The Art of the Helicopter John Watkinson - Karatunov.net

28 The Art of the Helicopter
2.6 Moments and couples
So far only forces that all conveniently act at one point have been considered. In reality
forces can also act at a distance from a point. When a force does not pass through a point
the result is called a moment with respect to that point. The moment is equal to the force
multiplied by the distance at right angles to the force, as shown in Figure 2.7. Applying
a moment to an object will cause it to turn and accelerate along simultaneously.
If two equal and opposite forces act a distance apart, the result is a pure turning
effort known as a couple or as torque. A helicopter engine produces a couple at the
output shaft in order to drive the blades. The reaction to this couple attempts to twist
the engine against its mountings. The transmission conveys the engine power to the
rotor shaft. The rotor shaft exerts a couple on the rotor head in order to drive the
blades round. The torque reaction to this couple attempts to rotate the transmission,
and the helicopter hanging from it, the opposite way. One of the jobs of the designer is
to find a means to prevent this rotation.
When a body is supported at the CM, it will remain in the initial attitude. Figure 2.8
shows that if the support is not at the CM, the body will rotate. It may swing from side
to side, but eventually will come to rest with the CM below the point of support.
It is often assumed that the CM of the helicopter is below the rotor shaft, but this
may not be the case. Figure 2.9 shows how a helicopter hovers with the CM displaced.
The CM tends to hang directly beneath the rotor head, and the pilot has to displace
the cyclic control in order to keep the disc horizontal so the rotor thrust vector is
straight up. Clearly if the CM is a long way from the mast, a substantial amount of
cyclic control will be used up to compensate, and there may not be enough left to
control the machine. In addition the bearings and joints in the rotor head find it harder
to transmit power when the shaft and the disc are not aligned.
Fig. 2.7 (a) A moment about a point is the product of the force and the distance. (b) A pure couple results from
two equal and opposite forces that do not coincide.