The Art of the Helicopter John Watkinson - Karatunov.net

Introduction to helicopter dynamics 73
Fig. 3.10 The blade reaction is usefully resolved into components both in and orthogonal to the tip path plane.
These allow the rotor thrust and torque to be derived. In the presence of inflow, the angle of attack is the amount
by which the pitch angle exceeds the angle of the relative airflow.
just changes the collective pitch and the system computes the engine power for itself.
Correlators will be described in Chapter 6.
3.9 The rotor as an actuator
Without considering constructional details, it is possible to conceive of an ideal hovering
rotor as an actuator disc that somehow accelerates air downwards over a circular
region and develops thrust from the reaction. In this case the operation of an ideal
rotor can be analysed theoretically from the change of momentum of the air passing
through. The concept of an ideal rotor is useful because it can act as a benchmark with
which to compare real designs. Clearly the performance of the ideal rotor can only be
approached, but never exceeded.
Figure 3.11(a) shows the actuator concept which makes some simplifying assumptions.
One of these is that the air is somehow constrained to flow only within the tapering
column shown, known as a stream tube, and doesn’t mix with the surrounding air. The
mass of air passing any horizontal plane in the column per unit time must be constant.
The actuator causes a pressure difference to exist across itself. This pressure must be
given by the thrust divided by the disc area. A further assumption is that this pressure
is uniform. The pressure difference across the actuator can only be sustained locally.
Figure 3.11(b) shows that at a distance, the pressure must be the same as static pressure.
To allow the pressure difference across the actuator, the pressure must have a falling
gradient along the streamlines except at the actuator itself.
Bernouilli’s theorem can be used to predict what happens along a stream tube.
Bernouilli’s theorem is simply another example of conservation of energy. Air has
a static pressure and a dynamic pressure due to its motion. Bernouilli’s theorem states
that the sum of the two, known as the head, remains constant. As a result when static
pressure falls, the dynamic pressure must increase to compensate. As the density doesn’t
change significantly, the velocity must increase. Clearly Bernouilli’s theorem does not
hold across the actuator, as energy is put into the air there.
Except for the pressure step at the actuator, the air in the stream tube experiences a
falling pressure gradient which causes the stream to accelerate and contract. This is the
phenomenon of wake contraction seen in propellers and rotors. Thus the velocity with