This is a somewhat confusingly written article about a famously confusing topic. It directly parallels arguments about how sailboats are able to sail. Sails are also airfoils so similar mechanics come into play. Interestingly, because a sail has effectively no thickness, both sides of the sail always have the same length, which immediately calls the Bernoulli argument into question. Sailboats are also interesting because they generate all their power from the wind and yet can also sail faster than the wind at times.
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.
The billiard ball model works fine when you include the impact of other billboard balls on each other resulting in vortexes etc. It’s simply computationally expensive to do so.
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.
A nice first approximation extension of the billiard ball model is to look at a stalled wing in comparison to an un-stalled: the down side will continue to "deflect the balls" just fine. But while the un-stalled upper side of a wing will also draw air downwards in an orderly way, the stalled upper side pulls a tail of vortices forwards. Not strictly a billiard ball model anymore, but even the crudest model of turbulent flow is enough to get the general idea.
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.
Symmetric airfoils (which do exist) are considered to have a centerline in the obvious (symmetric) place, but this doesn't have anything to do with angle of attack. For various reasons, aerobatic planes sometimes have symmetric airfoils with an angle of incidence of zero—that is, the aircraft centerline and airfoil centerline are parallel.
I am saying the choice of centerline for an airfoil is arbitrary in terms of aerodynamic forces. The angle of incidence is then based on that arbitrary centerline. The aircraft’s angle of attack is independent of the above and therefore confusing.
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.
> Aka simple 2d diagrams don’t result in wingtip devices
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.
> Thus if you instead lay that teardrop so the bottom is flat
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.
>Interestingly, because a sail has effectively no thickness, both sides of the sail always have the same length, which immediately calls the Bernoulli argument into question
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...
my understanding is that Bernoulli's principle also involves equal transit times. Meaning that the same two positions need to rejoin later.
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.
It isn't at all. Bernoulli never asserted that particles are bound in any way, he just discovered a relationship between static and dynamic pressure. I don't know why people apply his name to the equal transit time theory of lift; there is no real association.
Perhaps because it is always drawn that way, that the same streamline gets separated then goes over the wing, then goes back together. Then in big letters it says Bernoulli principle.
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.
If you don't assume equal transit, then there's no reason to expect the particles above the wing to move faster than those below. And without that, there's no reason Bernoulli's principle would come into play at all.
There are other ways to expect differences in velocity. A bit like the venturi effect in a pipe constriction, a constant flow rate will have to involve faster velocity when the area of flow reduces.
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.
Yes there is. Suction on upper surface to maintain attached flow -> lower pressure -> increased speed to conserve momentum. Bernoulli's relationship holds true along a streamline, equal transit time doesn't.
I disagree that bernoulli's principle demands equal transit times, but I think it is an irrelevant point.
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.
The "Equal transit time" is one of the "lie to children" explanations of lift. In fact, classic wings depend on inequal speed caused by a vortex behind the wing - which is also an oversimplified model. Such "bootstrap" vortex causes an opposite vortex to form around the wing, giving difference in speed of air on both sides. Once you have the airflow in the right way, Bernoulli's principle gives you lift.
That's the very simplified version of a simplified explanation used in aviation teaching materials :)
Viscosity is responsible for drag via the boundary layer and flow separation. You can absolutely account for lift with an ideal inviscid fluid, tools like Xfoil with inviscid solvers accurately match experimental data but ignore stall. It’s a pressure effect, see my other post in this thread. The viscous solvers can handle drag, separation and stall.
What you're getting at is the Kutta condition: https://physics.stackexchange.com/questions/135707/what-is-a.... This only arises in viscous flow and ensures that the upper and lower flows leave the trailing edge smoothly. Without this, the flow would not be turned.
Take a drafting triangle that has 30-60-90 degree corners. Place it between two objects, and squeeze the triangle between them. It'll move to the side faster than the two objects move together.
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 like our brains aren't meant to handle resolving that not only is it pushed through, it's sucked into a thin and ever moving void. It's pushed and pulled at the same time, in otherwords, part of the continuum.
Suction isn't a real thing, though. It's just our description of when lower pressure on one side of a thing allows the thing to be moved by the higher pressure on the other side.
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.
I'm not sure it's that simple, and my physics knowledge isn't so strong but if it's a gradient, the force of the push can't exist without being the same thing as the force of the pull. They seem to be one in the same, the force isn't onna particular side, it's the effect of the delta between points on the gradient.
That's exactly how I mentally model it. You have to imagine it like a stone skimming the surface of the fluid on one side, and a bubble "sucking" the other side into it.
It's two concurrent visualizations of the same force.
It's like our brains aren't meant to handle resolving that not only is it pushed through, it's sucked into a thin and ever moving but thin void. It's pushed and pulled at the same time.
Imagine a sailboat pointed 90° relative to the wind so that the wind is coming right at its side. The sail is curved so that it takes that wind and redirects it towards the rear of the boat, giving it forward thrust.
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.
That is not a conventional land yacht, but I'm sure there are land yachts that can go faster than the wind, by exactly the same principle as sailboats.
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.
There is one complication here: as the boat accelerates, the relative wind moves forward.
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.
you can look at kiters and windsurfers - even on a mild wind they glide very fast - orthogonal to the wind you get constant ( i.e. practically independent of your speed) force driving you forward, and it accelerates you until it matches the force of the water and air resistance to your movement which grows with your speed.
"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. "
my analogy: if you have ever launched a pumpkin or watermelon seed by squeezing it between your fingertips just so then you can understand how the craft can move faster than whatever provides the impulse.
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.
> There's the big square sailed ones which always have to move downwind.
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.)
Well said, and I just want to add some detail about how square-rigged ships are able to sail close-hauled:
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)
> A single huge fore-and-aft sail would be too hard to handle
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).
> The main reasons square-rigged ships fell out of fashion, as far as I know, are mostly logistically.
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.
Yes, more modern versions of square rigs (using motors, or designed without the yards -- again, spinnakers) do have vastly reduced need for the crew. But I was focusing on traditional rigs.
> The main reasons square-rigged ships fell out of fashion, as far as I know, are mostly logistically.
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.
I've always wondered since learning slightly more in college physics. What is supposed to make the air going over the top of the wing suddenly go faster than the air going over the bottom of the wing in the Bernoulli model?
The way I was always taught the Bernoulli explanation was that the speed difference created the lower pressure which causes the lift. So it seems a little circular, what's causing the low pressure in your version of it? Is it a mix because any time the flow separates from the wing it leaves a low pressure area that attaches the flow to the wing?
Is it just me or are the description of 'Burnoulli's Theorem' and 'Co-dependency of Lift's Four Elements' separately in the two images identical erroneous? Just agreeing that that is confusing.
A solar sail doesn't work via aerodynamic lift. It works on conservation of momentum. Also, the biggest contributor to force on a solar sail is not solar wind, but radiation.
Right, radiation -- thank you. Nevertheless, you think that conservation of momentum is not the ultimate source of aerodynamic lift? It's not an electromagnetic phenomenon, obviously, neither gravitational -- so it has to be mechanical. Where that energy is otherwise coming from? Or are you claiming that aerodynamic lift is a fundamental force?
Energy can just as well be E = mgh (potential energy) or rotational energy E = 1/2Iw^2, or elastic energy E=1/2kx^2, chemical energy, nuclear energy etc. with momentum nowhere to be found in those formulas. When we talk about energy conservation we mean the conservation across all the forms of energy that the system can take on - that is what gets conserved.
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.
> 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.
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.
It feels that you've got some idea that I'm not understanding the difference between energy and momentum because it's a common misconception, and hold on it. I do understand that they are different. My objection is your insistence on them being "unrelated".
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?).
Correction: it will go up given an ignorably small jerk on the line at the lowest point. Not the best example, right... What I was trying to say is that one can trade rotational momentum to linear (and vice versa) as long as the kinetic energy of the system stays the same.
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.