The Art of the Helicopter John Watkinson - Karatunov.net

80 The Art of the Helicopter
upwards, the acceleration has a rearward component. The reaction to this is forward,
so the rotor can be driven against profile drag and transmission losses. At a suitable
setting of the collective pitch, the overall reaction on the blades is brought to the vertical
and so they will continue to turn at the same speed and provide lift. Note that in order
to produce lift the blade must have a positive angle of attack with respect to RAFand
so it is common for the blade to have positive pitch in autorotation.
The machine is moving steadily downwards using potential energy to overcome profile
drag. In fact the rotor is taking momentum from the air so that induced power
becomes negative and provides the profile power needed. The strict definition of autorotation
is the requirement for zero shaft torque. Where a rotor actually delivers shaft
power it is said to be windmilling or in the windmill brake state. A real helicopter
in autorotation is technically windmilling because the shaft torque is not zero. In the
absence of the engine, some shaft torque is needed to turn the tail rotor and any other
important items such as hydraulic pumps.
The speed of a blade element is proportional to radius. A further complication is that
most rotor blades have twist to improve the hover figure of merit, but in autorotation
the inflow is reversed and the twist is the opposite of what is needed. It can be seen
that on moving from tip to hub, the RAFdecreases in speed but the angle of attack
increases. As a result the central part of the blade, shown at Figure 3.13(a) is being
driven by the inflow and is windmilling. Figure 3.13(b) shows that the tips have a small
angle of attack and high airspeed. Profile drag dominates and L/D is poor, with the
total blade reaction being behind the vertical. This area of the blade is producing lift
and induced drag as if it was in the power-on condition. Figure 3.13(c) shows that
the innermost parts of the blades are stalled as they have a high angle of attack and
a low airspeed. The power needed to drive the tips and the inner parts of the blade
comes from the windmilling of the centre parts. Only a small section of each blade at
the boundary between the driven and driving regions is technically autorotating with
a vertical total blade reaction. Thus what is meant in practice by autorotation is that
the entire rotor has zero net torque. The entire rotor can also be considered to have an
L/D ratio and in autorotation the slowest rate of descent will be where this is used.
In practice the loss of performance in autorotation due to twisted blades is surprisingly
small. One reason for this is that the profile drag is determined only by the rotor
speed and is largely unaffected by local angle of attack. Another is that real blades
don’t have anything like ideal taper and also have root cut-out so the stalled inner part
of the rotor doesn’t absorb as much power as might be expected.
In autorotation there is still a pressure step across the rotor, but the inflow is now
from below. Figure 3.13(d) shows that as the rotor is taking momentum from the air,
the slipstream from the rotor is slower than the inflow. The pressure gradient along a
streamline is rising and so the wake expands.
In autorotation the best rate of descent will be where the entire rotor (not a blade
section) operates at L/Dmax.. The highest RRPM will also be obtained at L/Dmax.,giving
the greatest stored energy for landing. Figure 3.14 shows an autorotation diagram
in which the vertical axis is drag over lift and the horizontal axis is angle of attack α.
It will be seen from the figure that, at an idealized blade radius, the ratio of drag to lift
determines the angle ϕ which must also be the angle of RAFif the blade reaction is to be
vertical. If the pitch angle is θ, then ϕ = α−θ. The function α−θ is shown on the graph
to be a straight sloping line. The lowest profile drag will be at the bottom of the drag
‘bucket’ and the pitch angle to achieve that is where the line of α−θ intersects the α axis.
Most conventional helicopters will be rigged so that the minimum pitch stop on the
collective lever is at about this value. Thus operation in autorotation is in the region to
the right of the intersection, but not so far as the position of the dotted line where rotor