli "the wing is curved on the upside" explanation.
Which parts do you have a problem with?
> equations are not explanations.
As the article makes painstakingly clear.
The problem in that statement is an implied equivalence between having a good model and having a good understanding of the phenomena in question.
It's not so much a layman's understanding that's at issue, but having what's often called an "intuitive understanding" that doesn't resort to the model.
Sure, it's easy to plug in numbers in to a computerized model, and get answers back about the behavior, as from a black box, but it's quite a different thing to oneself have an intuitive understanding of what's going on.
It's often useful to have visualizations of mathematical models and equations precisely because complex models and equations are so difficult to understand, and this difficulty in understanding them highlights that models and equations are not the understanding itself.
>In inverted flight, the curved wing surface becomes the bottom surface, and according to Bernoulli’s theorem, it then generates reduced pressure below the wing. That lower pressure, added to the force of gravity, should have the overall effect of pulling the plane downward rather than holding it up.
This is not what Bournoulli's theorem states. Bournoulli's theorem doesn't say anything as to why fluid flows the way it flows. It just says for a fluid in a steady state flow, increases in speed are associated in decreased pressure. Hence the principle suggests, if you find a plane is able to fly steady upside down, then expect to find the air flowing faster over the wing on the opposite side of gravity under those conditions - just likewise when a plane is normally flying right side up.
Again why fluid flows the way it does around airfoils is separate question -and really the crux of the mystery here. Answers to this is probably hidden in the solutions to the Navier–Stokes existence and smoothness problem: https://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_existenc...
If you drill down and keep asking "but why", you'll eventually encounter phenomenon you can't explain.
Bernoulli's principle and e.g. the equal-travel-time Bernoulli explanation of lift are totally different things. The point the article is making is that common explanations of lift like the latter are typically incomplete or misleading, if not outright incorrect, regardless of whether they invoke uncontroversial scientific results.
The article also discusses what an actual correct and complete explanation might look like, but (IIRC) outright states that the formal theoretical side of things is uncontroversial as it stands today.
Also Philippe Spalart's quote is right on the money: "It's easy to explain how a rocket works, but explaining how a wing works takes a rocket scientist".
Another example might be explaining why sticky tape is sticky.
Really, you need full Navier-Stokes behavior to explain all the forces acting on the wing. Bernoulli doesn't generalize to a full vector field, it's a simplified version of Navier-Stokes. Calling in the big guns doesn't make for an easy discussion.
(mechanical engineer, I figure I had like 1/3 of the fluids classes the real aerospace guys get).
Stick hand out window, tilt hand, feel wind push hand up. Wind hits bottom of hand, pushes it up. That's the main thing, and everyone already gets that if they've ever, like, experienced wind. Play with it a little and you can feel your hand respond a bit differently based on the kind of "shadow" it's casting in the wind. That's the rest of it, more or less. There, airplanes explained, certainly way better and closer to correct than "well you see the top of the wing is longer than the bottom, so Bernoulli's principle is the reason airplanes can fly..."
You don't have to suspect. Many aerobatic aircraft (not to mention many high performance military aircraft) have wings that are symmetrical top to bottom (they aren't exactly flat but the top-bottom symmetry is enough to prove the point). They still fly. (The article mentions this.)
Ground school was ages ago for me but I do recall a bit of it. I thought the laminar flow on the top was vital for lift even a slight ripple was bad. A flat wing top and bottom would not create lift or poor lift. Well at least for aircraft with flaps and aelerons that need consistent airflow to maintain control.
The difference in the bottom flat part of an aircraft wing compared to the curved top part is what creates the difference in velocity; faster bottom, slower top which creating lift. But again maybe not necessary if you are not in an aircraft that needs to be controlled.
The ramblings of a former private pilot student, but an eternal fan of physics.
The aerodynamics lesson is a cartoon basically.
For example, each sentence you wrote above is both true and false. :)
Start with a cube of still air, with zero mean velocity. Fly a plane through it, and that cube will have a mean downward velocity.
Are you saying if I have a cube suspended in space, and I put e.g. a drone inside it that just flies around in a circle inside the cube, the cube will start to move down? What then? Will the drone crash into the ceiling of the cube because it's independent from the cube itself?
My brain disagrees with this, but I'm a hacker, not a physicist.
But to your question, if it was a glass cube, I'm pretty sure the drone would hover in the middle of the cube while gravity pulls it down exactly like if the drone was turned off, based on conservation of momentum. Sure the drone is pushing the air down, but then the air hits the bottom, bounces up to the top, and then gets pushed by the drone again. It's (very literally) a closed system, so nothing happening inside is really noticeable outside, and vice-versa (steady state, if you smack the box the drone will notice).
A better analogy one of my favorite kids' shows (I think it was the German Wissen macht Ah) made was putting a heavy boat into a pot of water on a scale - of course the scale reflects the weight of the boat, it has to go somewhere.
Fluid dynamics is really damn complex. Wikipedia is actually not that bad.
I'm not sure that's a real thing that happens in real life or theoretical physics.
If the airfoil isn't moving, is anything happening? Or are you talking about a non-moving airfoil with air moving around it? It's impossible to tell the difference between a non-moving airfoil with air moving around it and a moving airfoil with still air around it, given that they're equivalent provided you define the reference frame correctly.
But yes, the relative motion is what matters.
It's like answering "how does a lightbulb work" by saying you put current in and it produces photons.
Most people have an intuitive understanding of the Laplace equation. For example lightning usually hits the peak of mountains. The reason is that in solutions of Laplace equations, field gradient is proportional to curvature. In fluid dynamics, this field is called the stream function. The top of airfoil is more curved than the bottom so the stream function gradient is higher on top which results in higher wind speeds over airfoil.
But the second ingredient is the Kutta condition which represents viscosity. If there were no viscosity, there would be no lift. The Kutta condition is applied to the tail (trailing edge) of airfoil. Without Kutta condition, the speed at the trailing edge would be infinity (because of Laplace equations. Speed around sharp corners is inevitably infinite). Viscosity prevents infinite velocities so we apply another condition at the trailing edge to make the air velocity smooth.
It's kind of complicated and I agree that there is no simple explanation to lift, but if you think about it for a little while, it's not that hard to grasp.
The result is a vortex bubble over the flat surface which effectively changes its geometry and aerodynamic behavior. See figure 2-12 in the following link:
Unfortunately, the author has fallen into the very trap that he is trying to explain. If you were to measure the velocity and pressure fields around the wing of an airplane flying inverted, you would find that they conform to Bernoulli (so long as the airplane is flying slowly enough that compressibility is not an issue, which is another source of complication.)
What the author is doing here is to accept some bogus, hand-waving arguments for why the airflow velocity changes around the wing, such as the equal transit-time 'theory', which is, quite simply, false. To answer that question, you need the Navier-Stokes equations (which are the application of Newton's laws to a viscous fluid), or some realistic approximation.
You may find this more informative:
https://fermatslibrary.com/s/how-airplanes-fly-a-physical-de...
There's also no discussion about what happens when you try and tilt a wing too far upwards - a stall - or why the simple buildup of ice on a wing can cause an otherwise fine wing to lose its ability to produce lift.
If you answer "yes", then the problem with that view is most evident in physics where equations and successfully tested predictions result in counter-intuitive "quantum weirdness" which is hard to reconcile with claims of understanding. As Feynman was supposed to have said, "If you think you understand quantum physics, you don't."
Another problem with such a view is it results in descriptions which sound absurd on their face, such as claims that when people look they see photons. But people look they see objects, fields of color, or have other experiences which are irreconcilable with the abstractions or equations created by physicists.
This is related to what is known in analytic philosophy circles and cognitive science as "the hard problem of consciousness", which is how one reconciles "scientific" explanations of how the mind works with people's actual experiences.
The big challenge seems to be making it explainable to someone with no domain knowledge.
The physical intuition I’ve found, is for plane flight, the plane must move faster in the direction parallel to the ground than the time it takes for those air molecules under the plane to move away and deform around the wing at some average velocity. In this manner, the plane can push off those air molecules as they’re unable to move out of the way quick enough to escape the force. Similar behavior to skipping a stone on water. For lift, you apply torque on the wing by changing the angle of attack. This also leads to some interesting ideas on wind.
There are actually two Bernoulli equations. Remember that Bernoulli’s work is derived for and is only valid along a streamline. A streamline is an imaginary curve that is tangent to the flow field. It’s not some invisible tube, it’s a mathematical representation of a vector field.
The first one is the well known one mentioned in the article. It relates pressure and velocity tangent to a streamline. So if the velocity is somehow increased the pressure drops.
The second equation deals with pressure changes due to curvature, i.e. force normal to a curving streamline.
On an airfoil there is an effective reduction in the area through which the air passes between the surface of the airfoil and a far field streamline unaffected by the airfoil. This increases the velocity (via the continuity equation) which in turn reduces the pressure. The curvature of the airfoil also curves the streamline close to the surface resulting in an additional pressure reduction normal to the surface. You can imagine how this affects a highly cambered airfoil.
If anyone is interested here are my lecture notes on the derivation.
https://nbviewer.jupyter.org/github/nolankucd/MEEN20010/blob...
Minor typo in your lecture notes just after equation (22).
"The assume the flow is steady, inviscid and and incompressible."
should be
"They assume..."
The complaint about using Newton's law is that it doesn't readily explain the low-pressure region above the wing. Let me give it a try.
Intuitively, all the forces on the wing are manifest as air pressure measured the wing surface and expressed as a force normal to the surface at that point. There are no other forces from the air. You sum them over the wing and the net force upward is called lift, the net force backward is call drag.
If there is net lift, that means the net normal forces summed over the wing are upward, implying that the pressure is low above the wing relative to below the wing.
The Newtonian explanation is that a force must be exerted to change the direction of the air. The net force on the air is in the direction that the air turns, and the reaction force on the wing is in the opposite direction.
On the underside of the wing the air is diverted downward and the reaction force on the wing is upward, and this is measured by the air pressure on underside of the wing.
On the top of the wing the air is again diverted downward and the reaction force on the top of the wing is again upward, and this is measured by a lowered air pressure, giving a net upward force.
The key ingredients that I took away from the above are that circulation and the Kutta condition are fundamental to explaining lift.
I think people's confusion with this situation is that there's no simple cause and effect. It's just that the fluid equations have a solution that has circulation and that gives lift, but you can't solve for it like you can with most mechanics problems, because you need a global solution that satisfies the fluid equations.
The fact that I do not understand the equations doesn't mean there is anything mysterious behind it.
There might be some artistry with regards to actually designing the aerodynamic shapes. We have no way of finding the best possible shape yet, this is largely a process of trial and error (though nowadays it can be automated with simulation without actually having to go through building physical model).
Mysterious doesn’t mean magical, it just means there’s an unexplained gap in what we understand, which is the case.
Anything could be said to be mysterious to somebody, there will always be somebody that has no knowledge to somebody. This way you can title anything as "mysterious" but it is not very useful (unless you count to bait clicks).
In general, you're right but for certain class of problems we absolutely have solutions. Just look up inverse methods whereby the input is a pressure distribution and the output is a shape. This is used often for designing airfoils, ducts, and other simple geometries.
https://www.youtube.com/watch?v=b_WmjWAGkLI
A microburst is a rare weather event where a cloud basically shoots air downwards up to 100mph:
I recommend checking out https://www.grc.nasa.gov/www/k-12/airplane/lift1.html which is much more complete explanation, and written for school age children - without the usual "lie to children" part that is common till you hit fluid dynamics at university level.
We absolutely DO understand how and why they stay in the air, we just don't have the hard numbers behind it.
The article claims the opposite: we do have the hard numbers behind it (we can predict how a wing behaves), but we don't have a good conceptual explanation for it at a layman's level (the how and why, if you so will).
They are very complicated and the complexity is required to understand all the weird edge cases
> But by themselves, equations are not explanations, and neither are their solutions. There is a second, nontechnical level of analysis that is intended to provide us with a physical, commonsense explanation of lift. The objective of the nontechnical approach is to give us an intuitive understanding of the actual forces and factors that are at work in holding an airplane aloft. This approach exists not on the level of numbers and equations but rather on the level of concepts and principles that are familiar and intelligible to nonspecialists.
It's funny to read this after many years of teaching myself to think "mathematically". The situation described above is in some ways the true mathematical ideal: to be able to describe our surroundings so precisely that intuition and perception blurs away, giving way instead to something stronger than what we can describe in human words. When you describe something to two different people, the objective is to adapt each explanation to their personal framework, much in the way an artist or musician would adapt to their audience.
However, the objective of mathematics is to take away exactly that: the variability in perhaps equally valid social or human explanations.
I do think that intuition and perception is a very important of mathematics, but I think it forms the first steps of the scientific method behind mathematics. Identify perceptions and intuitions and after that try to get to precision and rigour.
Mathematics aims not to be intelligible, but it is in fact a fortunate state of affairs that mathematics is intelligible to humans at all! It reminds me of what Eugene Wigner wrote about mathematics, titled The Unreasonable Effectiveness of Mathematics in the Natural Sciences. [1]
One thing that should be more clearly stated in the article is that it esentially claims that the mathematical descriptions themselves seem somewhat incomplete, the explanation of which I don't know, as the article tries to avoid mathematics in the first place.
[1] http://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html
It isn't the job of Newton's third law to explain that. It's job is to say that if you have 200 ton aircraft and want to keep it in the air, it has to push 200 tons of air down no matter if it does that with a carbon-fiber CFD-optimized wing or a barn door nailed to the airframe.
The thing is that what really matters is the orientation of the trailing edge. And in airplanes the trailing edge points downwards. It is not always obvious because of the way wing profiles are designed but it is almost always the case. We could have it level, but that would mean the plane will need to always fly nose up in order to create lift, it would be uncomfortable, and most likely not ideal from an aerodynamic perspective.
When you are flying upside down the natural orientation of the wing goes the opposite way, so the leading edge points up, and indeed you can't fly level with the nose pointing straight ahead. You need to point the nose up in order to compensate the natural wing orientation, and then point up even more to create actual lift.
Of course, there are some more advanced considerations. Performance will generally be reduced when flying upside down, because the wings are not designed to do so. However some wings have a symmetrical profile, and in theory, they could be flown equally well in any orientation.
Doesn't the leading edge being thick and rounded up top deflect away air from getting to the slant-plane right behind it creating a low pressure zone above the wing?
Same will apply in flat-wing cases because angle of attack will cause same effect.
What am I missing?
As a sailor with an amateur-ish passion for physics, the dynamics of lift are clear to me for years (Dunning Kruger?) and I would love to read about where the doubts regarding each of the theories lie.
The doubts reported in the info-graphics are really confusing, because both the increased speed and the low pressure area above the wing are easily explainable with vector arithmetic and fluid dynamic respectively. The statement that Bernoulli's principle does not explain planes flying upside down seems also very naive.
TLDR: We don't have a full solution that models flight.
We also don't have a full understanding of how bicycles work.
We do, actually. It's just hard to explain.
The entire article about how none of the current models fully explain how a plane stays in the air.
So what is this full solution you are talking about because my Aero professors must have done a bad job teaching the topic to me
> accounts of lift exist on two separate levels of abstraction: the technical and the nontechnical. [... The former] exists as a strictly mathematical theory, a realm in which the analysis medium consists of equations, symbols, computer simulations and numbers. There is little, if any, serious disagreement as to what the appropriate equations or their solutions are.
There are a systems of equations that allow us to model flight. But they are NOT a full model of flight characteristics, as a consequence of, like mentioned, lack of a full solution to the Navier Stokes equations
> The solutions of those equations and the output of the CFD simulations yield pressure-distribution predictions, airflow patterns and quantitative results that are the basis for today’s highly advanced aircraft designs. Still, they do not by themselves give a physical, qualitative explanation of lift.
However, mathematically these equations are difficult, we have very few explicit solutions and the question of whether solutions to these equations are well-behaved in all circumstances is a famous open problem. Indeed, it is one of the Millenium problems and solving it will make you very famous.
Also, your "I'll let the article speak for itself" is rude and naive.
In physics, it's mostly about pressure differentials.
When you try to get more specific than that in a forum comment, it means you probably don't really know what you're talking about.