The Art of the Helicopter John Watkinson - Karatunov.net

Introduction to helicopter dynamics 77
needed in the real helicopter where the actuator has the same diameter as the rotor.
This is the origin of the figure of merit.
3.13 Blade twist and taper
The forward velocity of the rotating blade increases linearly from zero at the shaft
to a maximum at the tip. This is not a good starting point from which to obtain
uniform inflow, but the rotor is the only practical approximation to an actuator disc that
anyone has devised. The figure of merit may be improved by twisting and tapering
the rotor blades. Figure 3.12(a) shows that in untwisted, untapered blades, the lift
will be produced increasingly toward the tips as a parabolic function, until tip loss
dominates.
Given the induced velocity is required to be uniform, it is easy to calculate the pitch
required at any radius to make the angle of attack constant along the blade so that
the whole blade operates at an efficient L/D ratio. However, in practice the induced
velocity will be a function of radius and such a twist will not be optimal. Twist that
takes account of induced velocity distribution is known as ideal twist. In fact ideal
twist is academic because the amount of twist would have to change as a function of
induced velocity and clearly it does not in any practical blade.
Ideal twist does not achieve uniform inflow, because of the reduced effectiveness of the
inner slow-moving parts of the blade. Tapering the blade as well as twisting it removes
area at the fast moving tips and places it in the slower moving areas where induced
velocity is ordinarily lower. Ideally, the rotor chord needs to be inversely proportional
to the radius. This results in an impractical rotor for a helicopter, but the technique
Fig. 3.12 (a) An untwisted, untapered blade has a parabolic lift distribution and far from uniform inflow.
(b) Taper and twist improve the uniformity of inflow.