## Power from Wind Problems

Posted in Cute Problems with tags , , on November 21, 2015 by telescoper

It has been a little while since I posted anything in the Cute Problems category so since today is quite a windy day I thought I’d give you this one, which leads to an extimate of the maximum power that can, in theory, be extracted from wind a windmill.

Assume that the wind far upstream and down-stream of the windmill has speed V and αV respectively, with 0≤α≤1, and let the wind speed at the sails of the windmill, which sweep out an area A, be v.

Now for the problems

(i) By equating the power absorbed by the mill to the rate of loss of kinetic energy of the wind, show that v/V=½(1+α).

(ii) Show that the power obtainable is proportional to AρV3 where ρ is the density of air.

(iii)  Show that the maximum power that can be extracted is 16/27 of the power available initially in the wind.

The final result is known as Betz’s Law and it works for any form of turbine, not just a windmill.

## Wind turbines aren’t noisy!

Posted in Uncategorized with tags , on September 27, 2011 by telescoper

I read this morning that a petition to the Welsh Assembly Government has been raised demanding that wind farms be switched off from time to time to give local residents “some respite from the noise they make”.

In fact wind turbines, even big ones, make far less noise than people seem to think, and certainly less than motor vehicles. So if you’ve got an objection to wind farms, please make it an honest one.