‘Flattening the Curve’ of the Square-Cube Law
Wind turbines keep getting bigger and bigger because their blades keep getting longer.
It’s simple math. If you want more energy, you need more wind. If you can’t make more wind (and we can’t), you have to capture more of it in one revolution of the blades. That’s what longer blades do as they spin. They create a bigger swept area (they cover more area in one revolution). This extracts more power output per turbine from the wind. That means more electricity generated. An obvious opportunity.
So, it makes sense that we are seeing the advent of 107, 108, and 115.5 m blades. And yet, with that opportunity comes challenges. Larger turbines must deal with the inescapable effects of scaling…mass.
In other words, managing blade weight is a big deal. The industry is fighting against the “square-cube law”.
The what?
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.
That’s why we do what we do at Atrevida Science…we are optimizing blades that flatten the square-cube curve…and power our future.
