Basics of Renewable Energy Supply - Renewable Energy: Technology, Economics and Environment - page 56

Nevertheless, a closed analytical description of the air flow conditions above
all types of area elevations could only be realised with significant difficulties, as
the concrete shape of the respective obstacle can hardly be captured exactly in
practice. Furthermore, the wind profile is additionally influenced by the initial
flow direction, the stratification stability and the roughness of the ground, among
others.
Therefore the effect of the change in velocity (Fig. 2.26) caused by orography
e.g. above the crest of escarpments, hills or ridges, is often named in relative
terms and defined as the Speed-Up-Ratio ∆ s or in short, the Speed-Up (Equation
(2.16)). v Wi is the mean wind velocity and ∆ h the corresponding altitude above
ground. The index x defines the cross-section through the elevation and the index
a a point on the upwind side of the hill, where the current is not influenced by it.

v ( ∆ h ) − v ( ∆ h )

Wi , x Wi , a

∆ s =

(2.16)

v ( ∆ h )

Wi , a

∆h ∆h ∆h ∆h

v Wi (∆h) v Wi (∆h)

v Wi (∆h) + ∆s (∆h) v Wi (∆h) + ∆s (∆h)

∆s max ∆s max

Hill Hill

h H h H

0.5 h H 0.5 h H

x x

l 1/2 l 1/2

Fig. 2.26 Coherences for a hill overflowed by air (for an explanation of the symbols see
text)

For flat two-dimensional chains of hills the approximation ∆ s = 2 h H / l 1/2 resp.
∆ s = 1.6 h H / l 1/2 can be used. h H is the height of the hill above the surroundings
and l 1/2 the so-called half-value length and thus the horizontal distance between
the peak and the half-value height (i.e. half the peak height of the hill). For exam-
ple, a maximum speed increase of around 60 % or more can result for typical val-
ues ( h H = 100 m; l 1/2 = 250 m), which then has a significant influence on, for ex-
ample, the energy yield of a wind mill.