Stability and Control — Page 286, Lesson 343

Let’s pick up right where we left off with dynamic stability. We’ve already covered static stability — that’s the initial tendency of an aircraft to return to equilibrium after a disturbance. Now, dynamic stability is about what happens after that initial tendency. It’s defined by the resulting motion with time. So if an aircraft is disturbed from equilibrium, the time history of that motion — how the displacement changes over time — tells us about its dynamic stability. In general, an aircraft shows positive dynamic stability if the amplitude of the motion decreases with time. Amplitude here means the size of the displacement from equilibrium. So if the aircraft wobbles but the wobbles get smaller and smaller, that’s positive dynamic stability. Now, the excerpt gives us six time-history diagrams — charts A through F. The first three, A, B, and C, are nonoscillatory modes. That means the motion happens without cyclic, or back-and-forth, oscillation. Let’s go through each. Chart A shows a system given an initial disturbance, and the motion simply subsides without oscillating. This mode is called subsidence, or dead beat return. The aircraft moves away from equilibrium, then smoothly returns and stops. This indicates positive static stability — because the initial tendency is to return to equilibrium — and positive dynamic stability — because the amplitude decreases with time. Chart B shows the mode of divergence. Here, the amplitude increases with time in a non-cyclic way. The aircraft moves further and further away from equilibrium. The initial tendency to continue in the displacement direction is evidence of static instability, and the increasing amplitude is proof of dynamic instability. So this is negative static and negative dynamic. Chart C illustrates pure neutral stability. If the original disturbance creates a displacement that then remains constant — the aircraft just stays displaced, neither returning nor diverging — the lack of tendency for motion and the constant amplitude indicate neutral static and neutral dynamic stability. Now, the next three charts, D, E, and F, are the oscillatory modes. These involve cyclic motion — the aircraft oscillates back and forth. One feature common to all three is that positive static stability is demonstrated by the initial tendency to return to equilibrium. But the resulting dynamic behaviour can be stable, neutral, or unstable. Chart D illustrates a damped oscillation. Here, the amplitude decreases with time. The reduction of amplitude indicates there is resistance to motion and that energy is being dissipated. This dissipation of energy — or damping — is necessary to provide positive dynamic stability. So the aircraft oscillates, but each swing is smaller than the last, eventually settling back to equilibrium. So the key contrast here: static stability is about the initial tendency, while dynamic stability is about the resulting motion over time. And damping — energy dissipation — is what turns a statically stable aircraft into a dynamically stable one.