I would apprreciate if you can derive the formula for instantaneous and the average wind power?

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  1. lonelyspirit says:

    Your question is quite vague, however, I searched the answer in accordance with my understanding of fluid mechanic and aerodynamics.

    The wind average velocity is usually taken to be 12 miles an hour, but if you plan to build your rotor to generate power, then you should try to measure the average wind velocity at that area using certain probe.

    The formula for wind power 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 is the formula you are looking for. A simplified example on how to calculate your wind power is shown here below:

    Air density is a variable factor and depends on elevation, temperature and pressure. Also upon the weather fronts.
    The weather front is considered too small to effect the electrical power output

    So the formula for air density may be expressed as:
    p = (1.325 x P) / T where T is the temperature in Fahrenheit + 459.69 and P is the pressure in inches of Mercury adjusted for elevation.

    Air density can be used to reflect the typical average air temperature (59°F) adjusted to sea level.

    For average wind power, use the formula with wind velocity is equal 12 miles per hour, For instantaneous wind power formula use the wind velocity to be as calculated in the area where the rotor is errected.

    The power equation then is simplified as follows:
    w = 0.0052 A v3
    where w is power in watts, and A is the cross-sectional area in square feet swept out by the wind turbine blades, and v is the wind speed in miles per hour.

    Swept Rotor Area = A = (pi) r2 where r is the rotor radius (half the diameter, or the distance from the hub to a blade tip). The equation states that the swept rotor area, A, is equal to (pi) or 3.14 times the square of the rotor radius.

    Assume a wind speed of 15 mph, standard air density, and a rotor radius of 10 feet. The rotor area (A) is equal to 3.14 times (10 ft.)2, or 314 square ft. Using the appropriate simplified power equation (English units), the wind power is:

    w = 0.0052 A v3
    w = 0.0052 (314 sq. ft.) (15 mph)3
    w = 0.0052 (314) (3375)
    w = 5,511 watts
    w = 5.511 kilowatts

    Hope you are satisfied!

    For details on how to derive the formula, the following site will provide detailed assistance. The information provided herein is extracted from that site!

    http://www.energy.iastate.edu/renewable/wind/wem/wem-08_power.html

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Erik

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I am about to be 50 and all my life I have been interested in technical things. Not sure if the special interest for the wind, and how to use the wind, started when I as a 5 year old boy and got my first sail dinghy.

Anyway, wind power and to build my own wind generator was a dream for several years. I studied many websites and also bought many courses before I finally built my own windmill. This site is about that journey and you will also find some more general articles about wind power.

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