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# Re: [Phys-l] Wind generator output versus wind speed.

Without a quick reply, let me present some of my own rambling thoughts--maybe someone can confirm/deny these.

The available energy may increase as the cube of the velocity (see below), but the transfer to the turbine is via momentum transfer and the air momentum at the blades goes as the square of the velocity (mass per second increases along with the actual momentum). But then we have a torque problem as well, as the wind is hitting different distances from the axis of rotation (effective lever arm then 1/2 of the blade length?). At the generator itself, doubling the rotational speed would double the rate of flux change and therefore double the induced emf, but that should quadruple the power through a fixed load V^2/R. So, I seem to get something on the order of a square dependency on wind speed, but reduced by efficiency factors in the various transfers--linear wind speed to blade rotational speed and generator efficiency. Published curves still look (to me) pretty linear over an appreciable range of wind speeds.

Rick (finding lower level energy texts quite lacking in dealing with wind energy--older texts like Jerry B. Marion's ignoring it all together!)

----- Original Message ----- From: "Rick Tarara" <rtarara@saintmarys.edu>

Here is a physics/engineering question.

From various texts, the theoretical maximum power transfer from wind to
electrical power is cubic in wind speed and also depends on the area swept
by the rotors. The cubic part comes from the KE which is of course
quadratic in speed but with the added linear factor of wind mass. All
that's fine, but when you look at the power curves of real wind turbines,
you see 'S' curves, with little power generated at low speed and levelling
to some max power at high speed. However, the curves look pretty linear
from the 'cut in' to the 'cut out' wind velocities--slopes greater than one.
We have the Pasco Energy Transfer Generators and are putting together a wind
energy lab, but we're also seeing a linear dependency (using a three speed
fan). Not sure I understand the linearity and certainly not sure how to
approach my Energy class (gen-ed students) with anything other than 'turbine
design is complex and the actual power transfer is a function of each
individual device'. Any insights would be appreciated.

http://www.clemson.edu/scies/wind/Poster-Schmidt.pdf

Slide 11 above shows some typical power curves--many others can be found
on-line.