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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

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.

starpilot 7y ago
What you're getting at is the Kutta condition: https://physics.stackexchange.com/questions/135707/what-is-a-physically-accurate-explanation-for-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.
simonebrunozzi 7y ago
> can also sail faster than the wind at times. Really? Can you elaborate?
- trhway 7y ago
  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. And of course here comes that: https://newatlas.com/wind-powered-car-world-record/11346/ 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. "
- meedimusic 7y ago
  apparent wind
- WalterBright 7y ago
  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.
  - luckyscs 7y ago
    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.
    - salawat 7y ago
      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.
Retric 7y ago
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 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.
- keanzu 7y ago
  > 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.
  - starpilot 7y ago
    2d wing does not have a wing "tip." It is infinite.
- usrusr 7y ago
  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.
Rury 7y ago
>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...
- glofish 7y ago
  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.
  - starpilot 7y ago
    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.
    - munificent 7y ago
      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.
      - 7y ago
j0e1 7y ago
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.
mike_ivanov 7y ago
> the fundamental reason airfoils in boats and places work the way they do requires viscosity There is no viscosity in solar wind, yet the solar sail is expected to work. EDIT: s/solar wind/solar radiation/
- phdp 7y ago
  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.
  - mike_ivanov 7y ago
    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?
    - glofish 7y ago
      conservation of momentum and conservation of energy both take place at the same time, but are independent concepts altogether 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.
      - mike_ivanov 7y ago
        > momentum has nothing to do with energy and vice versa. 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?
        glofish 7y ago
        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.
knolan 7y ago
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.
- deleted 7y ago
  [deleted]
rtkwe 7y ago
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?
- starpilot 7y ago
  Lower pressure region sucks the flow down to attach to the upper surface. As the pressure is reduced, speed must increase to conserve momentum.
  - rtkwe 7y ago
    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?

starpilot 7y ago

What you're getting at is the Kutta condition: https://physics.stackexchange.com/questions/135707/what-is-a-physically-accurate-explanation-for-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.

simonebrunozzi 7y ago

> can also sail faster than the wind at times. Really? Can you elaborate?

trhway 7y ago
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. And of course here comes that: https://newatlas.com/wind-powered-car-world-record/11346/ 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. "
meedimusic 7y ago
apparent wind
WalterBright 7y ago
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.
- luckyscs 7y ago
  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.
  - salawat 7y ago
    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.

Retric 7y ago

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 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.

keanzu 7y ago
> 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.
- starpilot 7y ago
  2d wing does not have a wing "tip." It is infinite.
usrusr 7y ago
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.

Rury 7y ago

>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...

glofish 7y ago
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.
- starpilot 7y ago
  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.
  - munificent 7y ago
    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.
    - 7y ago

j0e1 7y ago

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.

mike_ivanov 7y ago

> the fundamental reason airfoils in boats and places work the way they do requires viscosity There is no viscosity in solar wind, yet the solar sail is expected to work. EDIT: s/solar wind/solar radiation/

phdp 7y ago
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.
- mike_ivanov 7y ago
  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?
  - glofish 7y ago
    conservation of momentum and conservation of energy both take place at the same time, but are independent concepts altogether 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.
    - mike_ivanov 7y ago
      > momentum has nothing to do with energy and vice versa. 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?
      - glofish 7y ago
        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.

knolan 7y ago

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.

deleted 7y ago
[deleted]

rtkwe 7y ago

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?

starpilot 7y ago
Lower pressure region sucks the flow down to attach to the upper surface. As the pressure is reduced, speed must increase to conserve momentum.
- rtkwe 7y ago
  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?