The efficiency of wind turbines

Wind turbines derive their energy form the kinetic energy in wind. When the wind blows the turbine revolves and the turbine is connected to a generator which generates direct current electricity. The electricity is inverted into alternating current electricity and then fed into a grid or into a place where the electricity is used. There is a limit to the energy in any given amount of wind, but there is also a limit to the maximum amount of energy that any turbine can collect and harness.

According to Beltz’s law no turbine can capture more than 59.3% of the wind energy. Beltz’s coefficient is accordingly 0.593.

When it comes to wind turbines no turbine known can actually capture more than 59.3%. The turbine blades meet air resistance and the modern turbine generally appears to operate in the 20% to 30% efficiency range. There also energy losses by the inversion process and energy losses incurred in transmitting electricity long distances – typically from off the sea shore to population centres many miles away. Energy losses through transmission occur when the electrical cables get hot, converting some electrical energy into heat energy.

Beltz’s law applies to all turbines, big or small. Smaller turbines are significantly less efficient than big ones, because the energy generated depends upon (among other facts) the size of the blade. In fact it is a factor of the square of the blade, so if you compare wind turbines one with a metre rotor blade and another with a five metre blade but identical in all other respects in identical conditions the blade that is five times longer will generate 25 times more electricity.

This probably makes wind turbines for small domestic dwelling fairly irrelevant. Small turbines also suffer from the fact that they operate at levels where traditionally the wind is weaker and less dense. This is also important because while the square of the rotor blade is one of the factors that limit the energy derived another factor is the cube of the kinetic energy in the wind.

These limitations are governed by the laws of physics and have been proved mathematically. It is clear that turbines work best if they are very large and erected in windy places. The latter is obvious, but not perhaps the former.

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