The Stall: Separation and the Critical Angle

The subsonic module used the boundary layer whenever it needed it (for friction drag, for the slot, for vortex generators) and always promised the full story later. This is later. The stall is a boundary-layer event from beginning to end: a thin film of air losing a fight against a pressure rise. This lesson builds that film properly, laminar against turbulent, transition, separation, and then follows an aeroplane being flown slower and slower, degree by degree of angle of attack, through everything the pilot sees, feels and must not do on the way to the stall and just past it.

The boundary layer, properly defined

Air has viscosity: it sticks to surfaces. The molecules in direct contact with the wing do not move over it at all, and each layer above is dragged along a little faster than the one below, until, within a surprisingly short distance, the flow reaches the full local speed. That sheared film is the boundary layer: the thin layer between the surface and the free flow in which the velocity climbs from zero at the surface to effectively the free-stream value at its outer edge. Everything about friction, separation and the stall happens inside it.

The layer comes in two states, and the difference runs this whole module:

Laminar — near the leading edge: the air moves in smooth, parallel sheets that never mix. A laminar layer is extremely thin: on a wing, of the order of a millimetre or two; and because the shearing between its orderly sheets is gentle, its friction drag is low. That is its whole advantage, and designers chase it. Its weakness is the same orderliness: nothing stirs the layer, so the air closest to the surface, robbed of speed by friction, is never re-supplied with energy from above: the laminar layer is low on energy exactly where it matters.
Turbulent — downstream of the transition point, where the orderly sheets break down into mixing eddies: several times thicker (centimetres, growing toward the trailing edge) with higher friction drag from all that churning, but with one compensating virtue. The mixing continuously hauls fast air from the outer edge down toward the surface, so the turbulent layer's near-surface flow stays energetic.

Thin and cheap but weak; thick and costly but strong — that trade is the boundary layer in one sentence.

Separation, and who resists it

Why does the energy matter? Because of what the two-dimensional lessons called the pressure recovery. Behind the suction peak the pressure rises toward the trailing edge, and the boundary layer must climb that rise: flow moving from low pressure into higher pressure, decelerating all the way. The free flow outside has speed to spend; the layer's near-surface air, already slowed by friction, may not. Where it runs out, the flow stops following the surface, reverses underneath, and peels away: separation, at the separation point. And this is where the two layers part company: the laminar layer separates far more easily, because its unstirred near-surface air has the least energy and no way of getting more, while the turbulent layer's mixing keeps feeding energy down to the surface; it can climb a pressure rise that would have stripped a laminar layer off long before. Every boundary-layer device this course has met (the slot, the vortex generator) works by managing exactly this contest, and the stall-warning lesson ahead adds one more to the list.

Turning up the angle of attack

Now put the layer on a wing and slowly raise the angle of attack. Each degree deepens the suction peak near the leading edge, and a deeper valley means a steeper climb out: the pressure rise over the aft part of the wing grows harsher, and the flow over the aft part slows down more with every degree. The separation point answers. At cruise angles it sits near the trailing edge, giving up only a sliver of the surface; as α increases and the recovery steepens, it moves forward along the upper surface, and the separated region behind it widens. Meanwhile, under the nose, the forward stagnation point slides aft along the lower surface, the two-dimensional lesson's migration, now near its end stop. For a while the lift keeps rising: the growing angle adds more than the growing separation takes away. At the critical angle of attack,

\alpha_{crit}

, the balance tips: separation claims so much of the upper surface that lift can rise no further. This is the top of the lift curve,

C_{L\,max}

; beyond it the lift falls away, sharply on some wings, more gently on others: the stall.

Two companions travel with that widening separation, and the syllabus asks for both. The drag rises steeply: the growing separated wake adds form drag in quantity, on top of the induced drag already climbing with the lift coefficient; approaching the stall, the total drag curve is on its steep low-speed rise. And the centre of pressure moves: on a straight wing it presses aft as the suction peak collapses, pitching the aircraft nose-down at the break; on a swept wing the tips (which sit aft) tend to stall first, so the centre of pressure moves FORWARD and the aircraft pitches nose-UP into the stall: the dangerous reversal that the special-stalls lesson takes up in full.

What the pilot notices on the way

That widening separated region announces itself before the stall arrives, and the announcements are exam material. The separated air leaving the wing is not smooth; it is a broad, turbulent, eddying wake, and when that wake washes over the airframe behind the wing, most noticeably the tailplane, the aeroplane shakes: the natural pre-stall buffet. At the same time the flight controls go slack. The elevator and rudder sit in the low-energy wake, and the ailerons work in air whose dynamic pressure has fallen with the airspeed and, if separation spreads far enough outboard, in disturbed air too. Control forces lighten, responses grow sluggish, and the crisp feel of normal flight dissolves: a warning delivered through the pilot's hands.

The slack controls carry a danger of their own. Close to the stall, the instinct to lift a dropping wing with aileron is exactly wrong: deflecting an aileron down increases the local angle of attack of a wing section already at the edge of stalling, and can push that wing over the edge: the aircraft rolls further the way the pilot tried to stop, the entry condition for the spin of a later lesson. Large or abrupt control inputs of any kind, applied to surfaces working in disturbed slow air, can trigger the stall asymmetrically. The discipline near the stall: reduce the angle of attack first (pitch down), prevent further yaw with gentle rudder (never coarse rudder, which at this angle of attack is itself a spin trigger), and roll level with aileron only once the wing is flying again.

The stall and just after

Take a straight-wing aeroplane past the critical angle, and its normal post-stall behaviour is surprisingly benign, by design. The wing's lift falls sharply and the nose drops: the centre of pressure jumps aft at the stall, and the collapsing downwash unloads the tailplane's working conditions (both pitch the nose down) while the lift deficit, unable to keep supporting the weight, sets the aircraft sinking. One wing usually lets go slightly before the other, so a wing drop often comes with it. The nose-drop is the recovery half-done: with the nose down, the angle of attack falls back below the critical angle, the flow re-attaches, and the wing flies again: the pilot's job is to let it happen, ease out of the dive, and accept the height loss. This benign behaviour is the payoff of the docile root-first stall pattern that the subsonic module described for straight wings.

The deterrent buffet

One refinement of the buffet story closes the lesson. On many aeroplanes (large transports especially) the pre-stall buffet does not stay a gentle tremor: as the separation spreads, it grows into a shaking so heavy and unmistakable that no pilot would mistake it or willingly keep pulling through it. That is the deterrent buffet: buffet strong enough to deter any further increase in angle of attack. Certification builds on exactly this: where a wing has no sharp natural lift break, the deterrent buffet itself is accepted as the stall limit: the point at which the aircraft is defined to be stalled, from which the scheduled stall speeds are measured. The buffet is not merely a symptom on such aircraft; it is the boundary. And it has a high-speed twin: on a clean wing at high Mach number, shock-induced separation produces the same deterrent shaking from the FAST side: the buffet-boundary lesson of this module maps both walls.