A stall that is a place

Everything about a stall in the two rungs below treats it as an event: a boundary crossed, a peak passed, a damping lost. The recovery from an event is to undo it, and every stall drill ever written is a way of undoing it.

There is an arrangement in which a stall is not an event. It is a place — a second stable trim point, far past the peak, that the aircraft settles into and stays in.

What holds an aeroplane’s nose where it is #

Static longitudinal stability is a statement about a slope. The pitching moment must fall as the incidence rises: pitch up, and a nose-down moment must appear to put it back.

On a conventional aeroplane that slope comes almost entirely from the tailplane. The tail carries download — it is set at a negative incidence relative to the wing — and pitching the aircraft up raises the tail’s incidence too, which reduces its download, which is a nose-down moment. The wing’s own contribution is usually destabilising, because the centre of gravity is behind the aerodynamic centre, and the tail wins. That the wing has an aerodynamic centre at all — a point about which the moment does not change with incidence — is what makes the accounting this simple.

So the stability is the tail’s, and the tail’s authority is proportional to the dynamic pressure it sits in. That last clause is where everything in this essay lives.

The wake, and where it goes #

Past the stall the flow over the wing has separated, and what leaves the trailing edge is a thick, slow, turbulent wake carrying a small fraction of the free stream’s dynamic pressure — the same wake the drag was paid into, now much larger.

Where that wake goes depends on incidence, and it sweeps upward relative to the aircraft as the nose rises — carried by the downwash field, which is stronger and further developed the more lift the wing is making. A low tailplane is caught by it glancingly near the stall and is clear of it again as the incidence grows further. A tailplane on top of the fin is in the opposite position: it is clear at small incidence and squarely inside the wake at large.

The second zero #

With the tail’s dynamic pressure collapsed, its contribution to the moment collapses with it, and what is left is the wing’s own moment — which past the stall is nose-up, because separation moves the centre of pressure forward and the section’s own moment changes.

The pitching moment curve therefore turns around past the stall and comes back across zero. The calculation finds that second crossing at 31.5 degrees of incidence for the layout drawn, and — the part that matters — the slope there is negative.

A negative slope is stability. The aircraft at 31 degrees is as content there as it is in cruise: disturb it and it returns. There is nothing transient about the condition, nothing that resolves itself, and no sense in which the aircraft is falling out of anything. It is trimmed.

The descent rate in that state is large and the forward speed is small, so the aircraft comes down steeply, nose-high, wings roughly level, in a stable attitude, under control in roll — and cannot get out.

The circularity that makes it unrecoverable #

The obvious response is to push the nose down, and the reason that fails is worth stating precisely because it is the whole shape of the accident.

The elevator is part of the tailplane. The tailplane is inside the wake. So the control that would recover the aircraft is operating in the same collapsed dynamic pressure that removed the stability in the first place, and its authority has fallen by the same factor.

The calculation gives the number: the tail sees about twelve per cent of the free-stream dynamic pressure at the deep trim, so the elevator produces about an eighth of the moment it would produce outside the wake. Full nose-down deflection moves the deep trim by seven degrees and leaves it stable.

The condition disables the control that undoes it, which is a different kind of failure from a control being insufficient. An aircraft with an undersized elevator is a design error; an aircraft in a deep stall is in a state that is self-maintaining by construction.

What is actually done about it #

Since the aerodynamics cannot be argued with, the engineering answer is to prevent entry rather than to provide recovery, and every measure is a variation on that.

A stick pusher. An automatic system that forces the nose down as the incidence approaches the stall — not warns, pushes — and it is fitted precisely because a warning is useless if the condition it warns about cannot be recovered from. It is the standard fit on rear-engined T-tail transports and its existence is an admission about the layout.

Vortilons, strakes and stall strips. These are the same devices the previous rung names for spin resistance, doing a different job: Devices that fix where the wing stalls and how sharply, so that the wing’s own moment past the peak is less strongly nose-up and the second zero is pushed out of the attainable range.

And the layout itself. Most modern transport aircraft have their engines under the wing and their tailplanes low, which is not primarily about this — it is about engine access, weight and bending relief — but it removes the geometry that makes a deep stall available.

None of those is a recovery, and that is the honest summary. The T-tail deep stall is prevented, not survived, and the aircraft that established this were lost in flight test with the condition entered deliberately.

Two stable states, and the gap between them #

An aircraft with two stable trim points is a system with more than one answer, and that is a different kind of object from one with a single equilibrium.

Between the two stable crossings there is an unstable one — the moment curve must cross zero an odd number of times between two stable crossings, and it does. That middle crossing is the watershed: an aircraft disturbed past it falls into the deep trim, and one that stays below it returns to cruise.

So the question of whether an entry becomes a deep stall is a question about which side of a separatrix the aircraft ends up on, and it is decided by the dynamics rather than by the static diagram. A brisk pitch-up with enough rate carries the aircraft past the middle crossing on inertia alone; a gentle approach to the stall does not.

That is why the condition is entered by a manoeuvre and not by slow deceleration, and it is why the flight-test technique that found it — deliberate, aggressive entries — is the technique that finds it. An aircraft flown carefully into a stall in this layout behaves ordinarily, which is precisely what makes the trap worth a stick pusher.

And it explains the shape of the certification requirement. What must be demonstrated is not that the aircraft recovers from a deep stall; it is that no combination of control inputs within the flight envelope reaches one, which is a statement about a basin of attraction rather than about a recovery.

The same thing in three other places #

Two stable equilibria separated by an unstable one is a shape rather than an aeronautical curiosity, and naming its relatives makes it easier to recognise.

A separation bubble that will not reattach. Once the flow has let go, the pressure field it produces is not the one that would have kept it attached, so the state maintains itself — which is the hysteresis this essay’s last section points at, and it is the same self-maintaining structure one level down.

A hydraulic jump. A channel flow has two depths at one energy, one fast and one slow, and which one it is in depends on its history. The analogy is closer than it looks: both are systems where a conserved quantity permits two states and the transition between them is one-way.

And a stalled compressor stage. A blade row past its own diffusion limit has a second operating point at a much lower mass flow, and a compressor that falls into it does not come out until the whole machine is throttled back — which is the surge that the turbomachinery ladder names as its own worst failure.

What the three share with the deep stall is that the state is stable and the recovery is not available from inside it. In each case the correct engineering response has been the same: prevent entry, because the exit does not exist.

Why a low tail escapes and a high one does not #

The whole difference between the two curves in the first figure is one prescribed function — how much of the free stream’s dynamic pressure the tail sees, against incidence — so it is worth saying what governs that function, since it is the only assumption doing any work.

The wake leaves the trailing edge roughly along the local flow direction and is then carried by the downwash. At small incidence it passes below a high tail and above a low one; as the incidence rises it sweeps upward relative to the aircraft, so it reaches a high tail and leaves a low one.

Vertical position is therefore the whole design variable, and the arrangement’s name is the diagnosis. A tailplane at the top of the fin is typically a fuselage-height above the wing’s plane; the wake at thirty degrees of incidence has risen by roughly that much over the distance to the tail, which is why the two numbers meet at exactly the incidences that matter.

There are two secondary geometries worth naming, and both are consequences of the same picture.

Tail arm. A longer tail arm means more time for the wake to rise before it arrives, so a long fuselage puts the tail further into the wake at a given incidence. That works against the stability the same arm was lengthened to provide.

Flap setting. Extending flaps increases the wing’s lift and therefore its downwash, which drives the wake down relative to the tail — so a T-tail aircraft’s deep-stall susceptibility is different clean and in the landing configuration, and the certification testing has to cover both.

And a low tail has the opposite problem in a narrow band. It is caught by the wake near the stall and clear of it beyond, which produces a momentary loss of stability at the very incidence a stall happens at — the pitch-up that many conventional aircraft show at the stall and that a stick shaker warns about. It is the same mechanism, at a different depth, without the second trim point.

The instrument that has to be believed #

There is a practical consequence of an unrecoverable condition that is worth a paragraph, because it changes what an instrument is for.

On an aircraft that can recover from a stall, a stall warning is advice: it tells a pilot that a margin is being used up, and the pilot decides what to do about it. On an aircraft that cannot recover from what lies past the stall, a warning is not enough — the decision has to be taken out of the loop, which is what a stick pusher does.

That is a different kind of system and it is trusted differently. A pusher that fires when it should not is itself dangerous, so it is fitted with redundant sensors, cross-comparison and an inhibit, and its failure modes are analysed to a standard a warning device is not. The instrument’s authority is what makes it worth analysing.

The connection to the angle-of-attack instrument the first rung recommends is direct and it is where the two rungs meet. A pusher is driven from an angle-of-attack vane, because the angle is the quantity the wing responds to; and the vane’s calibration is against a clean wing, so a contaminated wing defeats it in exactly the way the first rung describes. The most authoritative instrument on the aircraft inherits the first rung’s caveat unchanged, and that is the sharpest reason the caveat matters.

What the picture cannot show #

The wake’s effect is modelled, not solved. The fraction of dynamic pressure the tail sees is a prescribed function of incidence — falling steeply for the high tail, gently for the low — and its shape is the essay’s main assumption. Nothing here computes a wake, its width or its position, and a real one’s behaviour depends on the wing’s planform, the fuselage and the flap setting.

The post-stall wing moment is prescribed too. That separation moves the centre of pressure forward is correct; how far, and how fast with incidence, is an input rather than a result.

A rigid aeroplane at one weight and one centre of gravity. The trim points move with the centre of gravity, and an aft centre of gravity makes the deep trim easier to reach and harder to leave — which is why the loading limits on such aircraft are what they are.

And nothing here is unsteady. The figures are equilibrium diagrams: they say where the aircraft can sit, not how it gets there or how long it takes. Whether a given entry actually reaches the deep trim depends on the dynamics — the pitch rate, the inertia, the elevator’s timing — and a static diagram cannot answer it.

The assertion behind these figures is the one that could reject and does the work: the conventional layout must have no stable trim past the stall and the T-tail must have one, so that the comparison is a comparison rather than two drawings of the same thing; and full nose-down elevator must fail to remove the deep trim, since a model in which the elevator recovered would be modelling a different and much less interesting aeroplane.

Who found it, and when #

The deep stall arrived with the rear-engined jet transport, which is to say around 1963, and it arrived in the worst possible way: in flight test, fatally, more than once. The BAC One-Eleven prototype was lost in October 1963 in a deep stall entered deliberately during stall testing; the crew’s inability to recover, and the recorder’s evidence of a stable high-incidence descent, is what identified the phenomenon.

The word “deep” was chosen carefully and it is the right one. The aircraft is not more stalled in the sense of being further past a boundary that means anything; it is at an incidence in a region where the ordinary categories do not apply, held there by a moment balance rather than by a failure.

Trident, One-Eleven, and later the T-tail business jets all carry the lesson in their certification requirements, and the stick pusher is its monument: a system whose whole purpose is to prevent an aircraft from reaching a place it can reach and cannot leave.

The word this rung is really about #

Both rungs below this one are complaints about a word doing two jobs. Stalling speed is a speed the wing does not know; stall-spin names a sequence as though it were a cause. This rung’s word is the same word again and its second job is the largest.

A stall in the rung below is a wing at 16 degrees, at the top of its lift curve, having just stopped making more lift for more angle. A deep stall is a wing at 31 degrees, on the flat part of the curve, in a flow field with almost nothing in common with the first. The two conditions are fifteen degrees apart, they behave completely differently, and one word covers both — which is why “the aircraft stalled” carries almost no information about what happened.

The vocabulary that would help exists in the technical literature and does not reach a cockpit: stall onset, post-stall, and deep stall are three distinct regimes with three different sets of governing behaviour, and the drills that apply in each are different drills.

What makes this more than pedantry is that the recoveries conflict. Reducing incidence recovers the first. The second needs the yaw stopped before the incidence is reduced. The third needs neither, because it needs not to have happened. A single word covering three conditions with three incompatible responses is a vocabulary that will be used wrongly under pressure, and it has been.

That is the shape of every entry in this field, arriving one last time on the ladder that started it: a term that is correct as far as it goes, generalised past the range in which its consequences hold.

Where the ladder goes next #

This anchor now has the stall as an angle, the stall as an instability in roll, and the stall as a trim point. The three are the same wing at three depths past the same peak.

The rung above is the flat spin, where this rung’s motion and the last one’s meet. An aircraft autorotating at very high incidence has lost its aerodynamic damping in all three axes at once, its control surfaces are all inside separated wakes, and it descends nearly level while rotating — a condition with the deep stall’s self-maintaining character and the spin’s rotation, and recoverable from neither’s drill. What makes it a distinct rung rather than a combination is that the inertial couplings between the axes, which are negligible in both of the rungs below, are what hold it.

The one beside it is the hysteresis this essay’s static diagrams point at and do not compute. The incidence at which an aircraft enters a stalled condition and the incidence at which it leaves one are not the same, because the separated flow does not reattach where it detached. That is a loop rather than a curve, its area is a genuine quantity, and it is the reason a stall recovery requires reducing the incidence considerably further than the value it stalled at — which is a state that depends on the path taken to reach it, in the terms this collection uses elsewhere.