What size rotor?

It is known that the maximum power that can be generated by a horizontal windmill is

PMAX  =  8/27. AV3,

where A is the area swept out by the blades, V is the wind speed, and is the air density.

Suppose we draw the graph of PMAX vs A, assuming that the other factors are constant.
Click the graph you think would look like this.

          

Is it an advantage to have a big rotor? What disadvantages would there be?

Check 


PMAX  =  8/27. AV 3

This graph cannot be correct:

it does not pass throught the origin.

When A = 0 we would expect PMAX = 0 too.


PMAX  =  8/27. AV3

This graph is correct.

It passes through the origin,

and has equation of the form

PMAX  =  k A  with  k > 0.

PMAX  =  8/27. AV 3

This graph cannot be correct:

this would represent
PMAX vs V.

For PMAX vs A, we expect a linear graph.



The graph indicates that the amount of power generated increases linearly with the size of the rotor. So bigger is better! On the other hand, the cost of manufacture has to be taken into account. Also, a large rotor is likely to fare badly in gale force winds.