The Art of the Helicopter John Watkinson - Karatunov.net

90 The Art of the Helicopter
shaft to the boundary of the reverse flow region. Figure 3.22(d) shows the expression
for d graphically and it will be seen that the reverse flow area is circular and that its
diameter increases with speed. Instantaneously the rotor is turning with respect to the
outer edge of the reverse flow region. The ratio of forward speed to tip speed is known
as the advance ratio µ which is the same as the ratio of the diameter of the reverse flow
region to the blade radius.
The retreating blade suffers reverse flow near the root; a small downward force may
be experienced because the retreating blade effectively has a negative angle of attack
due to flow reversal. Here is another reason for root cut-out, to reduce the amount of
useless reverse-flowed blade. However, as the area is proportional to the square of the
diameter, the amount of disc area lost to the reverse flow region is small. For example,
at µ = 0.4, the diameter of the reverse flow region is 0.2 of the rotor diameter but the
area lost is only 4%.
Owing to the huge difference between the airspeeds, if nothing were done, the advancing
blade would produce more lift and the retreating blade less. This would apply to
the rotor a roll couple toward the retreating side. The gyroscopic action of the rotor
would result in a response delayed by 90 ◦ of rotation corresponding to a rearward pitch
effect. This rearward couple is colloquially known as ‘flapback’ and it tends to reduce
the forward tilt of the machine and consequently reduces the forward component of
the rotor thrust, slowing the machine down.
Thus sustained forward flight requires a continuous application of forward cyclic
control that reduces the angle of attack of the advancing blade and increases that of
the retreating blade in order to balance the lift moments on the two sides of the rotor.
In cruise the amount of cyclic pitch applied may be of the order of 5 ◦ . Flapback results
in speed stability because it automatically opposes the cyclic control.
The more forward cyclic is applied, the higher will be the forward speed. Thus in
translational flight the fore-and-aft position of the cyclic stick primarily controls the
airspeed. If the airspeed is changed, the collective lever will need to be adjusted to
maintain height because tilting the rotor thrust vector alters its vertical component.
In forward flight the rotor has access to a greater mass of air. Thus the same momentum
increase and the same thrust can be obtained with a smaller induced velocity and
this reduces the power needed. Figure 3.23 shows that there is a minimum induced
power speed where the inflow velocity is the least.
3.21 Inflow and coning roll
In flight, there is a region of low pressure above the rotor and a region of high pressure
below. This pressure difference results in a tendency for air in the plane of the rotor
to move upwards. Figure 3.24(a) shows that this happens for some distance from the
edge of the disc. Simple inertia keeps the air moving upwards so that in translational
flight, the leading edge of the disc encounters upwash. The upwash ceases when the
downward impulse of the rotor cancels the upward momentum of the air mass.
In slow forward flight, Figure 3.24(b), the low pressure above the rotor has time to
bend the inflow increasingly downwards as it reaches the trailing edge of the disc. The
disc can be thought of as a low aspect ratio wing producing tip vortices which roll
inward at the top and down through the rear of the disc. The result is a reduction of
the angle of attack of the blade at the rear of the disc compared to that at the front.
The loss of lift at the rear of the disc is subject to the phase lag, or precession, of the
rotor and manifests itself as a roll to the advancing side, which is known as inflow roll.