Power density function

Power of the wind
Power density curve         In the page Energy of wind it was shown that the energy potential per second, the power, varies in proportion to the third power of the wind speed and in proportion to the density of the air, its weight per unit of volume.
        Combining things from previous pages it comes that if the power of each wind speed will be multiplied with the probability of each wind speed from the Weibull graph, then the distribution of wind energy at different wind speeds may be calculated. This distribution is called the power density.
        Notice, that the previous Weibull curve changes shape, because the high wind speeds have most of the power of the wind.

From power density to power output
        The graph above was drawn using the Wind Turbine Power Calculator of this web site. The following different areas may be distinguished:
- The area under the grey curve (all the way to the axis at the bottom) gives the amount of wind power per square metre wind flow we may expect at this particular site. In this case there is a mean wind speed of 7 m/s and a Weibull k=2, so it is 402 W/m2. Note that this is almost twice as much power as the wind has when it is blowing constantly at the average wind speed. The graph consists of a number of narrow vertical columns, one for each 0.1 m/s wind speed interval. The height of each column is the power (number of W/m2), which that particular wind speed contributes to the total amount of power available per square metre.
- The area under the blue curve tells how much of the wind power can be theoretically converted to mechanical power. According to the Betz' law, this is 16/27 of the total power in the wind.
- The total area under the red curve tells us how much electrical power a certain wind turbine will produce at this site. This will be shown in the page Power curve.

The important messages in the graph
        The most important thing to notice is that the bulk of wind energy will be found at wind speeds above the mean (average) wind speed at the site. This is not as surprising as it sounds, because as already explained, high wind speeds have much higher energy content than low wind speeds.

Cut-in and cut-out wind speeds
        Usually, wind turbines are designed to start running at wind speeds somewhere around 3 to 5 m/s. This is called the cut in wind speed. The blue area to the left shows the small amount of power that is lost due to the fact the turbine only cuts in after, say 5 m/s.
        The wind turbine will be programmed to stop at high wind speeds above, say 25 m/s, in order to avoid damaging the turbine or its surroundings. The stop wind speed is called the cut out wind speed. The tiny blue area to the right represents that loss of power.