Dynamic stability

In Chapter 11 we examined the stability of an aircraft from the simple view­point of whether a disturbance from the steady flight condition produced forces and moments that tended to restore the aircraft to this equilibrium state. This is known as static stability. Static stability is, however, not the end of the story. We can have a statically stable aeroplane which is still not satisfactory in practice because it oscillates about the equilibrium position (Fig. 12.1). If the amplitude of the oscillation grows with time then it is said to be negatively damped, and the aircraft is dynamically unstable.

Figure 12.1 illustrates the concepts of static and oscillatory dynamic stabil­ity for an aircraft flying with the wings level, without roll or bank. In this case it is the longitudinal motion of the aircraft that is of interest to us. Let us con­sider a statically stable aircraft which is slightly disturbed by increasing the angle of attack. The subsequent motion may take a wide variety of forms as shown in Fig. 12.1(a) to (c).

The first of these (Fig. 12.1(a)) shows a motion in which the aircraft simply returns to the state it was in before the disturbance was applied. The motion is thus stable and the motion is not oscillatory in nature. Figure 12.1(b) shows an oscillatory motion, but since the oscillations die out with time the motion is again dynamically as well as statically stable. Finally Fig. 12.1(c) shows the oscillations becoming greater with time rather than dying away. This motion is the dynamically unstable negatively damped motion referred to in the first paragraph. It is statically stable because whenever the aircraft is at a pitch angle that differs from its initial value, the moment acting on the aircraft is in the direction which tends to restore it to its original position.