In reading some posts recently, i realized a lot of people are having problems finding some of the mathematical equations that are related to wind power, so I figured it may be a good idea to provide some and maybe we can make a good FAQ with it all, so the resource is easily available. I'm sure there are many more that could be added, so feel free to chime in!
A simple equation for the Power in the Wind:
P = 1/2 ρ Π r2 V3
ρ = Density of the Air
r = Radius of your swept area
V = Wind Velocity
To find the co-efficient of power at a given
wind speed, all you have to do is divide the electricity produced by the total
energy available in the wind at that speed.
Cp = Electricity produced by the wind generator/Total energy available from wind
Betz Limit: 59.3%
Albert Betz calculated that no wind turbine could convert more than 59.3% of
the kinetic energy of the wind into mechanical energy. This is the theoretical
maximum coefficient of power for any wind generator. In reality most wind
generators fall into the 35%-45% range.
How do i figure my swept area?
Area=Πr2
Π = 3.14159 (pi)
r = radius of the circle. This is equal to the length of one of your blades.
(and you thought pie were round) {(couldn't resist that old chestnut)}
Tip Speed Ratio is critical to windmill designs; what is it?
TSR (λ) = Tip Speed Of a blade/Wind Speed
Ok so how do I figure out what my tip speed is?
Measure the rotor radius (length of one blade)
Speed = distance divided by time.
The distance traveled is the circumference (2Πr).
Speed: V The blades travel one circumference (2Πr) in a rotation time of T(seconds).
You will, of course need some way to ACCURATELY measure the RPM (revolutions per minute)
AND your windspeed.
Now for maximum theoretical power for tip speed ratio.
λ (maximum power) 4Πn
(n = number of blades)
Some handy conversion programs:
For Linux: http://www.unihedron.com/projects/gonvert/
or: http://www.netmeister.org/apps/kunit/
For Windows: http://joshmadison.com/article/convert-for-windows
