The Art of the Helicopter John Watkinson - Karatunov.net

Introduction to helicopter dynamics 75
proportional to the square of the induced velocity. Thus the power saved in an area of
reduced thrust does not compensate for the extra power needed in an area of increased
thrust because of the square law. It follows that the minimum power is required when
the thrust per unit area is constant.
Helicopter flight is dependent on a pressure difference across the rotor disc that
disturbs the air. Such pressure disturbances travel at the speed of sound and can thus
easily travel long distances from the helicopter. It should be clear that a helicopter
in flight is associated with the induced movement of a significant air mass. Such a
moving mass cannot change its velocity in an instant. Consequently a rapid change of
blade pitch does not result in an immediate change of inflow velocity. This will result
in an angle of attack initially higher than in the steady state and this may result in
a thrust overshoot. The same effect is observed in sailing vessels where there is a lag
between sheeting the sails and a change in sail reaction. The phenomenon is known as
dynamic inflow and is a macroscopic version of the dynamic overshoot phenomenon of
Figure 3.5. The inertia of the associated air mass will also have effects in translational
flight as will be seen in section 3.21.
3.10 Blade element theory
The actuator concept is useful, but it does not consider a number of real world factors,
not least profile drag. Blade element theory takes this into account and allows a more
accurate result to be obtained. In the hover the forward speed of some point on a blade
is proportional to the radius of that point. It is possible to analyse the performance
of a rotor by considering it to be made of small elements where the conditions over
each element are substantially constant. The overall result is obtained by adding up
the contribution from each element.
At each blade element, the inflow must be known so that the RAFand the effective
airspeed can be calculated. The characteristics of the blade section employed at that
element must be consulted to find the resultant aerodynamic force on the element that
will be resolved into an element of rotor thrust and an element of drag. All of the axial
thrusts from the elements can simply be added to find the total thrust. The drag of each
element is multiplied by the radius of the element concerned to obtain an element of
rotor torque. These elements are then added to obtain the total rotor torque.
Blade element analysis is only as accurate as the assumptions made about the inflow.
Actuator theory gives some idea about the inflow, but in a real rotor the inflow at the
tips and the blade roots will be non-ideal. More accurate results require the use of
vortex theory to take into consideration the conditions at the blade root and tip.
3.11 Disc loading
The thrust production mechanism in the helicopter creates a pressure difference, which
causes the air to accelerate downwards. To maintain height, the rotor then has to climb
up through the air at the same speed as the air is coming down. Work is being done
on the air and the power is the product of the weight of the helicopter and the induced
velocity. It follows that the power needed to hover can be minimized by reducing
the induced velocity. This can be achieved by reducing the disc loading. This is the
helicopter’s equivalent of span loading in a fixed-wing aircraft. Where power is limited,
as in piston engine helicopters, a low disc loading will be needed to extract more lift