# Static Stability

We consider the nature of the initial reaction to various forms of disturbance from equilibrium. Longitudinal and lateral motions are treated independently. The contributions of the rotor to forces and moments arise from two sources, variations in magnitude of the rotor force vector and variations in the inclination of this vector associated with disc tilt, which is defined by the blade flapping motion. This motion is highly dependent on hinge offset and blade Lock number – effectively the rotor control power. This is the ability to generate a moment about the rotor hub by the application of cyclic pitch and hence induce blade flapping which defines the rotor disc tilt.

8.3.1 Incidence**[8]** Disturbance

An upward imposed velocity (e. g. a gust) increases the incidence of all blades, giving an overall increase in thrust magnitude. Away from hover, the dissimilarity in relative airspeed on the advancing and retreating sides leads to an incremental flapping motion, which results in a nose – up tilt of the disc. Since the rotor centre lies above the aircraft CG, the pitching moment caused by the change of inclination is in a nose-up sense, that is destabilizing and increasingly so with increase of forward speed. In addition, the change in thrust magnitude itself generates a moment contribution, the effect of which depends upon the fore and aft location of the CG relative to the rotor centre. In a practical case, the thrust vector normally passes ahead of an aft CG location and behind a forward one, so the increase in thrust magnitude aggravates the destabilizing moment for an aft CG position and alleviates it for a forward one. The important characteristic therefore is a degradation of longitudinal static stability with respect to incidence, at high forward speed in combination with an aft CG position. This is also reflected in a degradation of dynamic stability under the same flight conditions. It should be noted that these fundamental arguments relate to rigid blades. With the advent of modern composite materials for blade construction, judicious exploitation of the distribution of inertial, elastic and aerodynamic loadings allows the possibility of tailoring the blade aeroelastic characteristics to alleviate the inherently destabilizing features just described.

Of the other factors contributing to static stability, the fuselage is normally destabilizing in incidence, a characteristic of all streamlined three-dimensional bodies. Hinge offset, imparting an effective stiffness, likewise aggravates the incidence instability. The one stabilizing contribution comes from the horizontal tailplane. Figure 8.4 represents the total situation

Figure 8.4 Contributions to static stability incidence |

diagrammatically. The tailplane compensates for the inherent instability of the fuselage, leaving the rotor contributions as the determining factors. Of these, the stiffness effect for an articulated rotor is generally of similar magnitude to the thrust vector tilt moment. With a hingeless rotor (Section 8.5) the stiffness effect is much greater. The effect is denoted in this figure as Ma; however, this effect is normally associated with a vertical velocity perturbation and so the derivative MW is frequently used in this context.

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