Wind Formula

How much power is in the wind?


    P = .5 * AD * (D^2*.7854) * V^3

Where:  P = power in watts
            AD = air density ( typically 1.22 at sea level )
            D = Diameter of prop ( in meters )
            V = Velocity of the wind ( in meters/sec )

So we could say in a 20mph (8.9 m/s) wind and a 6 ft dia ( 1.8 m) prop there is ...

    P = .5 * 1.22 * (1.8^2*.7854) * 8.9^3   or
    P= 1094 watts passing through the prop

Unfortunately we cant capture all of it and most blades range in the 20% to 40% range so we need to add this into our formula...

    P = .5 * 1.22 * (1.8^2*.7854) * 8.9^3 * .4
    P = 437 watts coming out of our blade at the shaft.  

Now there are some other losses we have to deal with...   The generator or alternator we are using isn't 100% efficient so we need to add this into the formula.  We can say that our blades are 40% efficient and our generator is 60% efficient so... Our overall efficiency would be ( .4 * .6 = .24 ) 24%.  So now we add that into the total and we get...

    P = .5 * 1.22 * (1.8^2*.7854) * 8.9^3 * .24
    P = 262 watts

This is the majority of the losses but there are others that we won't worry to much about at this point.  The formulas above will give you a close general idea of what your machine might produce. 

Here are a few formula's from Hugh Piggott's book "Wind Power workshop".  He has allowed me to put them up on my site via email.  Again I strongly recomend his books for anyone getting into wind power.
If you know what your alternator/generator will do in watts, this one will help determine the size prop you will need to run it....

    D = (P / ( Cp * rho / 2 * Pi / 4 * V^3 )) ^ 0.5
    Where      D = Diameter of prop in meters
                    P = power in watts
                    Cp = overall efficiency ( typically .15 to .20)
                    rho = air density ( 1.22 at sea level )
                    V = velocity of the wind in meters/second

If you have a prop you plan to use, this one will determine the power output you can expect...


    P = Cp * rho / 2 * Pi /4 * D^2 * V^3

To find the TSR ( tip speed ratio ) of a prop at a given output...


    TSR = rpm * Pi * D / 60 / V
   example:  say you find a generator that can produce 500 watts at 1000 rpm...
    TSR = 1000 * 3.14 * 2 / 60 / 10
    TSR = 10.46

Since 10.5 would be fairly tricky to obtain we can try others.  To calculate the rpm at a given TSR...


    rpm = 60 * V * tsr / ( Pi * D )
    example:  with a tsr = 6 we would get...
    rpm = 60 * 10 * 6 / ( Pi * 2)
    rpm = 573 rpm