5 blade vs 11 blade design

[Adriaan Kragten]

The vibration of a 2-bladed rotor isn't caused by the difference in moment of inertia between the horizontal and vertical position of the blades. If the yawing angular velocity is constant, there is no moment required for acceleration around the tower axis so it doesn't matter if the moment of inertia is large or small. If the yawing angular velocity varies, there is a small vibration around the tower axis.

But the real vibration is caused by the variation of the gyroscopic moment which is also present for a constant yawing angular velocity. The direction of the gyroscopic moment is perpendicular to the plane of the rotor axis and the tower axis. The gyroscopic moment is zero for the blades in the horizontal position because the direction of the speed of a mass element doesn't vary for this position. The gyroscopic moment is maximal for the blade in the vertical postion because the direction of the speed varies maximal at this point. After each revolution the head has yawed a little. Even this little variation of the direction of the speed causes a high force on a mass element as the rotational speed is very high, especially at the blade tip.

[kitestrings]

I'd understood that tower shadow could also be a contributor, the cyclic loading and unloading (or less loading) of the downward position blade.  I could imagine that it might be more of a factor with a sizable mono-tube tower, or perhaps an SSV (free-standing, lattice braced), but I have nothing to point to that would support the theory.  Do you know if this is true?

[DamonHD]

I also had heard that the tower shadowing issue was significant for 2 (and 1) blade turbines.

Rgds

Damon

[Adriaan Kragten]

The effect of tower shadow on vibration is especially important for rotors turning behind the tower but it is also present for 3-bladed rotors as every time a blade passes the shadow, a push on the blade will be felt. For rotors turning before the tower the effect is limited for a lattice tower with slender poles if the distance in between the blades and the tower is chosen large enough. But traditional Dutch windmills with a big stone tower suffer from the reduction of the wind speed in front of the tower and the blade angle is chosen negative to prevent that the sail flutters when the wing passes the tower.

The gyroscopic moment in the blade root varies for every single blade independent of the number of blades. However, it can be proven that the gyroscopic moment in the rotor shaft is not fluctuating for rotors with three or more blades. So you feel no vibration in the tower for a rotor with three or more blades but every single blade is bending frontwards and backwards during one revolution if the head is yawing.

The vibration in the rotor shaft for a 2-bladed rotor can be reduced strongly if the connection of the blade to the hub is made elastic. For some years I have tested the VIRYA-4.2 windmill with two wooden blades which were connected to the hub by a thin steel strip (size 8 * 120 * 1000 mm). The distance in between the blade tip and the tower must be rather large other wise a blade may touch the tower during very strong wind gusts (which has happend for my rotor at a wind speed of about 25 m/s during a thunder storm). I have increased the distance by introducing a tilt angle of 5 degrees in between the rotor shaft and the horizon. The power is reduced only a little by a tilt angle of 5 degrees.