Recently I was contacted by a Duch guy who had a big 8 m diameter Chinese wind turbine which would not turn out of the wind. The reason was that the eccentricity was much too small for the given rotor diameter and the influence of the so called selforientating moment was therefore too large if compared to the moment caused by the rotor thrust.
The selforientating moment is not well known by designers of wind turbines with fast running rotors. I did some measurements in the wind tunnel very long ago. The selforientating moment can be made dimensionless and becomes Cso in the same way as it is also done for the torque coefficient Cq (see chapter 6, KD 35).
The selforientating moment is caused by the expanding wake. Lets take a 2-bladed rotor which is streamed under a yaw angle delta. One blade is pointing forwards and one blade is pointing backwards. The forwards pointing blade is in the part of the expanding wake were the wind speed is a little higher than for the backwards pointing blade. The angle in between the forwards pointing blade and the wind direction will also be a bit larger than the angle in between the backwards pointing blade because the wind direction makes a small angle with the axis of the wake. This results in a slightly larger component of the wind speed perpendicular to the blade. These two effects make that the thrust on the forwards pointing blade is larger than that on the backwards pointing blade and this makes that the rotor wants to turn back perpendicular to the wind.
In my public report KD 409, "Development of an ecliptic safety system with a torsion spring" I give the dimensionsless moment coefficients of the rotor thrust, the side force on the rotor, the selforientating moment and the final rotor moment CMrotor of all three moments together if the eccentricity is 10 % of the rotor diameter. The selforientating moment is given in figure 4. It can be seen that it has a maximum at delta = 30°. The calculated values are given in table 1 and in figure 5. In figure 5 it can be seen that CMrotor is reduced substantially by the selforientating moment, even if a very large eccentricity of 10 % is chosen.
The eccentricity should be at least 5 % of the rotor diameter but the Chinese wind turbine had an eccentricity of only 1.375 % of the rotor diameter. For this very small eccentricity, the self orientating moment becomes equal to the moment of the thrust already at a small yaw angle delta and this means that the rotor stays turning at this small yaw angle at high wind speeds. This is true for any safety system.
It is easier to describe the ecliptic safety system in KD 409 than the hinged side vane system used in my VIRYA windmills or the inclined hinge main vane system as used in the wind turbines of Hugh Piggott. This is because the hinge axis is in parallel to the tower axis and because for my description, both axis coincide. So the moment around the hinge axis becomes the same as around the tower axis. A torsion spring also gives a simple description of the spring moment. The fact that the vane arm makes an angle of 45° with the horizon makes that the vane blade is alway in the undisturbed wind speed. The makes it easier to calculate the aerodynamic force acting on the vane blade. All these simplifications make that the delta-V curve can be predicted (see chapter 8 figure 9). But if you study KD 409, you will see that still a lot of mathematics is needed to make the correct calculations.
