Stability and Control — Page 260, Lesson 315

Let me walk you through this. We're looking at static longitudinal stability, and specifically how we read it off a graph of pitching moment coefficient, CM, against lift coefficient, CL. First, the key idea. The slope of the CM versus CL curve tells us the static stability of the aeroplane. If that slope is negative — the curve tilts downward as CL increases — the aeroplane is stable. If the slope is positive — the curve tilts upward — the aeroplane is unstable. And if the slope is zero — the curve is flat — we have neutral stability. Let me make that concrete. Suppose the aeroplane is trimmed at some equilibrium point, and then a disturbance pushes it to a higher CL. For a stable aeroplane, the change in pitching moment acts to bring it back. For an unstable aeroplane, the change in pitching moment only magnifies the disturbance. So if we disturb the unstable aeroplane to a higher CL, we get a positive change in CM, which drives continued, greater displacement. If we disturb it to a lower CL, we get a negative change in CM, which again tends to create continued displacement. Either way, the disturbance grows. That's why a positive slope means the aeroplane has no tendency to return to its original equilibrium and will not hold trim. Now, here's an important qualification. Ordinarily, for a conventional aeroplane configuration, static longitudinal stability does not vary with lift coefficient. In other words, the slope of CM versus CL does not change as CL changes. But that's not always true. There are three conditions that can cause noticeable changes in static stability at high lift coefficients — that is, at low speed. The first is if the aeroplane has sweepback. The second is if there's a large contribution of "power effect" on stability. The third is if there are significant changes in downwash at the horizontal tail. When any of those apply, we get the behaviour shown in graph C. Let me describe that curve. At low values of CL — that's high speed — the curve shows a good stable slope. As CL increases, the negative slope decreases slightly, so stability decreases. With continued increase in CL, the slope becomes zero, and we have neutral stability. Eventually, the slope becomes positive, and the aeroplane becomes unstable — we call that "pitch-up." So the takeaway, and I want you to remember this: at any lift coefficient, the static stability of the aeroplane is depicted by the slope of the curve of CM versus CL. Negative slope, stable. Zero slope, neutral. Positive slope, unstable, with pitch-up. That figure shows you the four cases side by side — stable, less stable, neutral, and unstable — so you can see how the slope of the CM versus CL curve changes as stability degrades.