The square-cube law says that a blade’s volume and weight are proportional to the cube of its length, but the extra energy captured only increases to the square of that length. This relationship is shown in the image above showing how a cube’s dimension when doubled results in a volume eight times the size.
In practice, the “square-cube law” means the price tag of a turbine (approximated by the volume of blade material and the towers and platforms needed to support the rotor) climbs faster than how much more energy it produces as its blade length increases. For example, 38 m blades on a 1.5 MW system would cost about $125k each but scaling up to just 47 m blades on a 3 MW system would cost about $300k for each blade.
So, flattening this curve continues to be THE focus in blade manufacturing. Make blades longer but manage their weight so they grow at less than the expected cubic rate, thus lowering the cost of electricity produced.
Over the years, innovative designs in aerodynamics, structures, and generators as well as advances in materials, control strategies, and power electronics, have flattened this curve…this expected growth to the power of “3” has been reduced to as low as 2.2. That’s impressive.