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Wind Power Density                              Assumptions

 

A clear 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 equation for wind power is:  wP = 1/2 r A v3  where wP is wind power, r is air density, A is the rotor area, and v is the wind speed

 

The simplified version of this equations is: wP = 0.625 A v3   where wP 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

 

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.

Wind Power Density for Calculator Example


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

Wind Energy Conversion Efficiency     Assumptions


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

 

Wind Turbine Efficiency for this Calculator Example is     26% efficiency

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

then use your own values in the free renewable energy comparison calculator available on the tab above.

 

Using the above actual Polaris Wind Turbine data and working backwards we see:

 

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

2. if  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.

 

Note, the .26 on the chart above and the value of 26% efficiency is a conincidence and only happens when the energy density is 1000 w per sq. m.

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