Page 100 - Fundamentals of Ocean Renewable Energy Generating Electricity From The Sea

Offshore Wind Chapter | 4 93

velocity of wind (u r ) at a reference height above the Earth (z r )isgiven (e.g.by
a meteorological station), Eq. (4.6) leads to
ln (z/z o )
u(z) = u(z r ) (4.7)
ln (z r /z o )
which can be used to estimate the wind velocity at other heights, such as the
hub-height of a wind turbine. Alternatively, the power law has also been used to
characterize the vertical distribution of wind velocity,
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z
u(z) = u(z r ) (4.8)
z r
If the wind velocity is measured/modelled at a particular height above the
ocean/land surface, the velocity of wind at the turbine height can be estimated
using the previous equations. For instance, Fig. 4.9 shows the distribution of
wind velocity using a logarithmic distribution (assuming two values for the bed
roughness) and power law. If the average measured velocity 10 m above the
ground is 11 m/s, the estimated velocity at 90 m above the ground is about 13.5–
15 m/s.

FIG. 4.9 Vertical distribution of mean wind velocity based on power law and logarithmic
distributions. For this example, the average measured velocity 10 m above the ground is 11 m/s, and
the estimated velocity at 90 m above the ground (e.g. turbine hub-height) is 13.6–15 m/s, depending
on the surface roughness.