The Art of the Helicopter John Watkinson - Karatunov.net

40 The Art of the Helicopter
that weights are added at various places along the axis to bring the CM of the slices
onto the axis. When balancing car wheels, note that weights may be fitted both to the
inner and outer rims to achieve this.
In the case of a helicopter rotor, the blades will be in the same plane and so the effects
due to Figure 2.19(b) will be small. However, a statically balanced rotor could still be
achieved if one blade were heavier than the other, if its CM were nearer the shaft. Thus
to dynamically balance a rotor, it is necessary that all of the blades should have exactly
the same mass, and the same radius of gyration. This means that the distribution
of mass along and across each blade should be identical and the CM should be at the
same point in three axes. In full size rotor blades, weight pockets are provided at various
places to allow these conditions to be met.
In model helicopters dynamic balancing is just as important, but a simplified
approach can be used. Figure 2.19(c) shows that the blades must be carefully weighed,
and a piece of covering material is cut to have exactly the same mass as the difference
in masses of the blades. The blades are assembled to the balanced rotor head, and
the covering material is applied to the lighter blade at a point where static balance is
achieved. It will then be found that the two blades have their CM in the same place and
so the rotor will be dynamically balanced. The same result will be obtained if the covering
is moved until both blades balance in the same place. In full-size helicopters
the leading edge of the blade may be protected with a replaceable plastic film. If
part of this comes off or the film is not fitted identically to each blade, vibration
may result.
2.12 The mechanics ofrotation
Figure 2.20(a) shows a steady rotation which could be a mass tethered by a string.
Tension in the string causes an inward force that accelerates the mass into a circular
path. The tension can be described as a rotating vector. When viewed from the side,
the displacement about the vertical axis appears sinusoidal. The vertical component
of the tension is also sinusoidal, and out of phase with the displacement. As the two
parameters have the same waveform, they must be proportional. In other words the
restoring force acting on the mass is proportional to the displacement.
Fig. 2.20 (a) A tethered mass is moving in a circle. If the component of this motion in one axis only is resolved,
the motion will be found to be the same as a mass supported on a spring, (b).