Harnessing Wind Power - Part 2

Mathematics contributes in many ways to the process of converting
wind power into usable energy. Large-scale weather models are used
to find suitable locations for wind farms, while more narrowly
focused models incorporating interactions arising from factors such
as wake effects and turbulence specify how to situate individual
turbines within a farm. In addition, computational fluid dynamics
describes air flow and drag around turbines. This helps determine
the optimal shapes for the blades, both structurally and
aerodynamically, to extract as much energy as possible, and keep
noise levels and costs down. Mathematics also helps answer two
fundamental questions about wind turbines. First, why three blades?
Turbines with fewer blades extract less energy and are noisier
(because the blades must turn faster). Those with more than three
blades would capture more energy but only about three percent more,
which doesn.t justify the increased cost. Second, what percentage
of wind energy can a turbine extract? Calculus and laws of
conservation provide the justification for Betz Law, which states
that no wind turbine can capture more than 60% of the energy in the
wind. Modern turbines generally gather 40-50%. So the answer to
someone who touts a turbine that can capture 65% of wind energy is
"All Betz" are off. For More Information: Wind Energy Explained:
Theory, Design and Application, Manwell, McGowan, and Rogers, 2010.