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NACA ACR L4H07, 1944.
5
Flight dynamics and control
5.1 Introduction
At first sight, the study of helicopter flight dynamics and control may seem very
complicated, since each blade possesses degrees of freedom in addition to those of
the fuselage. Fortunately, apart from some special cases of helicopter dynamic stability
such as the phenomenon of air resonance to be considered in Chapter 9 a knowledge
of the motion of the individual blades is not required, and for calculating the forces
and moments in disturbed flight it is sufficient to consider only the behaviour of the
rotor as a whole.
The simplifying assumptions which have enabled helicopter dynamics of flight
and dynamic stability to be handled in ‘classical’ form are due mainly to the original
work of Hohenemser1 and Sissingh2. These assumptions are as follows.
(i) In disturbed flight the rotor behaves as if the motion were a sequence of steady
conditions, i.e. the accelerations of the helicopter are small enough to have a
negligible effect on the rotor response. This assumption was justified in Chapter 1
where it was shown that the rotating blade could be represented by a second
order system having a natural frequency which is the same as the rotor angular
frequency; typical disturbed motion corresponds to forcing the blade at a very
low frequency ratio so that the rotor responds as if the instantaneous disturbance
were being applied steadily.
The rotor can thus be regarded as responding instantaneously to speed and
angular rates, just as is generally assumed for the fixed wing aircraft.
(ii) The rotor speed remains constant. This assumption is justified because not only
is the rotor speed controlled by the engine, but the changes of torque under
normal steady flight conditions are quite small. In autogyro flight neither of
these two conditions applies, and the rotor angular velocity variations may be
quite considerable.
(iii) Lateral and longitudinal motions are uncoupled and can be treated independently
of one another, as is normally the case with the fixed wing aircraft. Now, we
138 Bramwell’s Helicopter Dynamics
have seen that the rotor tilts sideways with forward speed, and we shall meet
other examples in which the lateral and longitudinal responses are coupled.
Nevertheless, it is assumed that the effects of coupling are quite small, and, for
the present purpose of studying the flight dynamics at a particular speed and
configuration, may be ignored.
Before dealing with the flight dynamics and the dynamic stability problem analytically,
let us consider the physical effects of velocity and angular rate disturbances on the
helicopter.
5.1.1 Forward speed disturbance
We have seen in Chapters 3 and 4 that, for constant collective pitch and inflow ratio
λ, the backward flapping angle a1 of the disc is almost exactly proportional to
forward speed. Figure 3.31, for example, shows that, even when θ0 and λ vary in
trimmed flight, a1 is still roughly linear with forward speed, and it follows that when
the forward speed is increased the rotor tilts back by an amount which is almost
independent of the original flight speed; a typical value is 1° for about 10 m/s. It is
found that the in-plane H-force, whose steady value is already very small, changes
very little so it can be assumed that the rotor thrust force tilts back with the disc,
Fig. 5.1.
The tilt of the thrust vector gives a backward force component, relative to the
original flight direction, and a nose up pitching moment. The thrust also changes but,
unlike the fixed wing aircraft, the change may be positive or negative depending on
the flight speed; for example, at high forward speed, when the disc will be tilted
forward at quite a large angle, a change of forward speed increases the flow through
the disc, reducing the blade incidence and causing a loss of thrust. Of course, if in
trimmed flight the thrust vector does not pass through the helicopter c.g., the change
of thrust will also contribute to the pitching moment, but it is usually found that the
total moment is dominated by the thrust tilt just described. With offset hinges or
hingeless blades there is an additional moment due to the disc tilt alone, as discussed
in Chapter 1. The fuselage drag also provides a substantial contribution to the backward
force, particularly at high speed.
δa1 H + δH
T + δT
Fig. 5.1 Rotor force and flapping in disturbed flight
c.g.
Flight dynamics and control 139
5.1.2 Vertical speed (incidence) disturbance
An upward (positive) velocity of the surrounding air mass imposed on the helicopter
increases the incidence of all the blades, and there is a consequent increase of the
　
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本文鏈接地址：Bramwell’s Helicopter Dynamics(71)