Ratio between wind speed and force

danielefua said:
1) both conservation laws (energy and momentum) are, of course, always valid (until experimentally proved wrong...) but quite independent. Somehow the conservation of momentum is easier to observe and deal with because its microscopic component, on the average, can be neglected. This is not true for the conservation of energy, where its microscopic part can be - and most of the times is indeed - relevant and can be tricky to be dealt with.
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Agreed. The big difference in fluid is that conservation of momentum works fine on systems with turbulence in them (as long as you have a good idea what is happening at the boundaries) but conservation of energy doesn't, or at least can't usefully be applied, because there are unknown mechanical -> heat conversions. If I had a pound for every student who tried to apply the Steady Flow Energy Equation through turbulence or across streamlines I'd have at least a fiver.

2) in your case (2) you should specify that the wind "does no work" on the stationary sail but indeed does work on other "things" (maybe even on the sail cloth fibers themselves... :). Moreover the wind DOES loose momentum hitting the sail the same way Easterly Winds loose momentum by blowing westward and give it back it to the Earth...
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And again, of course. In fluids, forces ALWAYS result from (or cause) momentum change.
 
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grumpy_o_g said:
I don't think JumbleDuck's having trouble with anything although he's being (I suspect deliberately) a little simplistic when he says kinetic energy rises on the leeward side of the sail. Ignoring stalled sails (which you could argue are simply sheets of cloth anyway), the speed generally increases but pressure (and hence density) decreases.
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Danger, Will Robinson, Danger. Accelerated flows get reduced pressure without reduced density, thanks to Uncle Bernouilli and his fun-packed bag o' principles. Think of hydrofoils: lots of pressure variation, no density variation worth noticing.

I can't speak for sails as I've never seen wind tunnel results but, if you look at an aerofoil section in a wind tunnel, the loss of kinetic energy in the air mass is surprisingly low compared to the lift produced - this shows just how inefficient downwind sailing really is. Once the sails are stalled a large proportion of the energy is used in simply moving the air around, rather than transferred to the sails.
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Agreed. A modern glider can easily manage a glide ratio of 60:1, which means that for each 60N of lift produced at right angles to the airflow and therefore by definition doing no work, only 1N of energy-sapping drag is produced.
 
JumbleDuck said:
...

But back to the point in hand: as an answer to "why does velocity squared appear in expressions for lift and drag" the answer "because kinetic energy is velocity squared" is just wrong. It would be lovely if it wasn't. Sorry. Kinetic energy flux in moving fluid is proportional to velocity3.
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This reminds me of being taught science:
You learn physics from 11-13 and it makes some kind of sense.
Then you do 'O' level, and the first thing they tell you is "You know what I taught you last year? Well it was all over-simplified. Now you get to learn it for real."
Then 'A' levels: "What you did at 'O' level was a lie. Now you can find out the Truth".
I went on to do a degree that bumped into the edge of physics and guess what? "Everything they teach you at A-Level is wrong. This is how it really works."

But I will say that this has been a very educational thread. I'm happy that I'm not going to have to do an exam in it, though.
 
danielefua said:
I am afraid that this sentence is misleading because conservation laws still apply!
...and please pardon me if cropping your sentence changed its meaning because, in good faith, I did not think so.

Daniel
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Let me try and clarify - yes, of course the laws of conservation apply - this is just classic Newtonian physics. I have assumed an un-stalled aerofoil section in a wind tunnel versus a stalled sail travelling dead downwind, which perhaps I didn't make clear enough.

An aerofoil section deflects the airflow in a particular, largely laminar flow, fashion when air flows over it at an angle of say 10°. In other words there is comparatively little turbulence. The force that is acting on the aerofoil is a higher than might be expected when compared to the force that is acting on the aerofoil when the airflow is hitting it at 90°. Intuitively you might say that, because there is less area exposed to the airflow the un-stalled section, it would be affected by the airflow the least but that's not actually the case.

The total energy involved is identical whether the aerofoil is at 10° or at 90° but, because the air has been deflected around either side in the latter case and is very turbulent, there is less energy actually transferred to the aerofoil. A comparatively large amount of energy is required to move the air around when creating that turbulence. If the aerofoil (or sail) is stalled then very little of that energy is transferred to the sail, it's used instead to create turbulence.

A partial analogy would be the energy used to create a boats wake, energy which does not actually drive the boat forwards - hence a boat tends to create the least wash at it's most efficient speed - because you are minimising it takes energy to create the wash or turbulence.
 
grumpy_o_g said:
Let me try and clarify - yes, of course the laws of conservation apply - this is just classic Newtonian physics. snip
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It should be added that the conservation laws apply not just to Newtonian physics but to relativistic and quantum physics. Although the latter is revolutionary, at root it is only a slight mathematical tinkering with Newtonian physics.
While Einstein had a problem with conservation when developing General Relativity, the mathematicians at Göttingen sorted it out for him.
 
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grumpy_o_g said:
Let me try and clarify - yes, of course the laws of conservation apply - this is just classic Newtonian physics. I have assumed an un-stalled aerofoil section in a wind tunnel versus a stalled sail travelling dead downwind, which perhaps I didn't make clear enough.

An aerofoil section deflects the airflow in a particular, largely laminar flow, fashion when air flows over it at an angle of say 10°. In other words there is comparatively little turbulence. The force that is acting on the aerofoil is a higher than might be expected when compared to the force that is acting on the aerofoil when the airflow is hitting it at 90°. Intuitively you might say that, because there is less area exposed to the airflow the un-stalled section, it would be affected by the airflow the least but that's not actually the case.

The total energy involved is identical whether the aerofoil is at 10° or at 90° but, because the air has been deflected around either side in the latter case and is very turbulent, there is less energy actually transferred to the aerofoil. A comparatively large amount of energy is required to move the air around when creating that turbulence. If the aerofoil (or sail) is stalled then very little of that energy is transferred to the sail, it's used instead to create turbulence.

A partial analogy would be the energy used to create a boats wake, energy which does not actually drive the boat forwards - hence a boat tends to create the least wash at it's most efficient speed - because you are minimising it takes energy to create the wash or turbulence.
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What you write is true but I like to expose another point of view somehow more intuitive although not able to solve the initial "square power law" problem.

Here we may talk only about momentum conservation which is the most important factor we care of.

In a laminar flow around an hydrofoil, although you may not notice it, the wind exiting the scene has acquired a momentum which is exactly opposite to the lift acted on the hydrofoil. In an obvious geometry, the incoming flow was horizontal while the outgoing flow is, on the average, slightly downward. Very crudely: a lot of "wind matter" passes by and a lot of lift can be obtained.

In a stalled flow against a perpendicular sail, on the average the outflow does not change direction so, obviously, there is no lift. What about momentum transfer from the wind to the sail in the same direction of the flow - what is called drag? Why is it so inefficient - and we, downwind sailors, know it? Here the explanation becomes very "handwaving", I am afraid: at the onset (in the transient phase) I believe there is quite a bit of momentum transfer but the process stops quickly as a steady state is reached and a lot of turbulence develops. In fact turbulence grows on both sides of the sail and, almost magically, assumes a spatial shape that actually dramatically modifies, on the average, the shape of the stalled sail as seen from the incoming wind. Now (with some imagination!) turbulence builds up a new almost solid boundary whose shape is pretty similar to the one of a nice ideal symmetrical wing profile with no lift whatsoever and, relatively, little drag (you may find it already depicted in post #29 of this thread). The incoming flow opens the way almost smoothly to the "unkempt" stalled sail and, then, closes the path almost smoothly after it exchanging little momentum. I could mention "far field" or "eddy diffusion" but it does not seem necessary and it may be even more confusing...

Regarding the word "magically" I used; my actual believe is that what I described is not at all magical but only related to the fact that nature always finds the shortest and least expensive way to solve its problems!

Very oversimplified and I hope none of the scientists here will shoot me!

Daniel
 
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>Cold air is heavier than warm air so the force on the sails is noticeably greater, this was very apparent when sailing in the UK compared to sailing in the Caribbean.
>>I find it difficult to believe that 7% 'feels' that different - which means people are very sensitive, or they cannot feel the difference, or its more than 7%. - or even some other effect

I can't find any reference to 7% which is a static figure in the UK tempreatures can vary fron below zero to a typical summer day of 28C .In the north Caribbean the mininum temperature is 28 C the further south you go, e.g Venezuela, it is 32 to 35C. So 7% can't' fit all. Also humidity has a big effect on wind force and the Caribbean is humid all of the time. The more water vapor that is in the air, the less dense the air becomes, that is why cold, dry air is much heavier than warm, humid air.
 
guernseyman said:
It's rather better established than experimental verification.
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I know it’s the first law you’re talking about but it reminded me that, cabin-bound in the pouring rain last week listening to Melvyn Bragg’s radio programme on perpetual motion machines, I was led to check what Sir Arthur Eddington wrote about the second law: “If someone points out to you that your pet theory of the universe is in disagreement with Maxwell's equations — then so much the worse for Maxwell's equations. If it is found to be contradicted by observation — well, these experimentalists do bungle things sometimes. But if your theory is found to be against the second law of thermodynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation.” :)
 
Hydrozoan said:
... what Sir Arthur Eddington wrote about the second law: “If someone points out to you that your pet theory of the universe is in disagreement with Maxwell's equations — then so much the worse for Maxwell's equations.” :)
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Hmm. I'll back James Clerk Maxwell against a pet theory every day. In one of my real world roles I have had to deal with a depressing number of members of the public convinced that their own notions trump a few hundred years of physics. Maxwell's Equations are a frequent target, invariably by people who don't understand them.
 
JumbleDuck said:
Hmm. I'll back James Clerk Maxwell against a pet theory every day. ...
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As I imagine Eddington would have done, too :) - he was using the expression rhetorically to show the strength of his belief (stated in the sentence before) that "The law that entropy always increases holds ... the supreme position among the laws of Nature".
 
Hydrozoan said:
As I imagine Eddington would have done, too :) - he was using the expression rhetorically to show the strength of his belief (stated in the sentence before) that "The law that entropy always increases holds ... the supreme position among the laws of Nature".
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Yeah, but diodes trash that one, dont they? Generating a potential difference in a thermally dead universe.....
 
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