# Calculate torque for a wind turbine

density=1.2041 kg/m^3
Power 1.65 MW
calculated swept area = 4,301 m^2
wind speed 12m/s

the rotor speed range is upto 20rpm

i want to calculate the torque but not quite sure how to go about it

Thanks for any help!

rock.freak667
Homework Helper
You can always use Power = Torque*angular velocity.

An important piece of information is that the velocity of a blade tip of a 3 blade rotor in a 12 m/s wind is about 60 m/s. This is because the tip-speed ratio equals velocity of blade tip/ velocity of wind. The tip-speed ratio for a 3 blade rotor is about 5, wind speed is 12 m/s.

You know the radius of the blade so you know the angular velocity, ω=V/r. Make sure ω
is less than 20 rpm.

As noted above power in the wind=τ*ω, the power in the wind is not 1.65 MW that is the rotor power you need to find the Power in the wind=rotor power/efficiency of turbine

You can find the efficiency of turbine(η) because rotor power=η*(.5*A*ρ*v^3)

η=rotor power/power in wind. η accounts for all the losses in generator, transmission etc.

Now you know power in the wind and ω so you can find Torque (τ)

Thanks a lot for the quick reply
I've done it this way:

We know the rotor is rated up to 20RPM hence so to change it to angular velocity we;
(20*2π)/60=2π/3

We also know P=τω 1.65MW= τ * 2π/3 τ=7.878×〖10〗^5

I've already done this before: (P=1.65mw)
Cp(η) = Rated power/Power = P/(½ρAv3) = 0.369 = 37%
(Power = ½ρAv3 = 4.47MW)

Again thanks a lot for the help :)