Stick Forces and Dynamic Longitudinal Stability

The previous lesson read static stability off a graph of moments; this lesson reads it off the pilot's hand. Stability is not an abstraction in the cockpit: it is a force the pilot feels when holding a speed away from trim, and a force felt again when pulling g in a turn or a pull-up. Then the lesson lets go of the stick and watches what happens over time: the two oscillations every aeroplane performs after a pitch disturbance, one quick and potentially violent, one slow and patient, and what altitude, CG position and the pilot's own reactions do to them.

Stick force against speed: stability you can feel

Trim the aircraft and the stick force is zero at exactly one speed: the trim speed. Now fly slower without re-trimming. A statically stable aircraft wants its trim speed back: it lowers the nose to re-accelerate, and to refuse it, holding the lower speed, the pilot must hold a pull. Fly faster than trim and the roles reverse: the aircraft noses up to slow down, and holding the higher speed takes a steady push. Pull below trim, push above — that pattern is static longitudinal stability translated into force, and certification demands it: the force must always lean against the speed change.

Plotted against IAS, this gives the stick force versus speed graph: zero at trim, pull forces on the slow side, push forces on the fast side, a line sloping downward through the trim point. Its gradient, how much force per knot of speed change, is stability as the pilot perceives it, and three things set how strong that perception is:

Distance from trim — the further from trim speed, the larger the force.
CG location — a forward CG steepens the gradient (each knot off trim costs more force, the stability is unmistakable), an aft (rearward) CG flattens it, and at the neutral point the force would fade to nothing.
Altitude — the gradient is felt flatter at altitude: the same aeroplane, perceived as less stable at the top of the envelope.

Two weakenings lie behind that feel, and the course takes them in turn: the next section makes the damping loss precise for manoeuvring, and the directional lesson adds how high cruise Mach blunts a surface's response.

Stick force per g: manoeuvring stability

The second force measure appears in manoeuvre. To pull g (in a level turn, a pull-up, a flare) the pilot deflects the elevator and holds a force against the aircraft's stability. The stick force per g is that force divided by the extra load factor: the pull needed for each g above the 1 g of level flight. It is the manoeuvring counterpart of the speed gradient, and it behaves very simply: the force rises linearly with load factor. Twice the extra g, twice the pull: pulling from 1 g to 3 g takes twice the force of pulling from 1 g to 2 g. On a graph of force against load factor the line runs straight from zero force at 1 g, and its slope is the stick force per g itself.

Certification prescribes both a minimum and a maximum for that slope, and each guards against a different accident. The minimum protects the structure: if the force per g were too light, a small, casual pull (turbulence jostling the pilot's arm, an over-eager correction) could reach the limit load factor before the pilot felt anything warning them off; reaching the structural limit must take a deliberate, unmistakable effort. The maximum protects manoeuvrability: the pilot must be able to pull the g the aircraft is certified for (to flare, to tighten a turn, to recover from an upset) without needing more force than a pilot can reasonably apply, and without exhausting themselves in sustained manoeuvring.

Stick force per g decreases with pressure altitude, and the mechanism matters more than the fact. Flying at the same IAS, the TAS climbs as the air thins. When the aircraft pitches at some rate, the tailplane, far from the CG, sweeps through the air, and that sweeping motion changes the tail's angle of attack: it is this α change that creates the tail force resisting the pitching, the aerodynamic damping (the resistance that opposes the motion itself). But the faster the aircraft travels through the air, the smaller the angle change that the same pitch rate produces at the tail: the tail's own motion is diluted by the larger airspeed. High TAS therefore means less opposition to the pull: less elevator force needed for each g, a shallower gradient. The aircraft that felt reassuringly firm at low level responds to a lighter touch at cruise altitude — one reason high-altitude handling demands restraint.

What sets the gradient: CG and trim

CG location — the dominant influence, working exactly as it did for static stability: a forward CG raises the stick force per g (more stability to overcome with every g pulled), an aft CG lowers it. Load the CG too far aft and the per-g force becomes dangerously light, another reason the certified aft limit sits where it does.

Trim setting — no influence on the stick force per g. Trim removes the steady force at the current 1 g condition, it moves the zero point the pilot starts from, but the extra force for each extra g is unchanged: the line moves, its slope does not. Exactly as on the Cm–α graph: trim shifts the line parallel; only a CG change alters its slope.

Dynamic longitudinal stability: the two oscillations

Now disturb the aircraft in pitch and let everything go. The concepts lesson defined dynamic stability, the quality of the response over time, and in pitch that response is the sum of two oscillations so different in character that they can be studied separately. The quick one is the short period: the aircraft pitches about its CG, angle of attack and load factor swinging, while the speed and altitude barely change — the oscillation is over too fast for them to respond. Its period is a matter of seconds, and in a well-behaved aircraft it is heavily damped: the tail's restoring and damping moments kill it within a cycle or two, often before the pilot has even identified what happened.

The slow one is the phugoid: a slow, large-scale exchange of speed and altitude at nearly constant angle of attack. The aircraft sinks below its trimmed state, speeds up, the extra speed lifts it back up, the climb bleeds the speed off, it sinks again: kinetic and potential energy traded back and forth with a period from tens of seconds to minutes. Its damping comes mostly from drag and is weak: the phugoid outlives the short period by many cycles — a long, slow oscillation that trim and autopilots quietly suppress in everyday flying.

Why the short period is the dangerous one

Of the two, the phugoid looks more dramatic on paper (it goes on and on) but the short period is the hazardous mode, for two reasons. First, loads: the short period swings the angle of attack, and at high dynamic pressure every degree of α is a large change of lift: a poorly damped short period can drive the load factor toward structural limits within seconds. Second, timescale: its period sits right at the pilot's reaction time. A pilot can always fly a phugoid out by hand (its cycle is slow enough that corrections arrive well in time) but corrections aimed at a short-period oscillation arrive about half a cycle later than they were needed, which is precisely wrong: the input meant to stop this swing lands in time to feed the next one.

Pilot-induced oscillations

That mistimed feeding has a name: the pilot-induced oscillation (PIO): pilot and aircraft coupled into an oscillation neither produces alone. The aircraft pitches; the pilot counters; but by the time the correction takes effect the aircraft has already reversed, so the input adds to the new swing instead of opposing the old one. Each cycle the correction grows more urgent, arrives just as wrongly, and the oscillation amplifies: the harder the pilot works, the worse it gets. The recovery is the one manoeuvre that feels most unnatural: release the controls (or freeze them centrally). Uncoupled from its pilot, the aircraft is just flying its short period, and the airframe's own damping, no longer overwhelmed by the pilot's inputs, ends it within a cycle or two.

Stick force against speed: stability you can feel

Check you understood

Stick force per g: manoeuvring stability

What sets the gradient: CG and trim

Dynamic longitudinal stability: the two oscillations

Why the short period is the dangerous one

Pilot-induced oscillations

Altitude and CG in the dynamics

What the exam asks