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Wind Turbines

 Old Wind TurbineThere are many designs of Wind Power Generator but the fundamental problem with them all is that wind power on a useful scale requires a large machine with resulting complexities of reliability and cost.
For small generators, regardless of the construction method, it is the available power that is the major issue.
The available power from a basic wind powered device is proportional to the swept area of the fan or blades, or other extraction mechanism, and the cube of the wind speed. Aerodynamic considerations to do with the extraction of energy from a moving air stream mean that the efficiency of such a machine can never be higher than approximately  59%  (Betz Law). To find out more about the definitions of energy and power click here.
The kinetic energy, E , in a moving air stream, neglecting secondary effects such as temperature, is
where M is the mass and V the velocity. 
The mass is derived from the volume of air times the density, and the volume is calculated from the area of the air stream times its velocity. Assuming a circular air stream this leads to the available power equation that can be easily modified for other shapes;
Where  is the ratio of the circle circumference to its diameter and is the efficiency ratio, the maximum value of which, 0.59, is given by Betz' law. The length of the blades or radius is r . In the UK typical average wind speeds (V) are around 5 metres per second . The density of air is about 1.2 kg per cubic metre
So assuming a 0.5 metre radius turbine (1 m diameter) the maximum available power that can be extracted from a typical average airflow is approximately 35 watts. This is just enough to light a low power electric light (a 40 watt bulb). Note that this takes no account of the variability of wind or the efficiency of the generator. Realistically these factors could be expected to reduce the average power by at least 50% and probably a lot more.
In the UK therefore the typical average power output in favourable conditions and with a 100% efficient coupling mechanism would be about 44 watts per square metre. This is equivalent to a windmill device about 1.2 metres in diameter after making a small allowance for the central hub. Figures are often quoted for windmill type devices that significantly exceed these values but they tend to use peak wind speeds and maximum output rather than the average. The power output increases in proportion to the cube of the wind speed so at 10 metres per second the power outputs on the table on the right will be 8 times bigger. We use 5 m per second because that is closer to the average power over a year. Wind turbines need a safety mechanism to stop the blades going too fast in storm conditions, so they can only operate effectively over a small range of wind speeds.
Because the power outputs increase significantly as the machine is increased in size, larger machines can be quite effective. A 20 metre diameter turbine in an offshore location with 10 metre per second winds might produce an average power output of around 100 KW but such devices need to be extremely robust, and therefore expensive, to be capable of withstanding storm conditions.