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Publication Title | Wind Power Siting

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Wind Power Siting by Larry Elliott

or many people the idea of producing household electrical power from a wind turbine is Fa romantic notion, a dream that rarely becomes a reality. Still for others, especially those living far from an electrical line or experiencing outrageous utility bills, it becomes a necessity. There are thousands of homes across the country now being powered by a wind turbine or combination of wind and other alternative electrical power inputs. Each installation's success or failure depends heavily on planning and correct installation. It is the

critical planning and siting stage of an installation that will be discussed in this article.

Wind As Fuel

Cars, boats, planes, power plants or garden tractors, these all have something in common, they are machines that produce useable work or power by consuming a fuel. The amount of work they do or power they produce is directly related to their size and how much fuel is available for their consumption. In the case of a wind turbine, its fuel is the wind. The power available from any turbine is dependent on how much wind is available to drive the turbine. The quantity of wind is expressed in terms of wind speed or velocity. The higher the wind speed, the greater the potential output power we may expect from a wind turbine.

Betz's Equation

In order to illustrate just how important this relationship between wind speed and power output can be, a little math and physics is in order. A formula that describes power to wind speed relationship in a wind turbine was developed in 1927 by a German scientist George Betz. This

formula states that the power available from a turbine is proportional to the cube of the wind's speed. In this equation P is the power produced in watts, E is the efficiency of the wind turbine in

3

Er A S P= 2

percent, Rho (r) is the density of air, A is area of the areo turbine in silhouette in square feet, and S is the wind speed in miles per hour. The power which can be expected from a wind turbine is equal to the efficiency of the turbine multiplied by the energy delivered per unit time by the wind to the turbine. The energy delivered per unit time is equal to:

where m(t) is the mass of the wind impinging on the turbine blades per unit time and S is the wind's speed. The quantity m(t) is equal to rAS.

A combination of these two equations yields

2

m(t) S

Betz's equation. In an average form this equation can be reduced to:

by assuming standard air density and normalized turbine efficiency.

3

2

Power by the Cube!

P = 0.0006137 A S

Basically all this math boils down to: the power available from the wind is proportional to the cube of its speed. As an example of this, let's assume we have a turbine that

produces 100 watts in a 8 mph wind. At 16 mph you may expect this turbine to double its output to 200 watts, but instead it will produce over 800 watts. Thus it can be seen that a doubling of wind speed increases power available by a factor of eight times. A very small change in wind speed translates to a rather large increase in available power. A more dramatic look at this change would be the following. Assume that you have a wind turbine located at a marginally windy site that produces 100 watts in an 8 mph wind. If you had an increase in wind speed of only 1 mph your output would be 133 watts or an increase of 33%. Even small changes in annual average wind speed can determine whether or not your site is a cost-effective candidate for wind power.

How To Determine Wind Speed

Average wind speed is the critical factor that determines the economic effectiveness of wind machines. Let's look at some methods of determining wind speed. For those individuals who have lived for several years at a particular site, you probably have some idea of how

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Home Power 1 November 1987

Wind

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