6 Why Are Turbine Blades in Groups of 3?
Why are turbine blades in groups of 3?
- A condition called chatter occurs when a turbine with two blades attempts to yaw.
- This condition occurs because the moment of inertia of a blade is significantly greater when it is horizontal than when it is vertical to the ground.
Moment of Inertia for the blade when horizontal
- The moment of a two-blade system when it is horizontal to the ground is given by
1/12 ML2 where M is the mass and L is the length of both blades.
- If an AW-1500 turbine had only two blades, the moment of inertia when the blades are horizontal would be 1/12(11,560 kg)(80.6 meters)2 = 6.26 x 106 kg-meters.
Moment of Inertia for the blade when vertical
- The moment of a two-blade system when it is perpendicular to the horizon is given by
- 1/2 Mr2 where M is the mass and r is the radius of one of the blades.
- If an AW-1500 turbine had only two blades, the moment of inertia when the blades are vertical would be 1/2(11,560 kg)(1 meter)2 = 5,780 kg-meters2.
- Note the 1-meter radius of a blade is an estimate and the blade is not a true cylinder, but this is a useful model.
The Difference in Moment of Inertia
- For a hypothetical 2 blade setup, the horizontal moment of inertia would be 6.26 x 10^6 kg-meters^2, and when vertical would be 5,780 kg-meters2.
- The horizontal moment is over 1,000 times greater than the vertical moment.
- This difference causes chatter
3 Blades to the rescue!
- For 3 blades, the moment of inertia is always the same since the x and y components of all the blades balance out each other at any point in its rotation.