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Some numbers with wind turbines

by jostpuur
Tags: numbers, turbines, wind
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Dec19-13, 02:50 PM
P: 2,068

The rotor swept area is 4657 m^2, and wind speed is 11.5 m/s. Produced power 1.5MW.

I assumed that the air density is 1.2kg/m^3, and computed, that the theoretical upper limit for produced power would be 4.25MW. This was obtained by computing the kinetic energy in an air mass of cylinder shape.

So the turbine extracts 35% of the kinetic energy of the air flow? Is that a reasonable percentage? Looks quite large to me. How could the three blades with relatively small surface area extract this much?
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Dec19-13, 03:37 PM
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That's absolutely a reasonable amount, and the way the blades can manage it is because the blades are high aspect ratio airfoils moving at fairly high speeds, so they affect a fairly large region of air around them. The turbines look like they spin slowly because of their large size, but if you work out the blade tip speed, it can be well in excess of a hundred miles per hour. If you're interested in the theoretical limits, you might like reading about Betz's Law, which describes the theoretical maximum energy you can extract with a wind turbine in a free stream.
Dec20-13, 08:24 AM
P: 2,068
I could tell that my "theoretical upper limit" wasn't really the best (lowest) possible upper limit, but I didn't know about the Betz's law, so thanks for the link.

I was suspecting that there is something peculiar about the relatively small blades moving with high speeds, but I wasn't sure if my numbers were right, and I wanted confirmation.

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