The Art of the Helicopter John Watkinson - Karatunov.net

Fig. 2.16 The definition of a radian. See text.
Technical background 37
Fig. 2.17 A sine wave is one component of a rotation. When a rotation is viewed from two places at right
angles, one will see a sine wave and the other will see a cosine wave. The constant phase shift between sine
and cosine is 90 ◦ and should not be confused with the time variant phase angle due to the rotation.
would be phase shifted by 120 ◦ from that of the next blade, whereas the phase angle of
a blade changes continuously as it rotates. In helicopters the phase angle is taken to be
the angle between the blade and a line drawn directly aft from the rotor hub.
Geometrically it is possible to calculate the height or displacement of the sine wave in
Figure 2.17 because it is given by the radius multiplied by the sine of the phase angle. The
phase angle is obtained by multiplying the angular velocity ω by the time t. Frequency
f is measured in rotations per second or Hertz (Hz). Thus the phase angle at a time t
is given by ωt or 2πft.
A rotating object is not in static equilibrium even if the RPM is constant. With the
exception of those elements of the object which are on the axis of rotation, all other
elements are in a constant state of acceleration because their velocity is constantly
changing as they follow a curved path. Figure 2.18(a) shows that if an arbitrary increment
of time is taken, the velocity at the beginning is different from that at the end
and a small resultant vector is necessary to close the triangle. As the time increment