The Art of the Helicopter John Watkinson - Karatunov.net

Technical background 39
force would be complicated were it not for the fact that the blade mass appears for this
purpose to be concentrated at the radius of gyration. The figures for root tension are
quite impressive. In a typical model helicopter a tension of 500 N is normal. In a full
size helicopter 100 000 N is not unusual.
When a body of arbitrary shape is rotated, if the centre of mass is not on the axis
of rotation, forces must come from the bearings to accelerate the CM into a circular
path. This is the origin of vibration due to imbalance. In space no such forces can be
applied and the only way the rotation can occur is for the CM and the axis to align.
Thus rotating devices try to achieve such alignment and vibration results when bearings
prevent it.
Figure 2.19(a) shows that a simple balancing process consists of supporting the
assembly with the axis horizontal. If the CM does not coincide, gravity will turn the
assembly until the CM is beneath. Balance weights may be added until the assembly
will stay where it is left. In this condition the assembly is statically balanced, with no net
moments, but it may still vibrate when rotated. Figure 2.19(b) shows that a statically
balanced assembly can result with masses at different places along the axis of rotation.
This will be imbalanced when rotating.
The statically balanced body in Figure 2.19(b) will try to rotate along its mass
centroid. To eliminate vibration, the body must be dynamically balanced. This means
Fig. 2.19 Static balance (a) can be achieved when no overall moment results about the axis of rotation. (b) A
statically balanced system that will vibrate when rotated as it is not dynamically balanced and will tend to
turn about its mass centroid. (c) In model helicopters, dynamic balance is achieved by adding a small piece of
covering material. The mass needed is equal to the difference in mass of the two blades, and the position is
such that the blades balance in the same place.