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I have noticed that windmills are generally built in empty fields with no trees around, and I've been wondering why...

A windmill is generally way taller than trees and I can imagine that trees don't actually affect the flow (see picture).

enter image description here

But is this the reason why there is nothing around or is there something else that makes them waste so much space around? And is the velocity profile from the first figure a realistic one?

If I search for the theory of external convection, the velocity profile looks like this for flow over a plateau: enter image description here In the second case, wouldn't the velocity be higher if there is an obstacle? Or is it because the obstacle is a porous medium that damps the flow? And lastly, is the velocity profile at earth level looking like that? Is there really an origin to it, or is it fully turbulent all the way?

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  • $\begingroup$ My guess is ease of construction and permit concerns are prime reasons. But I'll wait for the resident wind energy expert and his answer. $\endgroup$ – mart Nov 23 '16 at 13:03
  • $\begingroup$ But after construction, you can plant trees. And yet, this does not happen. As for the permit, I don't see the connection with the trees. Can you please explain more what you mean by that? (Please keep in mind that we are speaking about some hundreds of square meters where there is nothing but fields (or crops in some sites). $\endgroup$ – Physther Nov 23 '16 at 13:44
  • $\begingroup$ @Paul "But after construction, you can plant tree" - Trees don't tend to grow well where there are high winds. Figure out the reason why for yourself ;) $\endgroup$ – alephzero Nov 23 '16 at 17:47
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    $\begingroup$ Where I live, the turbines may not be within several hundred m of any woodlot, stream, road, house etc. It's regulation, to protect those areas from both the disruption of construction and any ongoing disruption or risk that could arise during 20 years of operation. $\endgroup$ – Kate Gregory Nov 24 '16 at 18:03
  • $\begingroup$ Thank you, Kate! That's what I thought at the beginning. So I guess it's a combination of everything, physics, regulations, biology etc. $\endgroup$ – Physther Nov 24 '16 at 18:10
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Trees increase the turbulence of the air that reaches the turbines. That creates all sorts of uneven, rapidly-shifting loads on the blades and structure. That increases the maintenance costs, decreases availability, decreases the capacity factor, and decreases the life expectancy of the turbine. So, higher costs, lower revenue.

One of the ways we measure the impact is the surface roughness coefficient $z_0$. Here are the figures from the book "Wind Energy - The Facts". As you can see, forest and woodland has a much higher $z_0$ than open farmland - and that means higher turbulence.

Open land also makes physical access to the site easier. That's particularly important during construction, when very very long vehicles carry each blade (40-60 metres long) in one piece.

enter image description here

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  • $\begingroup$ Great! Thank you very much! That makes total sense! $\endgroup$ – Physther Nov 23 '16 at 14:36
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    $\begingroup$ Turbulence: which is also the explanation why with the most modern types (say hub heights of ~160 meters) are actually feasible and economically viable within forrests. Easier access is also only in part a problem as cultivated forrests have a sound infrastructure for heavy machinery such as harvesters. (Notwithstanding Other ecological concerns like birds.) $\endgroup$ – Ghanima Nov 24 '16 at 17:18
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There is a non-engineering reason as well: the people most open to placing turbines on their land are farmers who are interested in the extra income.

Turbines are not (yet) placed near built-up areas, which generally leaves large farms, undeveloped lots and nature reserves. Getting a building permit for a commercial enterprise in a nature reserve is close to impossible, and undeveloped lots may be zoned for housing, which would also prohibit the erection of wind turbines.

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  • $\begingroup$ That does sound like a good reason. Never thought about that. $\endgroup$ – Physther Nov 23 '16 at 17:10
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    $\begingroup$ That reason is only half the truth. In fact proprietors of forrests share the same incentive as "farmers" (or more precisely owners of the respective farmland). Having power plants erected there is a secondary income in both cases. (The question is asking about trees and forrests which are not necessarily nature reserves.) $\endgroup$ – Ghanima Nov 24 '16 at 17:20
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Look at how and why the "Betz limit" works.

As energy is lost in your first diagram to the trees, the airflow through and around the trees expands and slows down.

That slowdown reduces the energy available to the turbine.

(note. I am not the resident wind energy expert!)

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  • $\begingroup$ Thank you, Brian. Well, the kinetic energy below the propellers would be lower due to the trees, but no one cares about that part (as long as the trees are smaller). So with or without trees, the flow at the propeller level should not be affected, right? This, if the first picture represents a real case. If the second picture is more realistic, then yes, it will affect the flow. Betz's law is interesting, but I think irrelevant to this particular question. I didn't know about that, thought, so thanks! $\endgroup$ – Physther Nov 23 '16 at 13:41
  • $\begingroup$ No. The Betz insight is that the slower moving mass of air has to occupy a larger volume (think of a wide slow river instead of fast shallow rapids, both carrying the same mass flow). Therefore it must expand - and that means upwards, into the path of the turbine. Whether that change in flow is laminar or turbulent depends on the "Reynolds number" and the windspeed, but if it's turbulent you can expect bigger problems. $\endgroup$ – Brian Drummond Nov 23 '16 at 14:10

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