Stability and Control — Page 265, Lesson 322

Let’s pick this up right where the stability picture gets sharpest. We’ve been talking about static longitudinal stability, and now I want to walk you through the two big influences that can wreck it: where the centre of gravity sits, and what the engine is doing. First, the effect of CG position. A variation of CG position can cause large changes in the static longitudinal stability. In the conventional aeroplane configuration, those large changes in stability with CG variation are primarily due to the large changes in the wing contribution. So the wing is the big player here. If the incidence of all surfaces remains fixed, the effect of CG position on static longitudinal stability is typified by the chart in Figure 10.25. Let me describe what that chart shows, because it’s the heart of this idea. The chart plots pitching moment coefficient against lift coefficient — that’s the CM versus CL curve — for a series of CG positions. You’ll see lines labelled 10% MAC, 20% MAC, 30% MAC, 40% MAC, and 50% MAC. MAC is the mean aerodynamic chord, and the CG position is expressed as a percentage of that chord. As the CG is gradually moved aft — from 10% back toward 50% — the slope of that CM versus CL line changes. At the forward positions the slope is negative, which is the stable condition. As the CG moves aft, the aeroplane static stability decreases, then becomes neutral, then unstable. So the line gets flatter and flatter until it’s horizontal, and then it tips over to a positive slope, which is instability. Now, the CG position which produces zero slope and neutral static stability is referred to as the “neutral point.” That’s a term you must know cold. The neutral point may be imagined as the effective aerodynamic centre of the entire aeroplane configuration. What does that mean? With the CG at the neutral point, all changes in net lift effectively occur at that point, and no change in pitching moment results. In other words, if the aeroplane is disturbed in angle of attack, the lift change acts right through the CG, so there’s no moment arm to create a restoring or a diverging moment — hence neutral stability. And here’s the operational bottom line: the neutral point defines the most aft CG position without static instability. So you can never legally or safely load the aeroplane with the CG aft of the neutral point, because beyond it you have static instability. Now let’s move to the second influence: power effects. The effects of power may cause significant changes in trim lift coefficient and static longitudinal stability. Since the contribution to stability is evaluated by the change in moment coefficients, power effects will be most significant when the aeroplane operates at high power and low airspeeds — such as during approach and while taking off. That’s the critical flight regime, because there the thrust is large and the dynamic pressure is low, so the power contribution dominates. The effects of power are considered in two main categories. First, there are the direct effects resulting from the forces created by the propulsion unit itself. Next, there are the indirect effects of the slipstream and other associated flow which alter the forces and moments of the aerodynamic surfaces. So direct means the engine’s own forces; indirect means how the engine’s airflow changes what the wings and tail feel. Let’s take the direct effects first, illustrated in Figure 10.26. The vertical location of the thrust line defines one of the direct contributions to stability. If the thrust line is below the CG, as illustrated, a thrust increase will produce a positive or nose-up moment, and the effect is destabilizing. Think about that: thrust below the CG pushes the nose up, which increases angle of attack, which increases lift, which tends to pitch the nose up further — that’s a diverging, destabilizing tendency. So a low thrust line is destabilizing in the longitudinal sense. Now the indirect effect, shown in Figure 10.27. A propeller located ahead of the CG contributes a destabilizing effect. Here’s the mechanism. As shown in Figure 10.27, a rotating propeller inclined to the relative airflow causes a deflection of the airflow. The momentum change of the slipstream creates a normal force at the plane of the propeller. So the propeller is not just pulling forward — because it’s tilted relative to the airflow, it deflects the air, and that deflection produces a force perpendicular to the thrust, a normal force, acting right at the propeller disc. As this normal force will increase with an increase in aeroplane angle of attack, the effect will be destabilizing when the propeller is ahead of the CG. Why? Because when the aeroplane pitches up, the normal force grows, and since the propeller is ahead of the CG, that growing force pushes the nose up even more — again a diverging tendency. The magnitude of the unstable contribution depends on the distance from the CG to the propeller, and it is largest at high power and low dynamic pressure. So the further the propeller is ahead of the CG, the bigger the destabilizing arm, and the worse it gets exactly when you’re at high power and slow speed — takeoff and approach again. So to tie it together: you have two separate destabilizing mechanisms from power — the direct one from a low thrust line producing a nose-up moment, and the indirect one from the propeller ahead of the CG producing a normal force that grows with angle of attack. Both push you toward instability, and both are worst in the high-power, low-speed regime. And remember the neutral point from the CG discussion — that’s your hard limit. The CG must stay forward of the neutral point, and power effects are part of why the margins matter so much in real operations.