The Art of the Helicopter John Watkinson - Karatunov.net

36 The Art of the Helicopter
Fig. 2.15 Wavelength is defined as the distance between two points at the same place on adjacent cycles.
Wavelength is inversely proportional to frequency.
Because sound travels at a finite speed, the fixed observer at some distance from the
source will experience the disturbance at some later time. In the case of a transient, the
observer will detect a single replica of the original as it passes at the speed of sound.
In the case of the tuning fork, a periodic sound source, the pressure peaks and dips
follow one another away from the source at the speed of sound. For a given rate of
vibration of the source, a given peak will have propagated a constant distance before
the next peak occurs. This distance is called the wavelength lambda. Figure 2.15 shows
that wavelength is defined as the distance between any two identical points on the
whole cycle. If the source vibrates faster, successive peaks get closer together and the
wavelength gets shorter. The wavelength is inversely proportional to the frequency.
It is easy to remember that the wavelength of 1000 Hz is a foot (about 30 cm) at sea
level.
2.11 The mechanics ofoscillation
By definition helicopters contain a lot of rotating parts and for a proper understanding
of their characteristics, knowledge of the mechanics of rotation is essential. In physics,
the engineering quantity of RPM is not used. Instead the unit of angular velocity is
radians per second and the symbol used is ω. Figure 2.16 shows that a radian is a
natural unit of angle which is the angle subtended by unit circumference at unit radius.
As the circumference is given by 2π times the radius, then there will be 2π radians in
one revolution, such that one radian is about 57 ◦ .
Figure 2.17 shows a constant speed rotation viewed along the axis so that the motion
is circular. Imagine, however, the view from one side in the plane of the rotation. From a
distance, only a vertical oscillation will be observed and if the position is plotted against
time the resultant waveform will be a sine wave. The sine wave is unique because it
contains only a single frequency. All other waveforms contain more than one frequency.
Imagine a second viewer who is at right angles to the first viewer. He will observe
the same waveform, but at a different time. The displacement is given by multiplying
the radius by the cosine of the phase angle. When plotted on the same graph, the two
waveforms are phase shifted with respect to one another. In this case the phase shift is
90 ◦ and the two waveforms are said to be in quadrature. Incidentally the motions on
each side of a steam locomotive are in quadrature so that it can always get started (the
term used is quartering). Note that the phase angle of a signal is constantly changing
with time whereas the phase shift between two signals can be constant. It is important
that these two are not confused. In a three-bladed rotor, the motion of each blade