Page 58 - Fluid Power Engineering

36 Chapter Three

speed at hub height in stable laminar flow situations and over-
estimate when there is mixing and convection.
2. Approximation 2: Extrapolating 10-m wind speed data to 50 m
or higher using a constant shear value. The shear formula in
Eq. (2-10) is most accurate when it is used to extrapolate wind
speeds at heights that satisfy:

0.5 < h 2 /h 1 < 2

3. Approximation 3: Constant value of shear in all seasons and all
hours of a day. It is not uncommon to observe negative shear
during the daytime hours when there is significant thermal
mixing of air because of convection. Therefore, constant shear
based on annual wind speed averages can lead to inaccuracies
in energy computations.

Section “Uncertainty in Wind Speed Measurement with Anemome-
ters” in Chapter 6 contains guidelines on wind speed measurement
heights for accurate shear computation. Also, see section “Computed
Quantities: Wind Shear” in Chapter 6 for an example of wind shear
computation.

Understanding Wind Shear
In order to illustrate the impact of wind shear, consider the following:
Which location is preferable for a wind project?

a. Location with 4 m/s wind speed at 10 m in the desert with
low roughness
b. Location with 4 m/s wind speed at 10 m in a forested area
with high roughness
Location (a) has low roughness, which implies low friction on the
surface and low shear. For illustration purposes, choose shear = 0.15,
a constant value regardless of h 1 and h 2 . Using Eq. (3-10), at hub height
of, say, 80 m, the wind speed is 5.46 m/s.
Location (b) has high roughness, which implies high friction on
the surface and high shear. In this example, choose shear = 0.25. Using
Eq. (3-10), at hub height of 80 m, the wind speed is 6.72 m/s.
A location with higher roughness has higher wind speed at 80 m
height; this is counterintuitive. The reason is that both locations have
the same wind speed at 10 m. Therefore, at location (b) the “driving
energy” of wind at upper elevations is much higher and that energy
is able to overcome high level of friction near the surface.
An alternate way to visualize shear is to consider wind speed of 10
m/s at 200-m elevation and examine two locations with two different