Environmental Engineering Reference
In-Depth Information
density is the change in pressure with elevation. A 1,000 m increase in elevation will reduce the pressure
by 10%, and thus reduce the power by 10%. If only elevation is known, air density can be estimated by
l 1.226 (1.194*10 4 ) z
(3.4)
The standard density for comparing output of wind turbines is 1.226 kg/m 3 , which corresponds to
a temperature of 15°C and an air pressure of sea level. For example, the average density for Amarillo,
Texas, is around 1.1 kg/m 3 . When this value is compared to standard pressure, sea level, and 15°C
(288K), there would be 10% less power at Amarillo for the same wind speeds. With the measurement
of wind speed, pressure, and temperature, wind power potential can be calculated from Equation 3.2.
The energy per area for a time period of the same wind speed is
E
A
P
A t
kWh/m 2
(3.5)
3.4 WIND SHEAR
Wind shear is the change in wind speed or direction over some distance (Figure 3.4). There can
even be a vertical wind shear ( Figure 3.5 ) . The change in wind speed with height, a horizontal wind
shear, is an important factor in estimating wind turbine energy production. The change in wind
speed with height has been measured for different atmospheric conditions [3, chap. 4].
The general methods of estimating wind speeds at higher heights from known wind speed at
lower heights are power law, logarithm with surface roughness, and logarithm with surface rough-
ness that has zero wind velocity at ground level. The power law for wind shear is
A
¤
¦ ¥
³
µ ´
H
H
vv
(3.6)
0
0
where v 0 measured wind speed, H 0 height of known wind speed v 0 , and H height.
The wind shear exponent ] is around 1/7 (0.14) for a stable atmosphere (decrease in temperature
with height); however, it will vary, depending on terrain and atmospheric conditions. From Equation
3.6 the change in wind speed with height can be estimated ( Figure 3.6 ) . Notice that for A 0.14, the
wind power at 50 m is double the value at 10 m, a convenient way to estimate power, so many wind
maps give wind speed and power classes for 10 and 50 m heights. However, for wind farms, wind
power potential is determined for heights from 50 m to hub heights.
The wind shear exponent values in continental areas will be closer to 0.20 for heights of
10-40 m and above, with large differences from low values during the day to high values at night.
FIGURE 3.4 Left: Wind shear caused by a difference in wind speed with height. Right: Wind shear caused
by a difference in wind direction.
Search WWH ::




Custom Search