Small scale Wind Power: A calculation
Power Output =>
where P = power in watts,
α = an efficiency factor determined by the design of the turbine,
ρ = mass density of air,
r = radius of the wind turbine,
v = velocity of the air
As an example given on wikipedia (http://en.wikipedia.org/wiki/Wind_turbine), for the following typical values,
α = 0.59 or less (Betz' law)
ρ = 1.225 kilograms per cubic metre at 15 °C
r = 100 metre (diameter)
v = 28.8 km/h
the power output P can be around 1.5 MW
Now in typical Bnagalore conditions, the values for a domestic turbine are
α = 0.59 or less (Betz' law) (same)
ρ = 1.204 kilograms per cubic metre at 20°C (calculations done at 1.165 kilograms per cubic metre at 30 °C )
r = 1 metre
v = 10 km/h (source google weather)
and the power is = (1.5 MW) * (ρ2/ρ1) * (r2/r1)2 * (v2/v1)3
= (1.5MW) * (1.165) * (1/100)2 * (10/28.8)3
= 6.4 Watts approx
Also, the efficiency factor can go further down, and at an efficiency of say 30% we get almost 3 watt.
So to make it feasible - giving almost 60 Watt power, which is 20 times, either the diameter should be increased to almost upto 4.5 ()times - upto 4.5 metre or may be expect the wind to blow almost 2.7 (cube root of 20) times faster (at maybe 30 Km/hr), or a combination of both.
The first proposition is not actually good for domestic users with little or no roof space. The second can work in lot of coastal areas. The third can be worked out :)
