02-02-2014, 10:32 AM
(This post was last modified: 02-02-2014, 10:42 AM by JohnnyYesterday.)

While I did mention the square-cube law in the OP, I didn't explain just how much it affects something like a turbine. I'll let the first linked patent do it for me:

"The decision to use a single large rotor, rather than many small rotors, is based on a desire for simplicity, and economy of scale, but results in a whole new series of expenses: First, the circular area subtended by a spinning rotor is proportional to the diameter squared, while the rotor's actual volume (and hence its mass), is proportional to the diameter cubed. In other words, the larger the rotor, the less wind it can capture in relation to its mass. The significance of this cannot be overemphasized: The amount of wind available per unit rotor mass is inversely proportional to the rotor diameter. This means that a 10-meter rotor will capture 100 times as much wind as a 1-meter rotor, but will weigh 1000 times as much! So as its diameter has increased by an order of magnitude, its subtended wind collecting area per unit mass has decreased by an order of magnitude."

So if it doesn't matter how long a series of turbines is, the sensible thing to do is to make their diameters as small as possible.

"The decision to use a single large rotor, rather than many small rotors, is based on a desire for simplicity, and economy of scale, but results in a whole new series of expenses: First, the circular area subtended by a spinning rotor is proportional to the diameter squared, while the rotor's actual volume (and hence its mass), is proportional to the diameter cubed. In other words, the larger the rotor, the less wind it can capture in relation to its mass. The significance of this cannot be overemphasized: The amount of wind available per unit rotor mass is inversely proportional to the rotor diameter. This means that a 10-meter rotor will capture 100 times as much wind as a 1-meter rotor, but will weigh 1000 times as much! So as its diameter has increased by an order of magnitude, its subtended wind collecting area per unit mass has decreased by an order of magnitude."

So if it doesn't matter how long a series of turbines is, the sensible thing to do is to make their diameters as small as possible.