Ratio between wind speed and force

[grumpy_o_g]

Yes, very interesting thanks. But at the same time distressing that the power needed to overcome drag is actually the cube of relative wind speed, not the square (for bike riding). Or it may not be at all, because he also says that the relationship might be a complex polynomial.

Also interesting to learn the etymology of BASE jumping. I have always wondered why they called it that. I would have thought that jumping off the base of something would be quite boring. Now I know.

It's just about possible to draw up the curves for one particular aspect, such as aerodynamic form drag, with the boat in a particular state of trim. Add in the effect of gusts, sea state, ballast, displacement changes, helming styles, angle of heel, changes of sail plan, etc. and then consider those variable for each vector (lift, hydrodynamic form and induced drag, aerodynamic form and induced drag and you end up with dozens of different curves which need to be overlaid to get an answer which is still only true for one apparent wind angle.

ABout the only thing you can safely say is that the relationship won't be linear.

 

[guernseyman]

No, the effects change directly proportional to density.



Your explanation was wrong. Sorry.

So you think sailing contravenes the Law of Conservation of Energy?
Perhaps you could expound your revolutionary theory of sailing?

 

[JumbleDuck]

So you think sailing contravenes the Law of Conservation of Energy?
Perhaps you could expound your revolutionary theory of sailing?

Just because velocity² appears in two expressions doesn't mean that the two expressions are related. Your claim that force is proportional to v² because kinetic energy is proportional to v² can easily be shown to be wrong in two different way ways:

(1) Wind does not come to a halt at a sail; it merely changes velocity. Any KE loss is proportional to (delta |v|²), integrated over the whole affected volume. Remember that the wind which produces most of the force is on the leeward side of the sail and, since it is moving faster than the free-stream velocity, actually gains KE.

(2) Wind blowing past a stationary sail (on a moored boat, say) loses kinetic energy but, although it exerts a force, does no work.

I generally don't like appeals to authority, and especially to personal authority, but it may help here to mention that I have been researching, teaching and examining in fluid dynamics at university level for about 30 years now.

 

[Neeves]

That explains a lot. I had wondered at your apparent ease and comfort in this area. It must be refreshing to actually apply the knowledge to a 'hobby' - if you will excuse the word.

Jonathan

 

[guernseyman]

Just because velocity² appears in two expressions doesn't mean that the two expressions are related. Your claim that force is proportional to v² because kinetic energy is proportional to v² can easily be shown to be wrong in two different way ways:

(1) Wind does not come to a halt at a sail; it merely changes velocity. Any KE loss is proportional to (delta |v|²), integrated over the whole affected volume. Remember that the wind which produces most of the force is on the leeward side of the sail and, since it is moving faster than the free-stream velocity, actually gains KE.

(2) Wind blowing past a stationary sail (on a moored boat, say) loses kinetic energy but, although it exerts a force, does no work.

I generally don't like appeals to authority, and especially to personal authority, but it may help here to mention that I have been researching, teaching and examining in fluid dynamics at university level for about 30 years now.

I think you gave it away in your preceding post when you described my original post as an 'explanation'. It wasn't. You seem to be having trouble with the notion that, ultimately, a sail is driven by loss of kinetic energy of the wind. It has to - you can't get something for nothing (even though your second assertion seems to be suggesting that you can get nothing from something). As you say, it's quite complicated in practice. but I wonder if you can estimate how much my simple estimate differs from reality?

 

[danielefua]

Just because velocity² appears in two expressions doesn't mean that the two expressions are related. Your claim that force is proportional to v² because kinetic energy is proportional to v² can easily be shown to be wrong in two different way ways:

(1) Wind does not come to a halt at a sail; it merely changes velocity. Any KE loss is proportional to (delta |v|²), integrated over the whole affected volume. Remember that the wind which produces most of the force is on the leeward side of the sail and, since it is moving faster than the free-stream velocity, actually gains KE.

(2) Wind blowing past a stationary sail (on a moored boat, say) loses kinetic energy but, although it exerts a force, does no work.

I generally don't like appeals to authority, and especially to personal authority, but it may help here to mention that I have been researching, teaching and examining in fluid dynamics at university level for about 30 years now.

Your reasoning is perfectly right and I cannot but agree with you but, in order to close the argument, you should have clarified at least two additional points:
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.
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...

Daniel

 

[guernseyman]

snip
1) both conservation laws (energy and momentum) are, of course, always valid (until experimentally proved wrong...) but quite independent.
snip

While the conservation laws are not necessarily valid, they are better established than is commonly realised.

One hundred years ago the German mathematician (Emmy) Noether proved that each conservation law is the necessary consequence of a symmetry in the universe. Specifically, energy is conserved because of time invariance, and momentum is conserved because of location invariance. Other conservation laws are analogous.

 

[danielefua]

While the conservation laws are not necessarily valid, they are better established than is commonly realised.

One hundred years ago the German mathematician (Emmy) Noether proved that each conservation law is the necessary consequence of a symmetry in the universe. Specifically, energy is conserved because of time invariance, and momentum is conserved because of location invariance. Other conservation laws are analogous.

We are going a little off topic, don't we? When I was a young student, a famous text by Landau and Lifshitz was a milestone on what you write which is called an axiomatic approach. Whether it may be considered a better established starting point or not is a very personal taste I believe. You surely need much, much more analytical math than Galileo knew...

Daniel

 

[guernseyman]

We are going a little off topic, don't we? When I was a young student, a famous text by Landau and Lifshitz was a milestone on what you write which is called an axiomatic approach. Whether it may be considered a better established starting point or not is a very personal taste I believe. You surely need much, much more analytical math than Galileo knew...

Daniel

It's rather better established than experimental verification.

 

[Neeves]

This is beginning to read like a chapter in 'The Hitchhikers guide ... ' no wonder I focussed on Geology.

 

[guernseyman]

This is beginning to read like a chapter in 'The Hitchhikers guide ... ' no wonder I focussed on Geology.

At least you have an 'ology!

 

[grumpy_o_g]

I think you gave it away in your preceding post when you described my original post as an 'explanation'. It wasn't. You seem to be having trouble with the notion that, ultimately, a sail is driven by loss of kinetic energy of the wind. It has to - you can't get something for nothing (even though your second assertion seems to be suggesting that you can get nothing from something). As you say, it's quite complicated in practice. but I wonder if you can estimate how much my simple estimate differs from reality?

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. So each air molecule will have a higher kinetic energy but there will be fewer of them. On the leeward side the opposite is generally true. 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.

 

[bobgarrett]

Which is presumably why submarines have a bulbous bow, as do those protrusions on large commercial ships - oddly most performance yachts still have knife like bows.

But why do yachts have such a shaped bow? Anyone explain?

 

[Lon nan Gruagach]

But why do yachts have such a shaped bow? Anyone explain?

You mean why have pointy instead of bulb?
Assuming thats what you mean.....

The bulb on supertankers reduces wake by partly cancelling out the bow wave, this ends up with up to about 15% less drag. The length of the bulb is a function of vessel design speed, possibly directly proportional to it. So, if you want a bulb on a yacht that goes the same speed as a supertanker you would need a bulb of the same length as that of the larger boat. Possibly longer than the yacht it self?
I think that with yachts, being considerably lesser in beam that the bow wave is not such an issue, and that if a tanker wanted to use the same shape then it would have a very long, narrow, difficult to pack bow.

 

[lampshuk]

Oh, for heaven's sake. I wasn't deleting it, just editing it.

What I was saying was: yachts could, I suppose, be made to look like the "right" teardrop without doing the bulbous bow thing. Is that what Pogos are aiming for? But where would you put the engine, and I suppose you need to keep the weight at the front from being too great.

But what about a shape that is pointy at BOTH ends. How does that compare?

 

[danielefua]

... 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 ...

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

 

[LittleSister]

But why do yachts have such a shaped bow? Anyone explain?

I read somewhere that a bulb bow only works to advantage around a particular speed (that speed depending on its dimensions), and has an adverse effect at other speeds. So presumably a bulb is fine for tanker plodding round the oceans under engine at its design cruising speed for days and weeks at a time, but unlikely to be a net gain for a sailing boat that wants to go at the best speed it can make given the amount/direction of wind, and other factors.

 

[lampshuk]

Good explanation on wikipedia, including some stonking photos. https://en.wikipedia.org/wiki/Bulbous_bow

But this is still independent of the "which way round is the teardrop?" question.

 

[JumbleDuck]

I think you gave it away in your preceding post when you described my original post as an 'explanation'. It wasn't. You seem to be having trouble with the notion that, ultimately, a sail is driven by loss of kinetic energy of the wind.

The question being addressed was about the force on a sail. That depends on the momentum flux. Kinetic energy looks similar, but isn't what matters. If you take the idealised model of lift as the effect of a free stream flow on a vortex, there is no KE loss at all, although lift is developed. In real life, of course, there is a small energy loss (to heat) in the turbulent wake.

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.

 

[JumbleDuck]

That explains a lot. I had wondered at your apparent ease and comfort in this area. It must be refreshing to actually apply the knowledge to a 'hobby' - if you will excuse the word.

It can be fun, but over theorising can be a sin, too!