Wind resource and site assessment - Wind Power Generation and Wind Turbine Design - page 68

u ( h 1 ) and u ( h 2 ) are the wind speeds at heights h 1 and h 2 . This is merely an
engineering approximation where the wind shear exponent is a function of

height z , surface roughness, atmospheric stability and orography. Therefore,
a measured wind shear exponent is only valid for the specifi c measurement
heights and location and should thus never be used for vertical extrapolation
of the wind speed, which is unfortunately very often done leading to erroneous
results.
More helpful is the logarithmic law (log law) which in fl at terrain and neutral
conditions expresses the change of wind speed as a function of surface roughness:

α

u ⎛⎞ h

uh () =

*

ln

(7)

⎜ ⎝⎠

k z

0

The wind speed u depends on the friction velocity u * , the height above ground
h , the roughness length z 0 and the Kármán constant k , which equals 0.4. Applying
the above equation for two different heights and knowing the roughness length z 0
allows the extrapolation of the wind speed to a different height:

ln( hz / )

( ) ( )

uh = uh

2 0

(8)

22 11

ln( hz / )

10

The surface roughness length describes the roughness characteristics of the
terrain. It is formally the height (in m) at which the wind speed becomes zero
when the logarithmic wind profi le is extrapolated to zero wind speed. A corre-
sponding system uses roughness classes. A few examples of roughness lengths and
their corresponding classes are given in Table 3.
In offshore conditions the roughness length varies with the wave condition,
which in turn is a function of wind speed, wind direction, fetch, wave heights
and length. However, recent surveys have shown that the vertical profi le offshore
is heavily infl uenced by the effect of atmospheric stability [18], because the
roughness length offshore will in most cases be several orders of magnitude
smaller than onshore.

Table 3: Example surface roughness length and class.

Cover z 0 (m) z 0 as roughness class

Offshore 0.0002 0

Open terrain, grass, few isolated obstacles 0.03 1

Low crops, occasional large obstacles 0.10 2

High crops, scattered obstacles 0.25 2.7

Parkland, bushes, numerous obstacles 0.50 3.2

Regular large obstacle coverage
(suburb, forest)

0.5-1.0 3.2-3.7