Is there a limit to wind power?

[Skeptik22]

Is there a limit to the amount of energy which can be extracted from the wind?

There are a huge number of windfarms springing up around the world.. all taking energy from the wind.

The assumption seems to be that this is limitless and "free".

Clearly this is not possible.

The question is (I think) - how will the transfer of energy (from the wind) manifest itself on the climate, and could the impact be measured?

The only research I have seen to date, relates to finding the "best" location for a windmill, and some on the effect on local weather conditions.

 

[A.T.]

The question is (I think) - how will the transfer of energy (from the wind) manifest itself on the climate, and could the impact be measured?

So far we extract wind energy near to the ground, which is equivalent to putting up some high obstacles, like trees.

 

[Skeptik22]

Agreed ... the question still remains .. how much energy can you extract before it has an effect ... one could argue that any energy extracted must have some effect... but that it would be so insignificant that it cannot be detected .. the question is still ... if one continued to extract more and more ..at what point could the effect be detected?

Also agree that the immediate effect would be at ground level.. but there must be some point at which perturbations at ground level have an effect on the overall system?

My analogy would be of throwing pebbles into a river .. a couple would go unnoticed .. a lorryload would have some effect..

 

[A.T.]

one could argue that any energy extracted must have some effect...

On a global scale, that energy is extracted from the wind anyway by interaction with the ground / natural obstacles. On a local scale though, you change where it is extracted, and where and it gets dissipated as heat.

 

[Skeptik22]

that energy is extracted from the wind anyway

Sorry to be pedantic .. but the windfarm has been specifically added to the environment to extract N gigawatts which previously would have been involved in the climate system..

In the river analogy, the pebbles are added to the existing riverbed .. altering the flow..

 

[A.T.]

but the windfarm has been specifically added to the environment to extract N gigawatts which previously would have been involved in the climate system..

...and dissipated somewhere else. All the energy that goes into creating wind, is also dissipated by interaction with the surface/obstacles. Regardless what the obstacles are. The question is just where it and when it happens.

In the river analogy, the pebbles are added to the existing riverbed .. altering the flow..

Adding a layer of pebbles, which is only a tiny fraction of the river depth, will not have much effect on the river globally. Also, you have to consider all the wind obstacles humans have already removed and will keep removing by deforestation.

 

[Pierce610]

The energy can be absorbed from windpower until the wind exists. So the limit depends only by weather condition, firstly the global warming, since the impact of wind farms on it, also if they slow down the speed of air particles assorbing kinetic energy, is still probably too small to detect, like it happens with other masses of obstacles, or to make some previews. So I've really more interest about the risk of a global warming increase and I think the principal negative impact for a wind farm is still the rumour.

 

[CalcNerd]

Technically, you can't beat Betz! Someone (named Betz) did the math and found that you cannot extract more than approx. 60% of the energy of wind. ie do a mass flow problem with a circular area of where the wind propeller operates and the maximum amount of energy that can be extracted is not quite 60% theoretical. In reality, it is less, usually a LOT less.

And most (if not ALL) turbines have to feather (turn off and turn sideways) so as to not overload their power output capabilities once wind speeds exceed a certain value. This is because it is no longer safe to operate the turbines due to wind shear stress on their structure or buckling of their foundations. Wind speed energy is a cubic function. At low to moderate wind, there is very little energy to be harvested. Once the wind speed is above 15 mph, it starts to become attractive (lower winds can generate energy, but most turbines are underutilized with these breeze speeds). I believe 30-40 Mph is the typical cut out (turn off) speeds for most wind turbines, but you should reference other sources before you quote that. At 30 mph most turbines are running well over their design output ratings (ie in danger of burning up or wearing out their bearings, if they were operated for extended times)

That is why there needs to be a certain distance between large wind turbines for best energy capture (and safety, nobody wants to play dominos on a large scale).

Thanks A.T. I have edited to correct.

 

[A.T.]

Technically, you can't beat Bets!

Betz

 

[SteamKing]

Is there a limit to the amount of energy which can be extracted from the wind?

Yes, there is, but it's due to factors which have nothing to do with the amount of wind.

When the tax incentives and subsidies propping up the financial side of wind farms are removed, they tend to become an uneconomical means of power generation.

http://www.telegraph.co.uk/news/ear...m-plans-in-tatters-after-subsidy-rethink.html

 

[Skeptik22]

...and dissipated somewhere else. All the energy that goes into creating wind, is also dissipated by interaction with the surface/obstacles. Regardless what the obstacles are. The question is just where it and when it happens.

Adding a layer of pebbles, which is only a tiny fraction of the river depth, will not have much effect on the river globally. Also, you have to consider all the wind obstacles humans have already removed and will keep removing by deforestation.

Maybe my pebble analogy is not entirely valid .. I saw the lorryloads as piles rather than a thin uniform layer ... maybe a windmill is not such a barrier.

I have seen Betz before in another discussion and maybe I misunderstand ... If you have a wind hitting a mill what is the difference between the air prior to the mill and that downstream?

If N gigawatts have been removed .. is it slower ? denser? higher pressure?

 

[Skeptik22]

principal negative impact for a wind farm is still the rumour.[/QUOTE]http://www.telegraph.co.uk/news/ear...can-cause-climate-change-finds-new-study.html

 

[Pierce610]

http://www.telegraph.co.uk/news/ear...can-cause-climate-change-finds-new-study.html[/QUOTE]
yes, thanks, I'm just watching it: the kinetic energy is transferred from wind to turbines also with conversion in heat and so it's going to increase the local warming, and then the global one; surely this is not good.

 

[jbriggs444]

http://www.telegraph.co.uk/news/ear...can-cause-climate-change-finds-new-study.html
yes, thanks, I'm just watching it: the kinetic energy is transferred from wind to turbines also with conversion in heat and so it's going to increase the local warming, and then the global one; surely this is not good.

Kinetic energy to heat conversion has nothing to do with the climate effect reported in that article. With or without turbines, 100% of wind energy ends up as heat.

 

[Khashishi]

A windfarm has tougher restrictions than the Betz limit, because wind turbines in close proximity will interfere with each other. The front ones may get efficiencies close to the Betz limit (yes, turbines are that good), but they cause turbulence in the air stream which interferes with the efficiency of the back turbines. The calculation of efficiency becomes a lot more difficult. There is a limited amount of energy you can extract from some volume of air above a land area. You can increase the available energy by building taller turbines, but it gets more expensive and structurally difficult.

 

[A.T.]

maybe a windmill is not such a barrier.

It's comparable to a couple of high trees. You could compare the rate at which we are removing trees, to the rate we build windmills.

http://en.wikipedia.org/wiki/Deforestation_by_region

World annual deforestation is estimated as 13.7 million hectares a year, equal to the area of Greece. Only half of this area is compensated by new forests or forest growth.

 

[Skeptik22]

[QUOTE=It's comparable to a couple of high trees.

I was beginning to wonder of this really was a physics forum... question was not about whether a windfarm was a GOOD THING, or not. Nor was it about the cost .. it was about detecting and measuring the effect.

1 windmill = 2 tall trees

sounds like a measurement... and yet... I have 2 tall trees in my garden and am not aware of any Megawatts being dissipated

 

[Bystander]

.. it was about detecting and measuring the effect.

Rough numbers regarding wind energy: global average of 2 W/m² to maintain a global average wind speed of 10 m/s; that's also a global average energy of moving air that is ~ 500 kJ/m²; average viscous dissipation of 2 W/m². Play with those numbers as you will, keeping in mind that they are estimates. They may have been refined somewhat over the past fifty years, but they haven't changed much. How much interference in water transport, precipitation patterns, evapotranspiration, and other atmospheric transport might result from wind farms is anybody's guess, and to my knowledge, not been examined in any detail.

 

[A.T.]

I have 2 tall trees in my garden and am not aware of any Megawatts being dissipated

"A couple of" doesn’t mean exactly two. If the total size of the tree crowns is comparable to the disc area of the windmill, the removed wind energy will be comparable.

 

[Skeptik22]

is anybody's guess, and to my knowledge, not been examined in any detail.

Thanks for the numbers, although I am not sure what could be done with them.

This is interesting

http://www.mdpi.com/2072-4292/6/12/12234

 

[Skeptik22]

"A couple of" doesn’t mean exactly two. If the total size of the tree crowns is comparable to the disc area of the windmill, the removed wind energy will be comparable.

1 Windmill = 1 object with the same characteristics as a windmill ? http://web.iitd.ac.in/~drsbr/IMAGES/HornsRevTurbulence.jpg may give a way of detecting the effect .. so what about measurements?

Does Betz law imply that the wind behind the mill is exhausted ... or at least has less energy?

Is this air slower, denser, lower pressure?

Could a windfarm produce an area of "low pressure"

 

[OmCheeto]

Here's an interesting article:

Stanford Report, September 10, 2012
Wind could meet many times world's total power demand by 2030, Stanford researchers say

The researchers have dubbed this point the saturation wind power potential. The saturation potential, they say, is more than 250 terawatts if we could place an army of 100-meter-tall wind turbines across the entire land and water of planet Earth. Alternatively, if we placed them only on land (minus Antarctica) and along the coastal ocean, there is still some 80 terawatts available – about seven times the total power demand of all civilization. Hypothetical turbines operating in the jet streams 6 miles up in the atmosphere could extract as much as 380 terawatts.

"We're not saying, 'Put turbines everywhere,' but we have shown that there is no fundamental barrier to obtaining half or even several times the world's all-purpose power from wind by 2030. The potential is there, if we can build enough turbines," said Jacobson.

According to wiki:

Wind power capacity and production
Worldwide there are now over two hundred thousand wind turbines operating, with a total nameplate capacity of 282,482 MW as of end 2012.

Using the hypothetical 380 terawatts from the article, and the 282 Gw from wiki, I calculate that we currently have the capacity to remove ≈1/10 of 1% of the energy from the air.

I'm not sure if a study has been done of how much energy has not been redistributed due to deforestation over the last 6,000 years.
That might be something fun to model.

 

[A.T.]

1 Windmill = 1 object with the same characteristics as a windmill ?

Not sure what you are asking here

Does Betz law imply that the wind behind the mill is exhausted ... or at least has less energy?

Betz law limits how much less it can have behind a stationary turbine.
http://en.wikipedia.org/wiki/Betz's_law

 

[CWatters]

Is there a limit to the amount of energy which can be extracted from the wind?

http://www.nature.com/nclimate/journal/v3/n2/full/nclimate1683.html

Geophysical limits to global wind power

snip

We find wind turbines placed on Earth’s surface could extract kinetic energy at a rate of at least 400TW, whereas high-altitude wind power could extract more than 1,800TW. At these high rates of extraction, there are pronounced climatic consequences. However, we find that at the level of present global primary power demand (~ 18TW; ref. http://www.nature.com/nclimate/journal/v3/n2/full/nclimate1683.html#ref2), uniformly distributed wind turbines are unlikely to substantially affect the Earth’s climate.

 

[Pierce610]

How much is the energy of wind?
If its speed is 10 m/s, the density is about 1 kg/1 m^3 and its volume is 1 m^3, then the energy is 50 J.
How much is the power of wind?
If its speed, density, and volume are invariated and the surface is 1 m^2, then the power is 500 W.
How many watt are transferred in a turbine?
If speed is 10 m/s, almost enough to produce work and the power of the wind is 500 W for every m^2 and the efficiency is about 0,6, then the power transferrred is 300 W for every m^2. So the total depends by effective area of interaction.
In which ambiental conditions the speed of wind can be 10 m/s?
In a gas energy is the product PxV, at a certain temperature, and its delta is due to a variation o pressure, volume, or both.
So it must be for example a difference of pressure for making work.
To produce a speed of 10 m/s and an energy of 50 J it occours a difference of 50 Pa, mantaining costant the volume.
How much time this velocity can hold on?
If the volume of the gas is 1^m3 and the delta of pressure is 50 Pa, then the time is 0,1 s.
If the volume is 3600 m^3 and the delta of pressure is 500 Pa, then the time become one hour.
Can trees, and other obstacles reduce the wind?
They can reduce the speed, togher with an increase of the duration of the wind, because they are like a barrier that initially divide in two a chamber, holdin costant the difference of pressure, and then, opened, it allows the air flow; only a flying tree subtract watt.
How could we measure the impact of remixing warm and cold air during night by wind farm?
Mixing air makes it homogeneous; P x V and its delta depends on temperature and its value and the duration of wind could change; if we know in the normality the values of speed, difference of pressure and the duration of wind, we could compare them with those obtained in presence of wind farm.

I hope I've explained correctly it.

 

[Pierce610]

I said "If the volume is 3600 m^3 and the delta of pressure is 500 Pa, then the time become one hour."
I must correct in "if the volume is 36000 m^3 and the delta of pressure is 50 Pa, the speed is still 10/ms and the durating becomes one hour.

 

[OmCheeto]

...

Can trees, and other obstacles reduce the wind?
They can reduce the speed, togher with an increase of the duration of the wind, because they are like a barrier that initially divide in two a chamber, holdin costant the difference of pressure, and then, opened, it allows the air flow; only a flying tree subtract watt.
...
I hope I've explained correctly it.

I only checked the math on your first 3 answers, and they looked good to me, so I didn't check the rest.

The above assumption, about "flying trees", got me thinking though.

If you were to build a model of the Earth, by hanging a balloon from the ceiling, and attached a piece of tape to the perimeter, such that it stuck out, and then you blew on the tape to model a wind, wouldn't the wind impart a torque on the balloon, making it spin?

I tried figuring out this morning what the resultant torque on the Earth would be from a single hypothetical tree (20 meters tall, and 1 meter wide) with 1 Newton of force per square meter being extracted:

total force                                    20   N
rotational kinetic energy of Earth      2.138E+29   joules
radius of Earth                           6371000   m
mass of Earth                               6E+24   kg
torque                                   44597000   N*m

But then, as the meme tells us to do, I cried.

 

[billy_joule]

If you were to build a model of the Earth, by hanging a balloon from the ceiling, and attached a piece of tape to the perimeter, such that it stuck out, and then you blew on the tape to model a wind, wouldn't the wind impart a torque on the balloon, making it spin?.

Yes.
But wind does not come from outer space so the result is meaningless.

 

[sophiecentaur]

. I have 2 tall trees in my garden and am not aware of any Megawatts being dissipated

How would you be aware of that, in any case? How many MW of solar power are landing on your garden?
But what would be the efficiency of energy conversion with your two trees? As a transducer from moving air to heated tree, they could be very low in efficiency. Have you tried measuring air temperatures? Even if you have, could you actually relate them to power transfer?

 

[OmCheeto]

Yes.
But wind does not come from outer space so the result is meaningless.

Actually, I've heard that wind is solar powered, so the source of the wind is, in a roundabout kind of way, from outer space.

Anyways, we could duct tape a small fan onto a larger balloon, and do the experiment with, and without the protruding tape/tree.
I'm fairly certain, the results would be different.

 

[Skeptik22]

How would you be aware of that, in any case? How many MW of solar power are landing on your garden?
But what would be the efficiency of energy conversion with your two trees? As a transducer from moving air to heated tree, they could be very low in efficiency. Have you tried measuring air temperatures? Even if you have, could you actually relate them to power transfer?

Not sure how I would be aware .. I think that was the point.. UK insolation according to Wiki averages at 120 watts per sq metre.. I can see plants absorbing this, and temperature rises in the ground / brickwork etc ..

The figures quoted for windmills appear to be somewhat larger, and someone suggested that a windmill was the equivalent of a couple of trees ... it just intrigued me as to where this energy manifested itself.. I am fairly sure I do not have hot trees..

The idea of efficient energy transfer in trees is also intriguing .. where has the energy gone that has been efficiently converted... as opposed to that which has been inefficiently discarded ?

If this has been returned to the wind, then does a 1 windmill = x trees relation exist?

 

[CWatters]

I recall reading an article some years ago about a plan to fix electricity "generators" to trees. The idea being to generate electricity as the tree bends and flexes. I forget the details.

 

[OmCheeto]

...
The idea of efficient energy transfer in trees is also intriguing .. where has the energy gone that has been efficiently converted... as opposed to that which has been inefficiently discarded ?

Heat and torque.
If trees don't experience torque, then why do they fall over in wind storms?

I recall reading an article some years ago about a plan to fix electricity "generators" to trees. The idea being to generate electricity as the tree bends and flexes. I forget the details.

I'm always suspicious when architects and artists get involved in engineering problems:

Click on the image for the article at gizmag​

Very pretty, but probably very spendy for their output. But then again, until "those people" get over how "ugly" conventional wind turbines are, it might be a good idea.

 

[Tatersoup]

Probably off point, but you could do it until all birds that flew were nearing extinction from getting caught in the blades, causing the environmentalists who decided massive wind farms were green to implode on themselves.

 

[msumm21]

Regarding what a wind turbine does to the air locally, without getting too complicated it can be estimated using simple approximations (e.g. Betz as mentioned earlier) to get
1. the air slows down as it approaches the rotor
2. the pressure rises at it approaches the rotor
3. the pressure drops passing through the rotor
4. the pressure rises again after the rotor

Some numbers that might be useful are (precise numbers depend on a lot of things)
1. wind slows to about 2/3 it's normal speed at the rotor (this is optimal via a momentum theory calculation)
2. wind slows to about 1/3 it's speed downstream (in reality turbulence changes this a lot)
3. more than 1/2 the wind energy (kinetic) contained in the "cylinder of wind" that passed through the rotor is taken

Regarding what it does more globally, I don't know what kind of studies have been done. I assume they'd be very uncertain. The implication in a link from an earlier post that a 1C temperature change was caused by wind farms seems motivated by a political agenda, unless they have some really amazing physics to show that wind farms were responsible for the change.

Yeah those artistic wind machines are usually very inefficient in terms of energy extracted per unit area and cost, compared to a "normal" wind turbine.

 

[psycho rich]

Thanks for the numbers, although I am not sure what could be done with them.

This is interesting

http://www.mdpi.com/2072-4292/6/12/12234

I have noticed an increase in wind speed at our windsurfing beach as the tide rises.
We have also have had a large area of desert get covered with grass . That has had a big effect
The Big Island (world's largest mountain) cast a shadow nine miles out to sea.
I don't think human intervention can compare to natural changes.
A town I lived in didn't have flies (too windy) now has flies and fruit trees now bear fruit.
I heard a wind mill engineer say that most wind mills never amortize . Perhaps design improvements will change that

 

[gary350]

I did a lot of research on wind power about 10 years ago. For best results you need a different wind mill for each wind speed. The large 3 blade wind mills you see poping up all over the country side are for moderate wind speed about 15 mph.

The old farm wind mills that had about 12 to 14 blades in a circle will operate in 2 mph wind but above 15 mph the automatic brake shuts them down.

As I recall ever time the blade diameter doubles the power tripples.

For some reason people like to say, the 3 blade wind mills are sub sonic. NO S#%T. My bicycle is sub sonic. My SUV is sub sonic. My RV is sub sonic.

If your building a wind mill build it for the wind speed and conditions you have. Some places are not suited for wind mills like middle Tennessee where the wind is very gusty 5 mph for 45 seconds then 30 mph for 60 second then dead calm for 30 seconds then 15 mph for 45 seconds all day long day after day.

Wind mills need a safety brake for when the wind becomes too high the blade rotates parallel to the wind and the brake locks the blades.

 

[A.T.]

it just intrigued me as to where this energy manifested itself.. I am fairly sure I do not have hot trees..

Obstacles to wind create turbulence which over time dissipates as heat, somewhere downwind.

 

[msumm21]

As I recall ever time the blade diameter doubles the power tripples.

should be quadruples (power proportional to the area of the rotor)

If your building a wind mill build it for the wind speed and conditions you have. Some places are not suited for wind mills like middle Tennessee where the wind is very gusty 5 mph for 45 seconds then 30 mph for 60 second then dead calm for 30 seconds then 15 mph for 45 seconds all day long day after day.

Yep, large and consistent winds make wind turbines more economical.

Wind mills need a safety brake for when the wind becomes too high the blade rotates parallel to the wind and the brake locks the blades.

Yep, like anything they are only made strong enough to handle a certain amount of loads. Once the wind speed is high enough that those loads will be surpassed, the control system puts it into another mode to reduce the forces exerted on the blades. This can include what you said among other things.

 

[psycho rich]

should be quadruples (power proportional to the area of the rotor)
Yep, large and consistent winds make wind turbines more economical.
Yep, like anything they are only made strong enough to handle a certain amount of loads. Once the wind speed is high enough that those loads will be surpassed, the control system puts it into another mode to reduce the forces exerted on the blades. This can include what you said among other things.

should be quadruples (power proportional to the area of the rotor)
Yep, large and consistent winds make wind turbines more economical.
Yep, like anything they are only made strong enough to handle a certain amount of loads. Once the wind speed is high enough that those loads will be surpassed, the control system puts it into another mode to reduce the forces exerted on the blades. This can include what you said among other things.

A turbine designer has come up with a multi bladed wind mill . It has a large containment ring , allows much higher rotational speeds. The blades are self correcting (spring loaded). He has a sailing background and developed a self trimming blade. The blade has pivot aft of the center of effort . The spring tension forces the blade into the low wind speed position , as the apparent wind speed increases , the blade flattens out.
His wind mill has a much greater efficiency than the popular three design.

 

[msumm21]

A turbine designer has come up with a multi bladed wind mill . It has a large containment ring , allows much higher rotational speeds. The blades are self correcting (spring loaded). He has a sailing background and developed a self trimming blade. The blade has pivot aft of the center of effort . The spring tension forces the blade into the low wind speed position , as the apparent wind speed increases , the blade flattens out.
His wind mill has a much greater efficiency than the popular three design.

By efficiency here I assume you mean power extracted per unit area (not cost)? There have been lots of things like this proposed, e.g. diffuser augmented wind turbines for good aerodynamic efficiency, but I don't think anyone has ever found a way to make them compete with the typical wind turbines you see in most wind farms, in terms of the overall cost of energy.

 

[psycho rich]

By efficiency here I assume you mean power extracted per unit area (not cost)? There have been lots of things like this proposed, e.g. diffuser augmented wind turbines for good aerodynamic efficiency, but I don't think anyone has ever found a way to make them compete with the typical wind turbines you see in most wind farms, in terms of the overall cost of energy.

Good question , the design I'm talking about has much more blade area at the perimeter where the torque is higher. I can't remember his estimates on efficiency but I do remember being impressed . Someone said earlier that as the area doubles the force triples

 

[CWatters]

Increasing blade area doesn't necessarily improve performance. Adding blades or blade area increases torque but reduces rpm. As I understand it turbines need rpm more than they need torque. In addition.. Even if you add a short duct the airflow is not forced to go through the disc it can diverge and go around it.

 

[A.T.]

Even if you add a short duct the airflow is not forced to go through the disc it can diverge and go around it.

Can you shape the duct such that more air will go through the disc? In the same way a wing makes more air flow above it.

http://www.rtbx.nl/image/index4.jpg

 

[Andrew Mason]

When the tax incentives and subsidies propping up the financial side of wind farms are removed, they tend to become an uneconomical means of power generation.

http://www.telegraph.co.uk/news/ear...m-plans-in-tatters-after-subsidy-rethink.html

On the other hand, if you factor in the adverse health effects of fossil fuel burning, particularly coal, the death toll and injuries from mining coal (particularly in China) - not to even mention the eventual costs of global climate change - one may be able to make a case that power generation using fossil fuel is (already) more uneconomical.

AM

 

[psycho rich]

On the other hand, if you factor in the adverse health effects of fossil fuel burning, particularly coal, the death toll and injuries from mining coal (particularly in China) - not to even mention the eventual costs of global climate change - one may be able to make a case that power generation using fossil fuel is (already) more uneconomical.

AM

Perhaps a transmission could convert torque to increased r.p.m.
I for see a day when we use wind power to force sea water to higher elevations where it's run thru a solar still . The excess water is used for hydro power. It's a giant battery with no emissions .

 

[billy_joule]

Perhaps a transmission could convert torque to increased r.p.m.
I for see a day when we use wind power to force sea water to higher elevations where it's run thru a solar still . The excess water is used for hydro power. It's a giant battery with no emissions .

All the wind turbine schematics I've seen have gearboxes.
Pumped storage is in use around the world, current capacity is over 100 GW:
http://en.m.wikipedia.org/wiki/Pumped-storage_hydroelectricity

 

[Wes Tausend]

QUOTE Skeptic22 in post #1, "Is there a limit to the amount of energy which can be extracted from the wind?
There are a huge number of windfarms springing up around the world.. all taking energy from the wind.
The assumption seems to be that this is limitless and 'free'.
Clearly this is not possible".

Actually, the last statement is only partly true. The derived power is not "limitless", but it is "free". OmCheeto is correct in assessing that the atmospheric wind is solar powered, and that is what limits it, the total small percentage of solar power that falls upon earth. On the other hand, the derived power is "free" in the sense that if we do not use it, it is wasted elsewhere in friction losses with various earthern structure. Since all the wind is eventually lost to entrophy, and therefore converted to heat anyway, the net earthern energy change to windmills from trees etc (net change in what climate would have been with no manmade obstacles) is zero. The total earthern solar power undergoes entropy change back to heat, is re-radiated away into empty space in all cases and it is equal no matter which "windkiller" it comes from.

So A.T. and jbriggs444 are absolutely correct in their assessments. The idea that the wind energy is "free" is not only possible, but clearly mandatory.

Omcheeto always seems to offer interesting proposals to catch us off guard. He suggested that we could hang a balloon with a tab of tape protruding from it and passing wind would produce a global torque. This is sort of true if we set the experiment up and blow on the hanging balloon with a nearby fan. In actuality, I think the balloon will soon bob in the breeze and the tab will scoot around to the backside, perhaps oscillating from one side to the other because the moment the tab rotates all the way around to the other side, it will be blown backwards. Which brings up an another interesting scenario.

Suppose we attach the fan to the experimental balloon too. This may even be possible with the new tiny personal battery powered fans now available. In this case the little fan will always blow directly on the tab if we strategically place it. Unfortunately only part of the airflow will strike the tab and the rest will miss. I suggest that the balloon will rotate backwards since the fan will now basically operate as a fanjet motor with a minor contrary obstacle (the tab) in it's wake. The same would happen if we were to set up a sailboat and try to blow ourselves forward by catching the breeze from a forward-facing fan set up behind the sail on deck. The boat would likely sail backwards.

Suppose we did set the boat up and it did sail backwards? If we let it continue and it struck a reef, wouldn't this reef began to apply a continuous torque to mother Earth besides wrecking the rudder? Unfortunately the fan would create a small "waste" breeze behind us (ahead of the bow), and this would circle the Earth and create a headwind (against the stern). Except the waste exhaust would actually first dissipate against Earth from all the trees. But the trees would create a nulling counter-torque in doing so. The only thing that would create a complete rotational torque on Earth would be a chemically fueled rocket engine. I once naively proposed this to my young grandson as a method to slowly rotate the moon so we did not have to look at the same old side all the time. This is before I found out about tidal locking. Whoops.

One other thing to think about is that all the winds on Earth are due to rotating flows. Whenever the wind blows one way somewhere on earth, it is blowing the other way somewhere else. (Else the wind would pile up on one end.) The rotational flows are caused by the sun and related to Earth's natural rotation. The sun heats water and air which rises in pockets of both narrow and broad columns. When the air rises (warm air and vapor rise), other air must rush into fill the pressure void. This wind is also encouraged to rotate just as does a bathtub drain. We may say all atmospheric air movement is of this nature.

Which brings us to the reason windpower is desireable. A bit ago I said that not just air, but also water rises. Very few people realize that water is lighter than air (as vapor). So extra newly heated rising water is largely responsible for our current, more aggressive weather changes. The ocean water is being heated to an extra degree (literally) by extra greenhouse gases trapping heat near the ground. The warmer water therefore evaporates easier and rises more quickly, dragging more atmospheric air with it. Caught in the throes of global warming, we now have more overall earthern wind than we had before. The solar power delivered to Earth is pretty much the same to be sure. But less re-radiation of entrophical heat is escaping to outer space. Unfortunately the usual escape route is slightly more blocked mostly by the "thicker" blanket of greenhouse gases formed by fossil-fuel carbon dioxide and the boot-strap effect of more water vapor at any given time. We need windpower to off-set this.

It is true most wind generators won't amortize. That is because they are too small, basically toys. Modern commercial units do pay for themselves.

Wes
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[OmCheeto]

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Omcheeto always seems to offer interesting proposals to catch us off guard.
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Wonderful post!

And, I don't mean to catch anyone off guard. I just find some questions very interesting, and don't really have an answer, so I design over-simplified models in my head.

One thing I forgot,

Heat and torque.

was acoustic energy. Trees are very noisy when the wind blows. But, as you said; "Entropy".

But these hypothetical questions are very difficult to model. You have to start out with ideal "text book" initial conditions, and then start adding in your pieces of duct tape and fans.

I've been thinking about my "torque" comment the other day, and decided it might need more research. I may be completely wrong about it.

If the Earth were a solid perfect sphere, with no features, no moon, and no skin effect drag on the atmosphere, then the atmosphere would probably get tidally locked to the sun. If you added a single tree, at the equator, would not some of the energy of the atmosphere get transferred to the Earth, via the non-perfect tree?

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[CWatters]

Can you shape the duct such that more air will go through the disc? In the same way a wing makes more air flow above it.

Sure but instead of adding mass to make a duct it's better to add mass to the blades and tower to make them bigger (larger diameter). The swept area is proportional to the square of the blade length.