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Wind Power Density & Energy Conversion Efficiency

Wind power varies with wind speed and height above ground.

We have selected 1000 W/sq. m for 30m height (100 ft.) and 20 mph (9m/s) average annual wind speed. details: https://en.wikipedia.org/wiki/Wind_profile_power_law

Wind Turbine Efficiency Since conservation of mass requires that as much mass of air exits the turbine as enters it. Betz's law gives the maximal achievable extraction of wind power by a wind turbine as 59% of the total kinetic energy of the air flowing through the turbine.[15]

Commercial utility-connected turbines deliver 75% to 80% of the Betz limit of power extractable from the wind, at rated operating speed.[16][17]

Which is 45% overall efficiency from wind power in compared to electricity out.

https://en.wikipedia.org/wiki/Wind_turbine#Efficiency

Others report that actual wind turbine electrical efficiency is closer to 25%.

Per: https://www.wind-watch.org/faq-output.php

Our analysis Supports the 25% efficiency value:

If you disagree with the 26 % Efficiency value we have selected for the wind systems,

then use your own values in the free renewable energy comparison calculator availabe from the tab above.

In the calculator method the average peak energy density of the wind is multiplied by the system's efficiency to get the kW / sq m value.

At left is a different method (the Polaris method) to get the kW/ per sq m value.

Since the polaris method is more practical than a number ins a sales brochure we have used this method to obtain the turbine efficiency value.

As follows, (working backwards):

1. if the W/ sq m is .26 then this would be 260 watts per sq. m.

2. as the Energy density is 1000 W / sq m then the system efficiency is =

(260/1000)*100 = 26 % Efficiency.

Which is very close to but larger than the value reported by wind-watch.org.

A clean explanation of wind power density is at:

http://www.iowaenergycenter.org/wind-energy-manual/wind-and-wind-power/wind-speed-and-power/

Wind power is a measure of the energy available in the wind. It is a function of the cube (third power) of the wind speed. If the wind speed is doubled, power in the wind increases by a factor of eight.

The amount of power available in the wind is determined by the equation w = 1/2 r A v3 where w is power, r is air density, A is the rotor area, and v is the wind speed. This equation states that the power is equal to one-half, times the air density, times the rotor area, times the cube of the wind speed.

This wind power equation (simplified) is: w = 0.625 A v3

where w is power in watts, and A is the cross-sectional area in square meters swept out by the wind turbine blades, and v is the wind speed in meters per second

NOTE: - a wind speed of 1 m/sec. = 2.24 miles per hour.

- 1 sq. m = 10.76 sq. ft

Because of the wind’s normal variability, and the effect of this variability on the cube of the wind speed, the power equation should only be used for instantaneous or hourly wind speeds and not for long-term averages. To illustrate why, consider two places where the average speed is 15 mph. At the first location the wind always blows at 15 mph, giving a power density of 189 W/m2. At the second site the speed fluctuates. The wind is at 10 mph half the time (power density = 56 W/m2), and at 20 mph the other half (power density = 448 W/m2). The mean power density here is (56 W/m2 x 1/2) + (448 W/m2 x 1/2) or 252 W/m2. At both locations the mean speed is exactly 15 mph, but there is 33% more power at the site with varying speeds. - See more at: http://www.iowaenergycenter.org/wind-energy-manual/wind-and-wind-power/wind-speed-and-power/#sthash.AZnvFtWM.dpuf

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