Wind Power Calculations

http://www.energy.iastate.edu/WindManual/Text-Power.html

- The amount of power available in the wind is determined by the equation

w = ½ r A v³

w = power

r = air density

A = rotor area = 3.14*(2.6502 m) ² = 22.0658 m ²

v = wind speed (from graph, in Gary = 4.8872 m/s)

http://www.usatoday.com/weather/basics/density-calculations.htm

r = P/(T*R)

r = air density

P = pressure in Pascals (1 mb=100 Pa) (no data from website, but S.P. = 101325 Pa)

T = temperature in Kelvin (from graph, about 283 K in Gary, but this varied)

R = gas constant = 287

Example:

r = (101325 Pa)/(283K*287) = 1.2475 Kg/m³

Thus:

w = ½ *(1.2475 Kg/m³)*(22.0658 m ²)*(4.8872 m/s) ³ = 3213 Watts = 3.213 KW

- Wind power density (not to be confused with air density) is a term commonly used to describe the wind power available per unit area swept by the blades, or w/A.

Example: W.P.D. = 3213 W/ 22.0658 m ² = 145.6 w/ m ²

- Account for humidity. Water vapor in the air makes the air less dense, which means that on a humid day, the air won't be as dense as on a dry day. Our understanding air density text explains why this is so. Compared to the differences caused by pressure changes as weather systems move in, or at higher elevations, the changes caused by humidity are small. You could choose to ignore them. Or, you can calculate a figure called the "virtual temperature."

The formula for virtual temperature is as follows.

(1) Tv = Tk/[1-(E/P)*(1-0.622)]

Tv = virtual temperature, E= actual vapor pressure(mb), Tk= actual temperature in degrees Kelvin, P= barometric pressure(mb)

Note: To convert between Fahrenheit, Celsius and Kelvin, go to our temperature conversions page. This page has all the necessary formulas.

For example, suppose you have an actual temperature of 10 degrees Celsius (283 degrees Kelvin), a relative humidity of 50% and a barometric pressure of 1010 mb and you want to calculate virtual temperature.

First, you need to calculate the saturation vapor pressure(Es) using the following formula.

(2) Es=6.11*10.0**(7.5*Tc/(237.7+Tc))

Plugging in 10 degrees for Tc, you get Es=6.11*10**[(75)/(247.7)] = 6.11*10**[.3028] = 6.11*2 = 12.27 mb.

Note: You must use the temperature in degrees Celsius (Tc) in the Es formula above or it will not work.

Next, you use the relative humidity(RH) formula to calculate the actual vapor pressure(E).

(3) E=RH*Es/100

Plugging in 50 for RH and 12.27 for Es, you get E=50*12.27/100 = 613.47/100 = 6.13 mb.

Finally, you are ready to calculate virtual temperature.

Plugging in 6.13 for E, 1010 for P, and 283 degrees for Tk, you get Tv = 283/[1-(6.13/1010)*(1-0.622)] = 283/[1-(0.00607)*(0.378)] = 283/[1-(0.0023)] = 283/0.9977 = 283.65 degrees Kelvin = 10.65 degrees Celsius.