Stability and Control — Page 293, Lesson 351

Let’s start with the short period oscillation, because it sets the stage for why directional stability matters. Of the two modes of dynamic longitudinal stability, the short period oscillation is the one that really counts. It can generate damaging flight loads because of rapid changes in ‘g’ loading — that’s the acceleration you feel as the aircraft pitches. And it’s made worse by pilot response lag, which we call PIO — pilot-induced oscillation. So if the pilot reacts a little late, the oscillation can build up. Now, I told you earlier that pitch damping reduces the amplitude of oscillations. So the problems of dynamic stability become acute when aerodynamic damping is reduced. When does that happen? High altitude. At high altitude, density is low, and to maintain the same lift you need a high true airspeed — high TAS. That combination reduces aerodynamic damping. So the key takeaway here: dynamic stability is reduced at high altitude due to reduced aerodynamic damping. That’s a direct cause-and-effect chain. Now we move into directional stability and control. Directional stability is essentially “weathercock” stability. Think of a weather vane — it points into the wind. The aeroplane behaves the same way. It involves moments about the normal axis, and how those moments relate to yaw or sideslip angle. If an aeroplane has static directional stability, it will tend to return to equilibrium after a disturbance. The evidence of that stability is the development of yawing moments that restore the aeroplane to equilibrium. Let’s define the axis system. A positive yawing moment, given the symbol N, is a moment about the normal axis that tends to rotate the nose to the right. So positive N means the nose goes right. Now, just like with other aerodynamic quantities, it’s convenient to put yawing moment in coefficient form. Why? So we can evaluate static stability independent of weight, altitude, speed, and so on. The yawing moment coefficient is Cn. The equation is: Cn = N / (Q S b) Let me unpack that. N is the yawing moment. Q is dynamic pressure. S is wing area. b is wingspan. And Cn is the yawing moment coefficient, positive to the right. So the coefficient is based on the wing dimensions S and b, because the wing is the characteristic surface of the aeroplane. That’s why we use wing area and wingspan as the reference dimensions. Now, sideslip angle. This is the directional counterpart to angle of attack. The sideslip angle, given the symbol β — beta — relates the displacement of the aeroplane centre line from the relative airflow. It’s positive when the relative wind is displaced to the right of the aeroplane centre line. So if the airflow comes from the right of the nose, β is positive. Here’s the key relationship: a yaw to the left gives a sideslip to the right. That’s the geometry of it. The sideslip angle β is essentially the “directional angle of attack” of the aeroplane. It’s the primary reference in directional stability, and it also matters in lateral stability considerations. Static directional stability is appreciated by the response to sideslip — that’s how you see it working. So to tie it together: the short period oscillation is the critical dynamic mode, high altitude reduces damping and thus stability, and directional stability is all about the weathercock response to sideslip, quantified by the yawing moment coefficient Cn.