Stability and Control — Page 265, Lesson 318

Let's start with the wing, because it's the biggest aerodynamic surface on the aeroplane, and that means any change in its contribution can significantly change the whole aeroplane's stability. Look at Figure 10.19. You'll see the wing's lift, labelled L, acting at the aerodynamic centre, the AC. The centre of gravity, the CG, is shown aft of the AC. The key line here is the "unstable slope" — the change in lift versus angle of attack. When the CG is aft of the aerodynamic centre, the wing contribution is unstable. That's the fundamental idea: the wing alone, with the CG behind the AC, produces a destabilizing pitching moment. Now, the fuselage and nacelles. In most cases, their contribution is destabilizing too. Here's the mechanism: a symmetrical body in an airflow develops an unstable pitching moment when given an angle of attack. And critically, an increase in angle of attack produces an increase in that unstable pitching moment without the development of lift. So the fuselage and nacelles create an unstable moment that grows with angle of attack, but they generate negligible lift. Figure 10.20 shows the pressure distribution that creates this unstable moment on the body. So we have the wing destabilizing, the fuselage and nacelles destabilizing. What saves us? The horizontal tail. It usually provides the greatest stabilizing influence of all the components. Let's look at Figure 10.21. If the aeroplane is given an increase in angle of attack — whether by a gust or by control displacement — an increase in tail lift occurs at the aerodynamic centre of the tail. That increase in lift at the horizontal tail produces a negative, stabilizing moment about the aircraft CG. So the tail is our stabilizer. Now here's an important contrast. For a given vertical gust velocity and aircraft TAS — true airspeed — the wing moment is essentially determined by the CG position alone. But the tail moment is determined by the CG position and the effectiveness of the tailplane. And for a given moment arm, which is the CG position, the effectiveness of the tailplane depends on three things: downwash from the wing, dynamic pressure at the tailplane, and longitudinal dihedral. We'll get to downwash and dynamic pressure later, but let's focus on longitudinal dihedral now. Longitudinal dihedral is the difference between tailplane incidence and wing incidence. For longitudinal static stability, the tailplane incidence is smaller. Look at Figure 10.22: the wing is at 4 degrees incidence, the tailplane at 2 degrees. Now a vertical gust increases the angle of attack by 4 degrees. The wing goes from 4 to 8 degrees — that's a 100% increase. The tailplane goes from 2 to 6 degrees — that's a 200% increase. So the tailplane generates a greater percentage increase in lift than the wing for the same gust. That's the whole point of longitudinal dihedral: it guarantees that the positive contribution of the tailplane to static longitudinal stability will be sufficient to overcome the sum of the destabilizing moments from all the other components of the aeroplane.