Aerofoil and Wing Geometry - ATPL 081 — Principles of Flight

Before the next lesson puts forces on a wing, this one builds the vocabulary those forces are described with. Every shape parameter defined here is exam material in its own right ('describe the taper ratio' is a real question), but the deeper reason to learn them properly is that the whole subject argues in these words: the stall lessons will blame tip stall on taper, the high-speed lessons will credit sweep with delaying shock waves, and the stability module will lean on dihedral. A candidate who owns this vocabulary reads every later lesson faster.

The aerofoil section

Slice a wing parallel to the direction of flight and the cut surface you expose is the aerofoil section: the curved, teardrop-like profile that actually does the aerodynamic work. Its shape is a designed compromise, and each of the parameters below is one of the design choices. First, the two edges:

Leading edge — the front of the section, the first part to meet the oncoming air; here the flow divides into the stream passing over the upper surface and the stream passing under the lower one.
Trailing edge — the sharp rear edge where the two streams rejoin and leave the section. Its sharpness is not cosmetic: a sharp trailing edge forces the flow to stream off smoothly rearwards rather than curl around the back, and that clean departure is a precondition for the pressure pattern that generates lift.

The figure below maps every term this section is about to define. Keep referring back to it as each one is introduced.

The chord line is the straight line joining the leading edge to the trailing edge, and its length is the chord (symbol c). The chord line is the section's ruler and reference: the angle of attack in the next lesson is measured between the airflow and this line, and every position on the section (for example 'maximum thickness at 30% chord') is quoted as a percentage of the chord, measured back from the leading edge.

The thickness of the section is its depth from upper to lower surface, and it is quoted as the thickness-to-chord ratio (or relative thickness): maximum thickness divided by chord, in per cent. A training aircraft wing sits around 12–15%; a jet transport nearer 9–13%. Thicker sections give more room for the wing spar and fuel, generate lift more willingly at low speed and stall more gently, but they pay in drag, and, decisive for jets, they accelerate the flow over themselves more strongly, which lowers the critical Mach number: the speed at which the airflow over the section first reaches the local speed of sound, beyond which shock waves form (the high-speed module's subject). Where that maximum thickness sits matters too: the location of maximum thickness is quoted in % chord from the leading edge: around 25–30% for classic subsonic sections, and pushed further aft (aviation's word for rearward, toward the tail; its opposite, toward the nose, is forward) on high-speed sections to keep the acceleration of the flow, and therefore the shock formation, as mild and as late as possible.

Halfway between the upper and lower surfaces runs the camber line (or mean line): the curve every point of which lies equidistant from both surfaces. If the section is curved (upper surface more arched than the lower), the camber line bows above the chord line, and the maximum distance between the two, quoted in % chord, is the camber. Camber is the section's built-in asymmetry: a positively cambered section already deflects the flow downwards at zero angle of attack, so it generates lift before the wing is inclined at all. Typical cruise wings carry a few per cent of positive camber.

The nose radius describes how blunt or sharp the leading edge is: formally the radius of the circle that fits into the nose of the section. It is a quiet parameter until the stall lessons: a generous, blunt nose lets the flow negotiate high angles of attack progressively, giving a gentle stall with warning; a small, sharp nose makes the flow let go of the leading edge suddenly, giving the abrupt stall behaviour of thin high-speed wings.

Finally the symmetry distinction:

Symmetrical section — the camber line and the chord line coincide: the camber is zero, and the upper and lower surfaces are mirror images. Such a section generates no lift at zero angle of attack and behaves identically upright and inverted, which is exactly why tailplanes, fins and aerobatic wings use it.
Asymmetrical (cambered) section — has its camber line displaced from the chord line; above it for the usual positive camber: lift already at zero angle of attack, and better lifting economy the right way up. (Displaced below, the rarer negative camber of some tailplanes.)

The wing planform

The section describes one slice; the planform describes the whole wing as seen from directly above: rectangular, tapered, elliptical, swept or delta. Each planform is a compromise the later lessons will unpack; this lesson defines the measurements that describe any of them.

Two measurements set the planform's scale:

Span (symbol b) — the straight-line distance from wing tip to wing tip, measured right through the fuselage.
Wing area (symbol S) — the area of the planform, and by convention it includes the part of the wing 'buried' in the fuselage, as if leading and trailing edges continued to the centreline.

That convention matters because S is the reference area of the entire subject: the force coefficients the following lessons introduce divide a force by q and by this S, so everyone must agree what S means.

On a tapered wing the chord shrinks outboard, and three terms describe it:

Root chord — the chord where the wing meets the fuselage.
Tip chord — the chord at the tip.
Taper ratio (symbol $\lambda$ ) — their ratio, tip over root.

A rectangular wing has $\lambda = 1$ ; a pointed delta approaches 0. Designers taper wings because it concentrates lift where the structure is strongest and brings the lift distribution closer to the aerodynamically ideal elliptical shape, but the stall lessons will show the price: strong taper works its small tip sections at the highest local lift coefficients and pushes the stall towards the tips, where the ailerons live.

Two average chords compress the planform into one number each. The mean geometric chord is simply area over span:

That is the chord of the rectangular wing that would have the same span and area. The mean aerodynamic chord (MAC) is subtler: it is the chord measured where the wing behaves, aerodynamically, like the whole wing in miniature, and it is the industry's longitudinal ruler. Centre-of-gravity positions on the loadsheet, the aerodynamic centre in the stability module, forward and aft CG limits: all are quoted as percentages of the MAC ('CG at 27% MAC'). On a rectangular wing MAC and mean geometric chord coincide; on tapered and swept wings the MAC sits outboard of the root and is found from the manufacturer's data rather than computed in the exam.

The most consequential planform number is the aspect ratio, the wing's slenderness:

The second form, span squared over area, is the one to memorise: it works for any planform, tapered or not. Interpretation: a high aspect ratio means a long, narrow wing; a low one, short and stubby. Gliders sit at 20–35, airliners around 9–11, fighters at 2–4. The three-dimensional-airflow lesson will show why gliders go to such lengths: the longer and narrower the wing, the weaker the tip effects that create induced drag. The price is structural (a long slender wing is heavy or flexible) and a slower roll rate, which is why the fighter sits at the other extreme.

Three angles finish the planform picture, each one a lever a later module pulls. The first two:

Sweep angle — measured between the wing (conventionally its quarter-chord line) and the aircraft's lateral axis; sweeping the wing back is the jet age's answer to the compressibility problem (it raises the critical Mach number, as the high-speed module explains) at a cost in low-speed manners.
Dihedral angle — the upward tilt of the wings seen from the front (downward tilt is anhedral); its purpose is lateral stability: a sideslipping aircraft with dihedral meets the air at slightly different effective angles on each wing and rolls itself level again, the mechanism the stability module works through in detail.

Wing twist comes in two forms with one shared aim:

Geometric twist (washout) — mounts the tip sections at a smaller incidence than the root, so the tip meets the air at a lower angle of attack.
Aerodynamic twist — changes the section shape along the span to the same effect.

Both are stall insurance: they make the root reach its stalling angle first, so the buffet warning starts inboard while the tips (and the ailerons mounted on them) keep flying and keep the pilot in control.

Last, a definition the exam loves precisely because the world is sloppy with it. The angle of incidence is the fixed angle between the wing root's chord line and the fuselage's longitudinal axis: chosen once by the designer, typically so the cabin floor is level in cruise, and unchangeable in flight. It is NOT the angle of attack: the angle of attack (next lesson) is measured against the airflow and changes constantly as the aircraft manoeuvres. The confusion is worth guarding against, because some (particularly older British) textbooks use 'angle of incidence' for what EASA calls angle of attack; the exam follows the EASA meaning: incidence is fixed rigging, attack is flight-variable.

What the exam asks

This lesson's questions are definition work with two twists. The overview follows the learning objectives; expect to:

Describe every section parameter in one sentence: leading edge, trailing edge, chord line, thickness-to-chord ratio and the location of maximum thickness, camber line and camber, nose radius, symmetrical versus cambered sections

Describe every planform parameter: span, root and tip chord, taper ratio, wing area (including the fuselage-buried part), the planform shapes, mean geometric chord, MAC, aspect ratio, sweep, dihedral, wing twist, angle of incidence

Recognise the correct definition among near-misses: the classic distractors swap camber line and chord line, or define aspect ratio as span over area instead of span squared over area

Compute: aspect ratio from span and area, taper ratio from the two chords, mean geometric chord from area and span; one-line arithmetic with the formulas above

Match parameter to consequence: sweep → critical Mach number, dihedral → lateral stability, washout → stall sequence, nose radius → stall abruptness

Keep the fixed angle of incidence strictly apart from the flight-variable angle of attack

The aerofoil section

Check you understood

The wing planform

What the exam asks