Static and Dynamic Stability: Concepts - ATPL 081 — Principles of Flight

Every claim this module will make (about tails, CG limits, dihedral, Dutch roll) rests on a handful of definitions, and the exam tests the definitions themselves as eagerly as their consequences. This lesson lays them down: what stability means before and after a disturbance, how it trades against manoeuvrability, and the state an aeroplane must be in before the word stability even applies: equilibrium, of four forces and three moments.

Static stability: the first tendency

Disturb something that was resting and watch only its first tendency. That is static stability. Formally: static stability is the initial tendency of a body after a disturbance from equilibrium: toward it, away from it, or neither. Three outcomes are possible, and the classic picture below carries all three:

Positive static stability — displace a ball resting in a bowl and its first motion is back toward the bottom (statically stable).
Neutral static stability — displace a ball on a flat table and it has no tendency either way; it simply stays where the push left it.
Negative static stability — displace a ball balanced on a dome and its first motion is further away, accelerating (statically unstable).

An aeroplane is the same experiment in three dimensions: a gust pitches the nose up: does the aircraft's own aerodynamics push the nose back down, leave it where the gust put it, or pitch it up further?

Why are transport aeroplanes built statically stable? Because an unstable aircraft must be actively flown every second: every gust starts a departure that only immediate correction stops, and no crew can hand-fly that for hours (nor certify it for passengers). A statically stable aircraft does the first correcting itself: it can be trimmed, flown lightly, and trusted to absorb turbulence with its own aerodynamics. Stability is what makes an aeroplane restful to fly.

Manoeuvrability: the opposing quality

Manoeuvrability is the ease and quickness with which an aircraft can be made to change its flight condition: how readily it pitches, rolls and yaws when asked. And here is the module's first trade-off, one the exam loves: stability and manoeuvrability oppose each other. The very tendency that returns a stable aircraft to equilibrium also resists the pilot's deliberate attempts to leave it: a strongly stable aircraft answers the controls ponderously and needs large forces, while a marginally stable one flicks eagerly into any manoeuvre. Designers pick a point on that line: transport aircraft sit well toward stability (restful, predictable, certifiable), aerobatic and fighter types toward manoeuvrability, the extreme being deliberately unstable fighters that are flyable only because computers do the correcting.

Dynamic stability: what happens next

Static stability judged only the first tendency; dynamic stability judges the whole motion that follows. A statically stable aircraft starts back toward equilibrium, and usually arrives with momentum, overshoots, and comes back again: an oscillation. (Heavily damped, it can also settle back without ever overshooting, the aperiodic case below.) Dynamic stability asks what that oscillation does with time:

Positive dynamic stability — the swings shrink and the motion dies back to equilibrium (damped).
Neutral dynamic stability — the swings continue at constant amplitude, never growing, never dying.
Negative dynamic stability — each swing is bigger than the last: a divergent oscillation, the treacherous case where a statically stable aircraft still ends up out of control.

And motion need not swing at all. An aperiodic (non-oscillatory) motion:

subsides smoothly back to equilibrium (subsidence).
departs smoothly and ever faster (divergence).

Periodic or aperiodic, the question is the same: does the motion die out, persist, or grow?

Hold on to the relationship between the two stabilities: static stability is necessary but not sufficient for dynamic stability. Without the initial returning tendency there is nothing to oscillate about: a statically unstable aircraft simply departs. But the returning tendency alone does not guarantee the oscillation dies: that takes damping (the aerodynamic resistance to the motion itself, which drains the oscillation's energy), and damping is exactly what thins out at high altitude — a thread that the end of this module picks up.

The precondition: equilibrium

Stability describes the response to a disturbance from equilibrium — so before any of it applies, the aircraft must actually be in equilibrium: a state in which, left alone, it continues exactly as it is. That demands two things at once. The sum of all forces must be zero, or the aircraft accelerates along some direction; and the sum of all moments must be zero, or it starts to rotate. Steady, trimmed flight, cruise, a steady climb, a steady glide, is precisely this double balance, and everything this module examines is a small disturbance laid on top of it.

The forces in the balance

The force half of the balance contains the four the whole course has used: lift, weight, thrust and drag. In steady level flight the pairs balance directly: lift carries weight, thrust matches drag. In steady climbs and glides the same four rearrange along and across the tilted flight path (weight gaining a component along it), but the rule is unchanged: in equilibrium the four sum to zero. The flight-mechanics module works these balances case by case; stability needs only the fact of the balance.

The moments about three axes

The moment half needs the aircraft's three axes, all passing through the centre of gravity:

Lateral axis (wingtip to wingtip) — the pitching moment: the module's longitudinal chapters live here, balancing wing, tailplane and thrust-line moments.
Longitudinal axis (nose to tail) — the rolling moment.
Normal axis (vertical through the CG) — the yawing moment.

Equilibrium requires all three sums to be zero simultaneously.

And if a sum of moments is not zero? Then the aircraft is not in equilibrium about that axis: the unbalanced moment produces an angular acceleration, and the aircraft begins to rotate: pitching, rolling or yawing at an increasing rate until something (aerodynamics, the pilot, or the stability this module builds) supplies the countering moment. An out-of-trim aircraft is exactly this on a small scale: a residual pitching moment that the pilot must hold against, or trim away, continuously.

What the exam asks

Definition questions, asked nearly word for word. The overview, following the learning objectives:

Define static stability, identify positive/neutral/negative conditions, and explain why aeroplanes are designed statically stable

Explain manoeuvrability, and its relationship with static stability: they oppose each other

Define dynamic stability, identify positive/neutral/negative motions, and periodic against aperiodic motion

Explain equilibrium of forces and moments as the precondition for static stability

Identify the forces in the equilibrium: lift, weight, thrust, drag

Identify the moments about the three axes, and discuss the effect of a non-zero sum of moments