Stability and Control — Page 246, Lesson 300

Let’s pick up with the aerodynamic centre, because it’s the single most important reference point for everything we’re about to do in stability. I want you to picture the wing in flight. The lift force doesn’t act through one fixed spot — as the angle of attack changes, the centre of pressure, the CP, moves along the chord. That makes the CP awkward to work with, because the arm, the distance from the CP to any reference point, keeps changing. So for the study of stability, we deliberately choose a stationary point instead, and we call it the aerodynamic centre, the AC. Now, where is the AC? It sits at the quarter chord, which is 25% of the chord aft of the leading edge. That’s a fixed location on the wing, and that’s the whole point — it doesn’t move as angle of attack changes. Here’s the key behaviour, and I want you to hold onto it. The pitching moment about the AC is negative, meaning nose-down, and — this is the crucial part — that negative nose-down pitching moment does not change with changes in angle of attack. It stays constant. Why is that? Let’s reason through it. As angle of attack increases, the magnitude of the lift force increases. But at the same time, the centre of pressure moves forward, so the arm, the perpendicular distance from the AC to the line of action of the lift, gets smaller. The lift goes up, the arm comes down, and the product — lift times arm, which is the moment — stays the same. That’s why the pitching moment about the AC remains constant at normal angles of attack. And this only works at the AC, at the 25% chord point. If you picked any reference point in front of the AC, or behind it, the pitching moment would change with angle of attack, because the changing CP position would no longer be compensated. The AC is the one special point where the moment is invariant. One more important qualifier. The AC is located at 25% chord only when the airflow is subsonic. That’s a limitation you need to remember — at higher speeds, in transonic or supersonic flow, that location shifts, and we’ll deal with that later. For now, in subsonic conditions, the AC is fixed at the quarter chord, and for the study of stability we consider the lift to act through that point. So the takeaway: we replace the moving centre of pressure with the fixed aerodynamic centre, where the nose-down pitching moment is constant with angle of attack, and that gives us a clean, stable reference from which to analyse the whole aircraft’s stability.