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

1. Oct 16, 2014

### trc97

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

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2. Oct 16, 2014

### NTW

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...