Stability and Control — Page 260, Lesson 313

Let’s start with the CG limits, because that’s the heart of what you’re being asked to fill in. With the centre of gravity on the forward limit, static longitudinal stability is maximum, controllability is minimum, and stick force is high. With the CG on the aft limit, static longitudinal stability is minimum, controllability is maximum, and stick force is low. Now, why does the aft CG limit exist? It’s set to ensure a minimum degree of static longitudinal stability — you never want to go past that point, because beyond it you could lose stability altogether. The forward CG limit, on the other hand, is set to ensure a minimum degree of controllability under the worst circumstance — you need enough control authority to handle the aircraft even in the most demanding situation. So the forward limit protects controllability, the aft limit protects stability. Now let’s move to the graphic presentation of static longitudinal stability. Static longitudinal stability depends on the relationship between angle of attack and pitching moment. To study it, we look at the pitching moment contribution of each component of the aircraft — wing, tail, fuselage, and so on. And just like other aerodynamic forces, the pitching moment about the lateral axis is studied in coefficient form. The equation is: M = CM × Q × S × (MAC). Or rearranged, CM = M divided by [Q × S × (MAC)]. Let me define each symbol. M is the pitching moment about the CG, positive if in a nose-up direction. Q is dynamic pressure. S is wing area. MAC is the mean aerodynamic chord. And CM is the pitching moment coefficient. So we sum up the pitching moment coefficients contributed by all the various components, and plot them against lift coefficient — which is essentially angle of attack. Studying the plot of CM versus CL is a convenient way to relate the static longitudinal stability of an aeroplane. Look at Graph A. It shows the variation of CM with CL for an aeroplane with positive static longitudinal stability. The evidence of static stability is a tendency to return to equilibrium — or “trim” — upon displacement. The aeroplane is in trim when CM = 0. If it’s disturbed to some different CL, the pitching moment change tends to return the aircraft to the trim point. Say it’s disturbed to a higher CL — point y. A negative, or nose-down, pitching moment develops, which tends to decrease angle of attack back to trim. If it’s disturbed to a lower CL — point x — a positive, or nose-up, pitching moment develops, which tends to increase angle of attack back to trim. So positive static longitudinal stability is indicated by a negative slope of CM versus CL. The degree of stability is indicated by the slope of the curve — the red line. Now Graph B gives you a comparison of stable and unstable conditions. Positive static stability is the red curve with negative slope. Neutral static stability would be the result if the curve had zero slope. And if neutral stability existed, the aeroplane could be disturbed to a higher or lower lift coefficient without any change in pitching moment coefficient — it would just stay wherever it was disturbed to, with no tendency to return. So the key takeaway: the slope of the CM versus CL curve tells you both whether the aircraft is stable and how stable it is. Negative slope means stable, zero slope means neutral, and the steeper the negative slope, the greater the degree of static longitudinal stability.