Evolution of Modern Wind Turbines Part B: 1988 to 2008 - Wind Turbine Technology: Fundamental Concepts of Wind Turbine Engineering - page 178

energy output (proportional to its swept area) increases as the square of the diameter, while
the volume of material (and therefore its mass and cost) increases as the cube of the diameter.
According to this simpliied rule, costs for a larger turbine will grow faster than the energy
revenue, making further scale-up a losing economic game.
For years, engineers have successfully skirted the square-cube rule by making design
changes that alter the square-cube ratio of energy capture and cost, as follows:

· Taller towers lift the rotor into more-energetic winds, so energy capture in-

creases faster than the square of the rotor diameter.

· More eficient use of material trims weight, so masses and costs increase slow-

er than the cube of the rotor diameter.

Advancements in Rotor Design

As wind turbines grow in size, so do their blades—from about 8 m in 1980 to more than
40 m for many land-based commercial systems today. Improved blade designs have enabled
the weight growth with increasing size to be kept to a much lower rate than simple geometric
scaling. As illustrated in Figure 3-43 [Grifin 2001], blade mass has recently been scaling
with rotor diameter at roughly an exponent of 2.3 (dashed line) versus the expected cubic ex-
ponent of 3 (dotted line). Also shown in this igure are preliminary estimates of even lower
weights possible for blades on a 104 m diameter rotor.

Figure 3-43. Results of a study indicating that the rate of increase in wind turbine
blade weight with rotor diameter is being signiicantly reduced by the introduction of
new technology. The dotted trend line indicates a 3.0-power weight growth according to an
elementary cubic rule, while the dashed line its the latest design weights with a 2.3-power
trend. [Grifin 2001]