Influence of surroundings and height

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The wind speed is usually recorded at a height of 10 m. Changes in elevation can change the wind speed in a distance of only a few hundred meters. Hills or mountains influence the wind speed significantly. On top of a mountain or on the luff side, which is perpendicular to the wind (see Figure 5.3), the wind speed can rise to become double the uninfluenced value. In contrast, the wind speed is much lower on the lee side.

Obstacles, plants or hills near a wind generator site can slow the wind significantly. Single obstacles are no problem if the total rotor area is over three times higher than the obstacle or if there is sufficient distance between the wind generator and the obstacle. However, this distance can be up to 35 times the obstacle height. Without proper clearance, wind turbulence can reduce the usable wind energy.

The wind speed increases with the height from ground because the wind is slowed down by the roughness of the ground. Wind generators usually have hub heights of more than 10 metres. For the estimation of the wind potential, additional wind speed measurements at other heights are necessary. However, if the type of ground cover is known, the wind speed at other heights can be calculated.

The wind speed v(h2) at height h2 can be calculated directly with the roughness length, z0 of the ground cover and the wind speed v(hx) at height hx:

Figure 5.3 Common Expressions for the Description of the Direction of the Wind

Figure 5.3 Common Expressions for the Description of the Direction of the Wind

Obstacles can cause a displacement of the boundary layer from the ground. This displacement can be considered by the parameter d. For widely scattered obstacles, parameter d is zero. In other cases d can be estimated as 70 per cent of the obstacle height.

The roughness length z0 describes the height at which the wind is slowed to zero. In other words, surfaces with a large roughness length have a large effect on the wind. Table 5.3 shows the classification of various ground classes depending on the roughness length.

The following example shows the influence of the ground cover. The same wind speed v(h1) = 10 m/s at a height h1 = 50 m above different ground classes is assumed. Equation (5.6) is applied to calculate the wind speed v(h2) at a height of h2 = 10 m. The displacement d for the boundary layer from the ground must be considered for higher obstacles in ground classes 6 to 8. Table 5.4 shows the calculated results. The wind speed decreases significantly with rising roughness lengths z0; thus, it does not make any sense to install wind power plants in built-up areas or large forests. The wind speed also increases significantly with height. For instance, the wind speed at a height of 50 m is 30 per cent higher than at 10 m for ground class 4. This must be considered for the installation of large wind turbines. The usable wind speed at the top of large wind towers is much higher than at the common measurement height of 10 m. Wind turbines of the megawatt class come with hub heights of between 50 and 70 m for coastal areas (ground class 1 to 3) and even higher for inland areas with higher roughness lengths.

This example should not give the impression that the wind speed is already independent of the ground at a height of 50 m. The wind speed usually becomes independent of the height, where the wind becomes known as geostrophic wind, at heights significantly exceeding 100 m from the ground.

Finally, the power law of Hellmann is another relation for the vertical distribution of wind speeds.

Table 5.3 Roughness Lengths z0 for Different Ground Classes

Ground class Roughness Description length z0 in m

Table 5.3 Roughness Lengths z0 for Different Ground Classes

Ground class Roughness Description length z0 in m

 1 - Sea 0.0002 Open sea 2 - Smooth 0.005 Mud flats 3 - Open 0.03 Open flat terrain, pasture 4 - Open to rough 0.1 Agricultural land with a low population 5 - Rough 0.25 Agricultural land with a high population 6 - Very rough 0.5 Park landscape with bushes and trees 7 - Closed 1 Regular obstacles (woods, village, suburb) 8 - Inner city 2 Centres of big cities with low and high buildings
 Table 5.4 Example of the Decrease in Wind Speed v(h2) at Height h2 = 10 m as a Function o f the Ground Class for v(h1) = 10 m/s at h1 = 50 m Ground z0 d v(h2) at h2 Ground zo d v(h2) at h2 class = 10 m class = 10 m 1 0.0002 m 0 m 8.71 m/s 5 0.25 m 0 m 6.96 m/s 2 0.005 m 0 m 8.25 m/s 6 0.5 m 3 m 5.81 m/s 3 0.03 m 0 m 7.83 m/s 7 1 m 5 m 4.23 m/s 4 0.1 m 0 m 7.41 m/s 8 2 m 6 m 2.24 m/s

Equation (5.6) becomes:

Equation (5.6) becomes:

For z = 10 m and z0 = 0.01 m, the parameter a is about 1/7; this equation is then called a 1/7 power law. However, this power law is only valid if the displacement d of the boundary layer from the ground is equal to zero.

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