What factors affect the efficiency of a wind mill/wind turbine? What is the physics related to it?

What factors affect the efficiency of a wind mill/wind turbine? What is the physics related to it?
What physics is related to it (secondary school - to early university level physics)? Also, how would a basic wind turbine be constructed and how would you go about testing the factors that affect the efficiency?

Best answer:

Answer by simplicitus
Efficiency (the ratio of actual power out to theoretical power out) is not the primary design goal for a windmill or turbine. The real goal is minimizing total cost per unit energy.

Efficiency is a factor, but initial cost, ease of maintenance, suitability to the context, etc. are all more important. (Just as with gasoline and diesel engines).

Thus, it is clear that theoretical efficiency goes up with the number of blades, but going from 1 blade to 2 increases efficiency by only 6%. Going from 2 to 3 blades increases efficiency by 3%.

http://en.wikipedia.org/wiki/Wind_turbine_design#Blade_count

Going from 2 blades to 3 blades might pay, but while 4 blades would be a little bit more efficient, the gain just isn't worth the costs. Similarly, a 3_D helical turbine can be more efficient that a planar turbine, but would be much too hard and expensive to build.

For another example, Darrieus wind turbines are never as efficient as propellor type turbines, but are still considered practical for power generation:

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

For one thing, they never have to rotate to face the wind; and their electronics can all be at ground level for ease of access:

http://en.wikipedia.org/wiki/Vertical-axis_wind_turbine

That's even more true of Savonius turbines:

http://en.wikipedia.org/wiki/Savonius_wind_turbine#Use

A subtle point is determining which "theoretical power" to count. In general, the higher you go the faster the wind and power goes up as the cube of the velocity.

http://en.wikipedia.org/wiki/Betz%27_law

So when you consider a vertical propellor, do you use the wind velocity at the axis? at the top tip? (In theory, you have to do an integral, but that assumes you know the distribution of wind speeds.)

And what do you do about storms? When the winds are too fast, the turbine cuts back on generating power, but what speed is "too much"? Do you design the turbine to handle 90% of the wind or 99% of the wind? You may get twice as much total energy out of the 99% turbine (because the 9% of the time that it is working while the other isn't, the wind is fast and has lots of energy) but the costs are much greater.

(BTW, recent analysis suggests that the best possible planar (simple propellor-type) turbine can only come away with 30% of the energy in the wind that goes through it.)

http://www.math.le.ac.uk/people/ag153/homepage/Gorlov2001.pdf

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