Basics of Renewable Energy Supply - Renewable Energy: Technology, Economics and Environment - page 55

the stratification stability into the observation of the vertical wind profile can be
useful. For wind mills, this is the segment from the start speed until reaching
nominal power.
For a quantitative description of the vertical wind profile of the planetary
boundary layer, various approaches have been developed in the past. However,
many descriptions of the vertical wind profile are unsuitable for general use due to
parameters being too difficult to determine. For engineering application purposes
a semi-empirical formula is commonly used.
The Hellmann approach /2-17/ (the so-called Hellmann altitude formula) is a
relatively simple approximation; it is defined according to Equation (2.15). v Wi,h is
the mean wind velocity at an altitude h and v Wi,ref is the wind speed at a reference
altitude h ref (mostly 10 m). α Hell is the altitude wind exponent (Hellmann-
Exponent, the roughness exponent) and a function of the roughness length as well
as the thermal stability in the planetary boundary layer.

α

⎛ ⎞

Hell

h

⎜
⎝

⎟
⎠

v = v (2.15)

Wi , h Wi , ref

h

ref

Table 2.3 shows approximations of α Hell for different surfaces near the coast
and for different stratification within the planetary boundary layer.
The exact estimate of the size of the exponent is nevertheless difficult. For
long-term observations of the mean wind velocity value to be expected at a certain
altitude of the planetary boundary layer, the exponent α Hell primarily is to be seen
as a function of the roughness length, as other influences reach equilibrium
throughout the course of a year.

Table 2.3 Approximation values for the Hellmann-Exponent dependent on location in
coastal regions and stratification stability /2-18/
Stability Open water surface Flat, open coast Cities, villages

0.27
0.34
0.60
In spite of the blurring with regard to Equation (2.15), the approximation is still
used in practice, as it delivers useful results for conditions that are not too extreme
and altitudes that are not too high /2-16/, /2-17/, /2-18/.

Unstable
Neutral
Stable

0.06
0.10
0.27

0.11
0.16
0.40

Influence of topography. The flow processes within the planetary boundary layer
are additionally influenced by the orography, as due to the low level of com-
pressibility of the air, the flow field above the orography is changed. Due to the
impact of the surface of the earth, vertical movements of the streaming air masses
are generated on both sides of an obstacle. Additionally, the horizontal flow is
accelerated on the upwind side and slowed down at the downwind side. Horizon-
tal flow deviations of the air current are also caused /2-20/.