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Homework Help: Wind turbine: Optimum pitch angle changes at different wind speeds

  1. Oct 16, 2014 #1
    1. The problem statement, all variables and given/known data
    As part of a school project, I'm investigating the optimum blade pitch angle for a simple 6-blade wind turbine, powered by the air flow from a desk fan. I have taken power output measurements using angles in 5° intervals from 0° to 30° and found the optimum to be 20° in 5 different wind speeds. No surprises there.

    However, at the lower wind speeds, the turbine was more efficient at higher pitch angles (ie. 25° outperformed 15°) and at higher wind speeds, the shallower angles were better. I cannot find a way to explain this short of putting it down to experimental error, as it seems to me that the opposite should be true due to stalling etc. The only reason I am reluctant to dismiss it as such is that the correlation occurred consistently through 5 different wind speeds (one of which in the middle was nearer symmetrical, showing 15° and 25° to be almost equal).

    Is this result significant in any way, or just an outcome of experimental uncertainty?

    Averaging the data and graphing, two wind speed examples:


    Red line - 15°
    Green line - 25°

    2. Relevant equations

    3. The attempt at a solution
    Much googling to no avail...

    Attached Files:

  2. jcsd
  3. Oct 16, 2014 #2


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    The key angle for the elementary aerodynamic force developed by a blade element of an airfoil is not the pitch, but the angle of attack. It is a function of the pitch, the angular velocity, the wind velocity and the twist of the blade at a given station. Every elementary force (for a very small station of the blade) will result in an elementary torque. The sum of all those elementary torques along the blade will result in a total torque per blade. That, multiplied by the angular velocity, would give you the theoretical power per blade.

    I am sorry, but I believe that too much simplification will lead to false results... Wind turbines (and propellers, their near relatives) are very complex things...
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