The Art of the Helicopter John Watkinson - Karatunov.net

Introduction to helicopter dynamics 65
Clearly such a wing will be creating a lot of drag at the small angles of attack needed
at high speeds. For high speed operation, the camber will need to be very small, but
this kind of wing will be inefficient if used at large angles of attack at low speed, hence
the use of flaps on fixed-wing aircraft. With a cambered section, air is still accelerated
downwards leaving the section even when the angle of attack is zero, and so a slight
negative angle of attack is necessary to obtain the zero lift condition.
Figure 3.3(b) shows a symmetrical section in which the camber line and the chord line
are one and the same. A symmetrical section is a streamlined flat plate. The curvature
prevents separation over the leading edge. At zero angle of attack, the airflow is also
symmetrical, and no net air reaction results. There is thus no induced drag, only profile
drag. If the angle of attack is made positive, air is accelerated down, and the reaction is
upwards. If the angle of attack is made negative, air is accelerated up and the reaction
is downwards.
The reader is cautioned against explanations of the origin of lift based on Bernouilli’s
theorem. Bernouilli made it quite clear that his theorem relates to conservation of
energy in flowing air such that the sum of the static and dynamic pressures remains
constant. Bernouilli’s theorem only applies if no energy is put into the air. However, a
wing or a rotor blade is an actuator that is exchanging energy with the air. This is clear
from the presence of induced drag. When energy is put into the airflow, Bernouilli’s
theorem simply doesn’t apply and the explanations based on it are flawed and should
be disregarded.
3.2 The centre of pressure
The lift developed by the blades is distributed over the chord, but not uniformly. The
centre of pressure is where a single force would act producing the same effect as the
distributed lift. In real airfoil sections, the centre of pressure is ahead of the mid-chord
point. If the blade is made of a material with uniform density, the centre of pressure
will be ahead of the centre of mass and, as Figure 3.4(a) shows, a couple results. This
couple would tend to twist the blade and increase the angle of attack, making the lift
greater and increasing the twist further. In extreme cases the blade will flutter; a violent
condition that will usually destroy any structure suffering from it.
In aircraft, wings can usually be made rigid enough to prevent flutter, but this cannot
be done with the long thin blades of the helicopter. The solution universally adopted is
to construct the blade so that the mass centroid (see Chapter 2) of the blade is ahead of
Couple Couple
(a) (b)
Fig. 3.4 (a) If the centre of lift is ahead of the CM, lift tends to increase the angle of attack. (b) If the centre of
lift is behind the CM, lift tends to reduce the angle of attack: a stable condition.