Spanwise Flow and Wingtip Vortices

Every lesson so far has flown an infinite wing: a two-dimensional section with no tips, where the flow stays neatly in its vertical plane. Real wings end. At the tip, the pressure difference the wing lives on finds a way around the edge, and that single leak reorganises the entire flow field. This lesson follows the consequences across the span: spanwise flow, the wingtip vortices, the shape of the lift distribution, and the wake an aircraft trails behind it: turbulence strong enough to upset the next aircraft on the approach. The drag all of this creates (induced drag) is the next lesson's subject.

The angle of attack, one more time

Before anything three-dimensional, one small change of reference. The angle of attack is still the angle between the relative airflow and a reference line, but for a two-dimensional section that reference is the chord line, while for the three-dimensional aeroplane the examiner's chosen reference is the longitudinal axis: the fuselage datum line running nose to tail. The two references differ by exactly the angle of incidence from the geometry lesson (the fixed angle at which the wing is bolted on), so the two α values differ by that constant. Nothing physical changed; only the ruler did. Exam questions state which reference they mean: read for it.

Far more important operationally: the angle of attack is not the attitude. Attitude (pitch attitude) is the angle between the longitudinal axis and the horizon: what you see out the window and on the attitude indicator. The angle of attack is measured against the relative airflow, which follows the flight path, wherever that leads. The two agree only in level flight. Push into a descent holding the nose level: the flight path now slopes down, the relative airflow comes from below the horizon, and the angle of attack is larger than the attitude suggests. The extreme makes it vivid: an aircraft mushing nearly level-nosed but sinking fast can be beyond the critical angle of attack: stalled with an apparently normal attitude. The attitude indicator shows where the nose points; only the flight path says where the air comes from. The airflow-and-force lesson's whole-aircraft figure drew exactly this geometry.

The flow around the whole aircraft

The streamline pattern of the two-dimensional lessons survives around the real machine, joined by its neighbours:

The wing — upwash ahead, crowded fast flow over the upper surface, downwash behind: as before.
The fuselage — a streamlined body at nearly zero effective camber: the flow splits at its nose, accelerates gently around the widest section, and closes again toward the tail, making little lift but its own share of friction and form drag.
The tail section — flies in air the wing has already deflected: the tailplane sits in the wing's downwash, so its local airflow arrives from above the free stream's direction, and everything the wing does to its downwash (every flap selection, every change of α) changes the tailplane's working conditions. The stability module builds on precisely this coupling.

Where spanwise flow comes from

Now to the tips. The wing works by keeping overpressure below and suction above: a pressure difference maintained across a surface that simply ends at the tip. Air does what pressure differences tell it: at the tip, the high-pressure air from below spills around the edge into the low-pressure region above. That escape at the ends tilts the pressure field along the whole span, and the flow over the surfaces picks up a sideways lean. On the lower surface the flow drifts outward, toward the tip: the high-pressure air is flowing toward the one place it can escape. On the upper surface the flow drifts inward, toward the root: air arriving over the tip crowds the outboard upper surface, and the suction is deepest inboard, so the surface flow leans away from the tip. Two sheets of air leave the trailing edge with opposite sideways drifts, meeting at an angle.

The wingtip vortices

Follow the spilling air around one tip and it does not just leak; it rolls. Coming up around the tip from the high-pressure side to the low, and swept rearward by the free stream at the same time, it corkscrews into a rotating column of air trailing behind the tip: the wingtip vortex. Seen from behind the aircraft, the right-hand vortex rotates anticlockwise and the left-hand one clockwise, both curling over the tip from below to above, which means that between the two vortices, across the whole span behind the aircraft, their rotation drives the air downward. The trailing vortices are therefore a downwash machine: they add to the downwash the section already produced, and (the detail the next lesson turns into drag) they bend the airflow down not only behind the wing but already at it. All along the trailing edge, the angled meeting of the two surface flows sheds a whole sheet of small vortices, and within a few spans this sheet rolls up into the two big tip vortices: tidy, persistent, and carrying the energy the wing spent making them.

How the lift spreads across the span

The tip leak also means the wing cannot lift evenly along its span. At the tips the pressure difference is being short-circuited, so the lift per metre of span falls away to zero at the tip; inboard, the wing works closer to its two-dimensional self. Plot lift per unit span against span position and you get the spanwise lift distribution. The aerodynamic ideal is the elliptical distribution (lift tapering along a smooth half-ellipse from root to tip) because, as the next lesson shows, it wastes the least energy in the trailing vortex sheet for a given span and total lift. Before comparing planforms, keep two different questions apart: where the load sits (lift per metre of span), and how hard each metre of wing works: the local lift coefficient, which is that load divided by the local chord. The stall follows the second question, not the first. With that distinction in hand, the planform decides how close a wing comes:

Elliptical planform (the Spitfire's wing): delivers the ideal distribution exactly.

Rectangular — the constant chord spreads the load more evenly than the ellipse: slightly less at the root, slightly more over the outer span. Divide that load by the constant chord and the local lift coefficient is highest at the root, so the root reaches its stalling angle first: the separated root flow buffets the tailplane as a natural stall warning while the tips, and the ailerons on them, keep flying, which is what makes rectangular wings so docile.

Strongly tapered — the shrinking chord concentrates the load inboard: more than the ellipse at the root, less toward the tip. But the load falls toward the tip more slowly than the chord shrinks, so each metre of the small tip chord is worked harder: the local lift coefficient rises toward the tip: the classic tip-stall tendency that the geometry lesson's washout exists to tame.

Moderate taper approximates the ellipse well, which, together with the geometry lesson's structural and stall arguments, is why moderate taper is what airliners actually fly. One honest qualifier on the word ideal: elliptical loading gives the minimum induced drag for a fixed span and fixed total lift. Constrain the root bending moment instead (the quantity that actually sizes the wing spar) and the optimum shifts slightly inboard of elliptical, which is why transport wings often deliberately carry a little more of their load inboard than the ellipse would.

Wake turbulence

To the aircraft flying behind, the trailing vortex pair is known as wake turbulence, and it is dangerous for a concrete reason: an aircraft that flies into one of the vortices is rolled by it. The vortex is a column of rotating air; an aircraft entering it near the core has one wing pushed upward and the other pushed downward, and if the vortex is strong enough (or the following aircraft small enough) that imposed roll can exceed the full authority of its ailerons: the pilot holds maximum opposite aileron and the aircraft rolls anyway. A light aircraft following a heavy one closely can be rolled past the vertical at a height where recovery is impossible. Everything that follows in this section (where the wake goes, how long it lives, which aircraft make it worst) exists to keep aircraft out of that situation. The cause is exactly what this lesson built: the tip vortices of a lifting wing, which is why the wake begins at rotation (when the wing starts lifting) and ends at touchdown. Behind the aircraft it takes the shape of two counter-rotating columns, each starting a short way inside its wingtip. They drift slowly downward (they sit in each other's downwash) and level off typically 500–1,000 ft below the flight path; near the ground they cannot keep sinking, so they move apart sideways, and a crosswind can hold one vortex stubbornly over the runway or carry it onto a parallel one. In calm air the pair persists for minutes, decaying fastest in strong wind and turbulence, which tear it up.

The parameters that set its severity read straight off the vortex-strength logic:

Weight — more lift, stronger vortices: the dominant factor, hence wake-turbulence separation categories by aircraft mass.

Speed — slower means higher $C_L$ , stronger vortices.

Configuration — clean concentrates the shed swirl at the tips.

Wingspan — for the same weight and speed, a shorter span packs the lift into a more tightly wound, stronger vortex pair; a longer span spreads the load and spaces the vortices further apart.

The memorable worst case: heavy, slow and clean: precisely a large aircraft shortly after rotation or on an intermediate approach. Which is why the separation minima protect exactly the aircraft rotating behind a departing heavy, and why you cross a preceding heavy's path above it, never below: its wake lives below and behind.