You could build one windmill per Autofac, but the power available from a windmill scales as the fifth power of the height, so it probably makes sense for a group of Autofacs to build one giant windmill to serve them all.
The swept area of a wind turbine scales as the second power of the height (assuming constant aspect ratios), and the velocity of wind increases with ~1/7 power with height. Since the power goes with the third power of the velocity, that means overall power ~height^2.4. The problem is that the amount of material required scales roughly with the 3rd power of the height. This would be exactly the case with constant aspect ratios. The actual case and the scale up of wind turbines over the last few decades has not scaled that fast, partly because of higher strength materials and partly because of optimization. Anyway, I agree there are economies of scale from micro wind turbines, but they aren’t that large from a material perspective (mostly driven by labour savings).
That would suggest that an equal mass of tiny wind turbines would be more efficient. But I see really big turbines all over the midwest. What’s the explanation?
As I mentioned, the mass scaling was lower than the 3rd power (also because the designs went from fixed to variable RPM and blade pitch, which reduces loading), so if it were lower than 2.4, that would mean larger wind turbines would use slightly lower mass per energy produced. But the main reason for large turbines is lower construction and maintenance labour per energy produced (this is especially true for offshore turbines where maintenance is very expensive).
The swept area of a wind turbine scales as the second power of the height (assuming constant aspect ratios), and the velocity of wind increases with ~1/7 power with height. Since the power goes with the third power of the velocity, that means overall power ~height^2.4. The problem is that the amount of material required scales roughly with the 3rd power of the height. This would be exactly the case with constant aspect ratios. The actual case and the scale up of wind turbines over the last few decades has not scaled that fast, partly because of higher strength materials and partly because of optimization. Anyway, I agree there are economies of scale from micro wind turbines, but they aren’t that large from a material perspective (mostly driven by labour savings).
Now I know more! Thanks.
That would suggest that an equal mass of tiny wind turbines would be more efficient. But I see really big turbines all over the midwest. What’s the explanation?
As I mentioned, the mass scaling was lower than the 3rd power (also because the designs went from fixed to variable RPM and blade pitch, which reduces loading), so if it were lower than 2.4, that would mean larger wind turbines would use slightly lower mass per energy produced. But the main reason for large turbines is lower construction and maintenance labour per energy produced (this is especially true for offshore turbines where maintenance is very expensive).