Airflow and Aerodynamic Force - ATPL 081 — Principles of Flight

The first lesson supplied the physics (Bernoulli, continuity, dynamic pressure); the second supplied the vocabulary of shapes. This lesson is the payoff: how moving air actually takes hold of an aerofoil, and how that grip is described as one resultant force, its two components (lift and drag) and a twisting moment. Everything the rest of the subject does is a refinement of the picture built here.

Describing moving air

Flow comes in two characters:

Steady flow — the conditions at any fixed point (speed, direction, pressure) do not change with time: watch one spot next to the wing and the air there behaves the same from one second to the next, even though individual air parcels are streaming past.
Unsteady flow — the picture itself changes with time: gusts, turbulence, and the churning separated flow near the stall are all unsteady.

Both are easy to picture. In a wind tunnel, smoke filaments drawing smooth, motionless lines past a model are steady flow made visible; behind a stalled wing, the same filaments tear and swirl: unsteadiness made visible. The buffet a pilot feels approaching the stall is that unsteadiness arriving at the airframe as a vibration. The distinction earns its keep because almost every tool in this subject, Bernoulli's equation first among them, assumes steady flow; where the flow turns genuinely unsteady, the neat theory frays, which is exactly why the stall gets its own module.

Steady flow can be drawn. A streamline is a line that is everywhere tangent to the local flow direction: the path a weightless particle would trace. Two properties follow directly from that definition, and the exam uses both: no air ever crosses a streamline (the flow runs along it, never through it), and two streamlines can never intersect: at an intersection the air would need two directions at once, which is impossible. Bundle a set of streamlines together and the enclosed volume is a stream tube: an invisible pipe whose walls no air crosses. That is precisely what makes the equation of continuity from the first lesson so widely useful: a stream tube behaves exactly like the venturi's solid tube, no walls required. Where streamlines crowd together the tube has narrowed, so the flow there is faster and, by Bernoulli, its static pressure lower; where they spread apart, the reverse. A streamline picture is therefore a pressure map: read the spacing and you read the pressures.

One more idealisation and the toolkit is complete:

Two-dimensional flow — the wing is imagined as infinitely long with the same section throughout, so the flow over every slice is identical and moves only in the plane of the section: chordwise and vertically, never along the span.
Three-dimensional flow — every real wing: the tips exist, pressure differences can reach around them, and the air acquires spanwise velocity components as well.

The leak has a definite mechanism: this lesson will shortly show that a lifting wing carries suction above and overpressure below, and at the tip those two regions meet with nothing between them, so air curls from the high-pressure underside around the tip into the low-pressure top, dragging the whole flow field slightly spanwise. The difference matters enormously (that curling flow becomes the tip vortices and induced drag of a later lesson), but it is studied separately on purpose: two-dimensional flow isolates what the section's shape does, and the three-dimensional effects are then added as corrections.

The angle of attack

Before the forces, the one variable they all answer to. The oncoming flow, as the aircraft experiences it, is called the relative airflow (or relative wind): it is equal and opposite to the aircraft's path through the air: fly forward and slightly upward, and the air comes at you from ahead and slightly above. The angle of attack (symbol α, alpha) is the angle between the chord line and that relative airflow. Note both halves of the definition: it is measured against the airflow, not the horizon (an aircraft can hold a large angle of attack in level, climbing or descending flight alike) and against the chord line, the fixed reference the geometry lesson established. Unlike the rigging-fixed angle of incidence, the angle of attack changes continuously in flight, under the pilot's direct control through the elevator. It is the master variable of this subject: nearly every curve in the lessons ahead (lift, drag, moment, stall) is plotted against α.

Three different angles share this neighbourhood, and exam distractors are built by swapping them. The way to keep them apart is to name each angle's two reference lines: every angle is a pair, and no two of these share the same pair:

Angle of attack — chord line ↔ relative airflow. Changes continuously in flight; the aerodynamic angle.
Angle of incidence — chord line ↔ fuselage longitudinal axis. Fixed by the designer when the wing was rigged; no control input can change it.
Pitch attitude — fuselage axis ↔ horizon. What the attitude indicator displays. It is the only one involving the horizon, and by itself it says nothing about how the wing meets the air.

The pressure distribution and the resultant force

Combine the streamline picture with Bernoulli and the origin of aerodynamic force appears. At a positive angle of attack the flow splits at the stagnation point just under the nose: the one spot where the air is brought completely to rest and the full total pressure acts. Over the curved upper surface the stream tubes narrow, the flow accelerates well above the free-stream speed, and the static pressure falls distinctly below the surrounding atmospheric static: a suction acting outward on the skin. Under the lower surface the flow is slowed somewhat, and its static pressure rises modestly above ambient. Every point of the section's surface therefore carries its own pressure, the whole pattern forming the pressure distribution, and the upper surface's suction typically contributes roughly twice as much to the total force as the lower surface's overpressure, a proportion worth remembering because candidates habitually credit the wrong surface. The full anatomy of this pattern (how it reshapes as camber and angle of attack change, the upwash ahead of the wing and downwash behind it, how the stagnation point migrates, and why the centre of pressure and the aerodynamic centre are two different points) is the entire subject of the next lesson; here the pattern only needs to exist and to sum.

Sum all of those little pressures over the whole surface (plus a small skin-friction contribution the drag lessons return to) and they add to a single resultant aerodynamic force. Its point of origin on the chord line (the point through which the resultant acts) is the centre of pressure (CP). Its direction: tilted upwards and rearwards: upwards because the pressure imbalance mostly pushes the section away from its upper surface, rearwards because the air also resists being pushed through. The centre of pressure is not a fixed point: it sits typically around a quarter to a third of the chord back from the leading edge and moves as the angle of attack changes, a behaviour with consequences that the stability lessons pick up.

Lift and drag

One tilted force is awkward to work with, so it is resolved into two components defined against the relative airflow:

Lift — the component perpendicular to the relative airflow.
Drag — the component parallel to it, acting rearwards.

The reference matters and the exam tests it mercilessly: lift is NOT defined as perpendicular to the chord line, and NOT as pointing away from the earth. In a climb or a descent the relative airflow is inclined, so the lift vector is inclined with it: perpendicular to the flight path, not vertical. Splitting the force this way is not cosmetic bookkeeping: lift is the useful part, the reaction that carries the weight, while drag is the tax paid for generating it, the part thrust must continuously pay off. Both, being pressure forces, scale with the dynamic pressure q of the first lesson: double the q and, other things equal, the whole resultant doubles with both its components.

One more consequence of the definition, and the answer to a natural question: what happens to the split when the aircraft is not flying straight and level? Nothing — and that is the point. The components follow the relative airflow, wherever it comes from. In level flight the airflow is horizontal, so lift happens to point vertically. In a climb or descent the path is inclined, the airflow is inclined with it, and lift leans accordingly. And when the aircraft banks, the whole aircraft (wing, chord line and lift vector together) rolls about the flight path, so lift now points partly sideways: that sideways part is what curves the aircraft into the turn, and only the remaining vertical part is left to carry the weight, which is why a level turn demands more total lift than level flight. How much more (and how thrust, drag, lift and weight balance in climbs, glides, turns and engine-out flight) is the business of the flight-mechanics module at the end of this course; this lesson fixes the definitions those balances are built from.

The aerodynamic moment

The pressure distribution does one more thing: because the suction and overpressure are spread unevenly along the chord, the aerodynamic force also twists the section. This twisting tendency is the aerodynamic moment (a pitching moment, in newton-metres): the tendency of the distributed pressures to rotate the section nose-up or nose-down about whichever reference point it is quoted about. A moment is always force times arm (the same reason a door opens easily from its handle and barely from its hinge), so the twist depends not just on how hard the pressures push but on where along the chord they push relative to the reference point: suction acting ahead of the reference twists the nose up, the same suction acting behind it twists the nose down. Its size therefore depends on everything that shapes the pressure pattern and its leverage: the dynamic pressure, the wing area, the chord length (the arm the forces work with), the camber of the section, and the angle of attack. The sign convention to memorise: nose-down is negative, nose-up is positive.

Camber decides the moment's character; take the three section families in turn:

Symmetrical section — produces no aerodynamic moment about its quarter-chord point: its upper and lower pressure patterns are mirror images that twist equally in opposite senses, and this holds at any normal angle of attack, one reason symmetrical sections suit tailplanes, which must behave predictably in both directions. The mirror symmetry has a second consequence worth noting now: the centre of pressure stays put (at that same quarter-chord point) instead of wandering as the angle of attack changes; the next lesson makes much of that contrast.
Positively cambered — carries, about that same quarter-chord point, a constant nose-down (negative) pitching moment: the aft part of a cambered section keeps generating suction well behind the quarter-chord, and lift acting behind the reference point twists the nose down.
Negatively cambered — mirrors this with a nose-up (positive) moment.

That built-in nose-down twist of every ordinary cambered wing is what the horizontal tailplane spends its life balancing: the opening problem of the stability module.

What the exam asks

This lesson's questions probe whether the definitions are exact. The overview follows the learning objectives; expect to:

Describe steady versus unsteady airflow, and say why the steady assumption underlies the theory

Explain what a streamline and a stream tube are, and use their properties: no flow across, no intersections, crowding means faster flow and lower static pressure

Describe the airflow through a narrowing or widening stream tube with continuity and Bernoulli: including numerically, computing the speed change and the static-pressure change

Explain the difference between two-dimensional flow (no spanwise component, every slice identical) and three-dimensional flow around a real wing

Define the angle of attack (chord line versus relative airflow) and keep it apart from the angle of incidence and from the horizon

Describe where the resultant force originates (the centre of pressure) and its direction (upwards and rearwards)

Resolve the resultant into lift and drag and state each component's direction (lift perpendicular to the relative airflow, drag parallel to it), reassemble them with Pythagoras, and apply the split in any attitude: in a bank the lift vector tilts with the aircraft, so less of it is left to carry the weight

Define the aerodynamic moment and list what it depends on: dynamic pressure, area, chord, camber, angle of attack

State the moment behaviour by section type: symmetrical: none about quarter-chord; positive camber: nose-down (negative); negative camber: nose-up (positive)