LONGITUDINAL DYNAMIC STABILITY AND CONTROL RESPONSE
Whilst static stability is concerned with an aircraft’s initial motion following a perturbation, dynamic stability determines the aircraft’s longer-term response to such a disturbance. An aircraft is dynamically stable if, following the removal of a disturbing force, it returns to its equilibrium position. Control response, on the other hand, is concerned with the response of the aircraft to a control input made by the pilot. This section examines the longitudinal dynamic stability and control response of a single main rotor helicopter in both the hover and forward flight. The analysis of the motions is simplified, as before, by assuming that there are no cross-coupling effects. This is rather less easily justified than for fixed wing aircraft, and care must be exercised in this respect. Before looking at the dynamic modes in detail, it is worth reminding ourselves of the derivatives which influence the longitudinal motion.
4.9.1 Longitudinal derivatives
In the longitudinal plane, the variation of X-force, Z-force and pitching moment, M, with respect to forward and vertical velocities, pitch rate and collective and longitudinal cyclic control movements must be considered.
188.8.131.52 Forward velocity derivatives
(1) Forward force due to forward velocity (Xu). The advancing blade sees an increase in forward speed as an increase in relative airspeed whilst the retreating blade see it as a decrease in relative airspeed. Assuming a phase angle of 90°, this causes the rotor disk to flap further back, which in turn causes the thrust vector to tilt rearwards resulting in a decrease in X-force. The flapback also results in an increase in rotor thrust and in Я-force. Fuselage drag also increases with speed and at forward speeds in the range 35 to 50kts this contribution can be equal to that of the main rotor. The overall effect of all these contributions is to return the aircraft to its equilibrium position. To summarize, there are stabilizing contributions to Xu from the backward tilt of the main rotor; the change in magnitude of the thrust vector; the change in fuselage drag; and the change in rotor in-plane force.
(2) Vertical force due to forward velocity (Zu). This derivative is zero in the hover as one would expect, and at low forward speeds an increase in forward speed will cause an increase in rotor lift. However, the amount of disk tilt is an important parameter in the determination of the rotor lift. At high forward speeds the tilt may be large and an increase in speed may then result in a decrease in rotor lift. The force Zu is therefore zero at the hover, becomes negative (remember Z is positive downwards) and then positive. It may be undesirable for Zu to be negative, however, and in this respect an aerodynamically clean fuselage is advantageous as a reduction in overall fuselage drag will result in a smaller disk tilt for a given speed.
(3) Pitching moment due to forward speed (Mu). An increase in forward speed causes the disk to flap back and hence tilts the thrust vector rearwards causing a nose – up pitching moment which gives a stabilizing (positive) contribution to Mu. A horizontal stabilizer also contributes significantly to the overall value of Mu, its effect depending on its setting angle and on the downwash changes resulting from the speed changes. The fuselage can also contribute to Mu, its contribution depending on the change in fuselage lift and drag with changes in speed and the distance of its centre of pressure from the CG. This derivative has a major effect on the dynamic motion of the helicopter and, although a positive value of Mu is necessary for static stability with respect to forward speed changes, if excessive, it will cause dynamic instability.