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Homework Help: Calculate torque for a wind turbine

  1. Apr 24, 2012 #1
    density=1.2041 kg/m^3
    Power 1.65 MW
    Rotor radius (blade length) = 37m
    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!
  2. jcsd
  3. Apr 25, 2012 #2


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    You can always use Power = Torque*angular velocity.
  4. Apr 26, 2012 #3
    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)
  5. Apr 26, 2012 #4
    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;

    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 :)
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