A SIMPLE CALCULATION OF A WIND TURBINE ROTOR
Ricardo A. Bastianon
Wind Energy and Fluid Dynamics Consultant
This paper presents a simple way to calculate the rotor blade shape of an horizontal
wind turbine designed to generate electrical energy.
The resulting rotor is rather close to the one capable of capturing the maximum energy
available in the wind and on the other hand its calculation is extremely simple.
The electrical power Pe that can be generated by a wind turbine is:
Cp = Power coefficient of the rotor (for a good rotor Cp = 0.40)
ηg = electric generator efficiency (for a good generator ηg = 0.90. If the generator comes
from the automotive industry ηg = 0.50)
ηt = transmission efficiency. If the turbine has a speed multiplier: ηt = 0.90 for gearbox,
ηt = 0.85 for chains and for belt ηt = 0.8. If we have direct transmission ηt = 1).
ρ = 1,225 kg/m3 = air density at sea level.
V = wind velocity for which the wind turbine generates the electric power Pe.
V = 9 m /sec for reasonable wind area. V = 11 m /sec for strong wind regions.
= rotor swept area. D = rotor diameter.
Where D is the wind turbine rotor diameter capable of generating the electrical power
Pe when facing a wind speed V.
We assume that the tangential velocity of the rotor blade tip is approximately
60 m / sec.
Where ω is the rotor angular velocity and
is the rotor radius.
The revolutions per minute is
and we defi