WIND SPEED & HEIGHT??the Bigger the Better the Best??

Wind speed and height are interconnected. Generally, wind speed increases with height above the surface. This is due to several factors:

1. Frictional Force: The frictional force of the surface diminishes with height. Surface objects such as trees, rocks, houses, etc., slow the air as it collides into them. The influence of this friction is less with height above the ground, thus the wind speed increases with height.
2. Surface Roughness and Obstacles: Wind speed is much affected by factors such as the roughness of the ground and the presence of buildings, trees, and other obstacles in the vicinity.
3. Atmospheric Stability: The wind profile power law is a relationship between the wind speeds at one height, and those at another. The exponent (α) in the power law is an empirically derived coefficient that varies dependent upon the stability of the atmosphere. For neutral stability conditions, α is approximately 1/7, or 0.143.Let’s consider an example. If we know the wind speed at a reference height (let’s say 10 meters), we can estimate the wind speed at a certain height (let’s say 50 meters) using the wind profile power law4. The relationship would be rearranged to:

it’s important to note that when a constant exponent is used, it does not account for the roughness of the surface, the displacement of calm winds from the surface due to the presence of obstacles (i.e., zero-plane displacement), or the stability of the atmosphere. Therefore, in places where trees or structures impede the near-surface wind, the use of a constant 1/7 exponent may yield quite erroneous estimates, and the log wind profile is preferred.

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In the field of wind power assessments, this relationship is crucial as wind speeds at the height of a turbine (around 50 meters) must be estimated from near surface wind observations (around 10 meters).

Turbine towers are becoming taller to capture more energy, since winds generally increase as altitudes increase. The change in wind speed with altitude is called wind shear. At higher heights above the ground, wind can flow more freely, with less friction from obstacles on the earth’s surface such as trees and other vegetation, buildings, and mountains. Most wind turbine towers taller than 100 meters with higher than-average wind shear.

A turbine’s rotor diameter, or the width of the circle swept by the rotating blades has also grown over the years. The average rotor diameter of newly installed wind turbines?is?over 130 meters?(~430 feet) longer than a football field, and almost twice the wingspan of a 747.

Larger rotor diameters allow wind turbines to sweep more area, capture more wind, and produce more electricity. A turbine with longer blades will be able to capture more of the available wind than shorter blades even in areas with relatively less wind.

Wind Speed VS Height

One of the most important factors that affect the optimal height for a wind turbine is the wind speed. The higher the wind speed, the more power the turbine can produce. However, wind speed is not constant across different heights. It increases with height due to the reduced friction and turbulence from the ground and obstacles. This is called the wind shear effect.

To account for this effect, you can use the power law formula, which relates the wind speed at different heights: v2 = v1 * (h2 / h1) ^ a where v2 is the wind speed at height h2, v1 is the wind speed at height h1, and a is the wind shear exponent, which varies depending on the terrain and surface roughness.

The Beaufort scale, also known as the Beaufort wind force scale, is an empirical measure that relates wind speed to observed conditions at sea or on land. It was devised in 1805 by the Irish hydrographer Francis Beaufort, who later became Rear Admiral.

The scale ranges from 0 (calm) to 12 (hurricane), with each level having specific descriptions of the wind conditions and specifications for use at sea or on land. For example, a Beaufort scale of 0 indicates calm conditions with smoke rising vertically, while a scale of 12 indicates hurricane conditions with devastation and very poor visibility.

The wind speeds you hear quoted in weather or news reports are always measured at 10 meters above the ground using meteorological instruments. They do not reflect the wind speeds that you would feel on the ground. At 2 meters, wind speed may be only 50-70% of these figures.

The Beaufort scale is widely used in meteorology, navigation, and other fields where wind force and its effects are important. It’s a practical tool for estimating wind speeds and understanding their potential impacts.

Blade Size & Height

Another factor that affects the optimal height for a wind turbine is the blade size. The larger the blade size, the more area the turbine can sweep and capture the wind energy. However, larger blades also have higher costs, weights, and stresses. Therefore, there is a trade-off between blade size and height. To account for this trade-off, you can use the blade element momentum theory, which relates the power output of a wind turbine to the blade size and wind speed: P = 0.5 ρ A Cp v^3

where P is the power output, ρ is the air density, A is the swept area, Cp is the power coefficient, and v is the wind speed.

The power coefficient depends on the blade design and pitch angle, and it has a maximum value of 0.59 according to Betz's law.