Stability and Control — Page 286, Lesson 345

Let's pick up right where we left off — we've been looking at how an aircraft responds after a disturbance, and we've covered the static side of things. Now I want to walk you through what happens when we add time into the picture, because that's the difference between static and dynamic stability. We've got two charts to look at here, Chart E and Chart F, and they show two very different ways an aircraft can behave over time after being disturbed. Let's start with Chart E. This shows what we call an undamped oscillation. The key word is "undamped" — that means there's no damping in the system. Damping is the force that absorbs energy from a motion and gradually brings it to rest. If there's no damping at all, the oscillation just continues, and here's the critical part: the amplitude — that's the size of the swing away from and back toward the equilibrium position — does not reduce with time. It stays the same, cycle after cycle. Now here's the subtle point. This undamped oscillation actually shows positive static stability, because the aircraft does tend to return toward the equilibrium position. But because the oscillation never dies out, we say it has neutral dynamic stability. So you can have positive static stability and neutral dynamic stability at the same time. To actually eliminate that continued oscillation, we need positive damping — damping that actively removes energy from the motion. Let me give you the example from the text, because it's a really good one. Think of a car with worn shock absorbers — those are also called "dampers." The car lacks sufficient dynamic stability, and the continued oscillatory motion is both unpleasant and potentially dangerous. In exactly the same sense, an aircraft must have sufficient damping to rapidly dissipate any oscillatory motion that would affect the safe operation of the aircraft. And here's the practical point: when natural aerodynamic damping cannot be obtained, artificial damping must be provided to give the necessary positive dynamic stability. That's why you see things like yaw dampers on transport aircraft — they're providing artificial damping where the natural aerodynamics aren't enough. Now let's move to Chart F, which shows a divergent oscillation. This is a different and more serious beast. The motion is still statically stable — it tends to return to the equilibrium position. But here's the catch: each subsequent return to equilibrium is with increasing velocity, such that the amplitude continues to increase with time. So instead of the oscillation staying the same size like in Chart E, it gets bigger and bigger with each cycle. That means dynamic instability exists. Why does this happen? The text tells us: divergent oscillation results when energy is supplied to the motion rather than dissipated by positive damping. So instead of the system absorbing energy and settling down, energy is being added to the motion, and that's what we call negative damping. And here's a really important real-world example of this. If a pilot unknowingly makes control inputs which are near the natural frequency of the aeroplane in pitch — that's the frequency at which the aircraft naturally wants to oscillate — then energy is added to the system, negative damping exists, and we get what's called Pilot Induced Oscillation, or PIO. That's the dangerous back-and-forth pitching that can occur when the pilot's inputs are in phase with the aircraft's natural motion, each input adding energy instead of removing it. Now, I want to make sure you understand the logical relationship between static and dynamic stability, because this is a classic exam point. The text states it very clearly: the existence of static stability does not guarantee the existence of dynamic stability. You can have static stability without dynamic stability — that's exactly what Charts E and F show. However, the existence of dynamic stability implies the existence of static stability. If the motion is dynamically stable — meaning it settles down over time — then it must also be statically stable, because it has to tend to return to equilibrium in the first place. And then there's the bold statement: IF AN AIRCRAFT IS STATICALLY UNSTABLE, IT CANNOT BE DYNAMICALLY STABLE. That's a hard rule. If the aircraft doesn't even tend to return to equilibrium, there's no way it can settle down over time. So why does all this matter for certification? The text tells us that any aircraft must demonstrate the required degrees of static and dynamic stability. If the aircraft were allowed to have static instability with a rapid rate of divergence, it would be very difficult, if not impossible, to fly. And in addition, positive dynamic stability is mandatory in certain areas to prevent objectionable continued oscillations of the aircraft. So let me tie this together for you. Static stability is about the initial tendency — does the aircraft want to come back? Dynamic stability is about what actually happens over time — does it come back and stay back, or does it keep oscillating, or does it get worse? Chart E shows us neutral dynamic stability with an undamped oscillation that never dies out. Chart F shows us negative dynamic stability with a divergent oscillation that gets worse. And the relationship between the two is one-way: static stability doesn't guarantee dynamic stability, but dynamic stability always requires static stability.