Stability and Control — Page 253, Lesson 301

Let's look at why a wing alone is unstable, and then how adding a tailplane fixes it. First, the key idea: an aircraft rotates around its center of gravity, the CG. Every force acting on the aircraft produces a moment — a turning effect — about that CG, equal to the force multiplied by the perpendicular distance, which we call the arm. Now, consider the wing alone. The wing's lift acts at its aerodynamic centre, the AC — the point where the lift force is considered to act. For a wing on its own, the AC is in front of the CG. That's the crucial fact: the AC is ahead of the CG. Now imagine a vertical gust hits the aircraft. That gust momentarily changes the relative airflow, increasing the angle of attack. A higher angle of attack means more lift — a change in lift, which we call ΔL. That change in lift, ΔL, acts at the wing's AC, and it's multiplied by the arm 'x' — the distance from the wing AC to the CG. So ΔL times arm 'x' generates a positive, nose-up pitching moment about the CG. Why is that unstable? Because that nose-up moment tends to increase the angle of attack even further. More angle of attack means even more lift, which means an even stronger nose-up moment. It's a self-reinforcing, divergent tendency. The wing on its own would simply rotate nose-up about the CG and keep going. That's why we say a wing alone is statically unstable — it has no tendency to return to its original attitude; it has a tendency to move further away from it. Now let's add a tailplane. The tailplane is positioned specifically to generate a stabilizing pitching moment about the aircraft CG. Consider the same vertical gust. The gust also increases the angle of attack of the tailplane, which increases the tailplane lift — a change in tailplane lift, ΔLt. That ΔLt acts at the tailplane's aerodynamic centre, and it's multiplied by arm 'y' — the distance from the tailplane AC to the aircraft CG. This generates a negative, nose-down pitching moment about the CG. So now we have two moments to consider: the wing moment and the tail moment. The wing moment is a function of the change in wing lift, ΔL, multiplied by arm 'x'. The tail moment is a function of the change in tailplane lift, ΔLt, multiplied by arm 'y'. Here's the key condition for stability: if the tail moment is greater than the wing moment, the sum of the moments is not zero. The resultant is a nose-down moment, which gives an angular acceleration about the CG. That nose-down angular acceleration returns the aircraft towards its original position of equilibrium. The greater the tail moment relative to the wing moment, the greater the rate of acceleration back towards equilibrium. But too much angular acceleration is not good — you don't want the aircraft snapping back violently. Now, the length of both arms depends on the CG position. If the CG is moved to a more forward position, the tail arm 'y' becomes larger and the wing arm 'x' becomes smaller. A more forward CG position therefore increases static longitudinal stability — because the stabilizing tail moment gets a longer lever arm, while the destabilizing wing moment gets a shorter one. So the bottom line: if the nose-down, negative tail moment is greater than the nose-up, positive wing moment, the aircraft will have static longitudinal stability. That's the whole balancing act — the tailplane's job is to overpower the wing's natural instability and pull the aircraft back to equilibrium after a disturbance.