Atmosphere & aerofoil

081 Principles of FlightChapter 1

The flight environment

Key fact

The atmosphere extends to approximately 500 miles / 900 km. Pressure, density, and temperature decrease with altitude. Air is compressible and has weight. Dry air performs better than humid air because water vapour is less dense than dry air.

Formula — Universal gas law

p / (ρ × T) = constant

Where p = pressure (N/m²), ρ = density (kg/m³), T = absolute temperature (K). Applies to a perfect gas.

Key fact

Density ∝ pressure — double pressure, double density. Density ∝ 1/temperature — double temperature, halve density. Humidity decreases density (dry air at ISA MSL ≈ 1.225 kg/m³; water vapour ≈ 0.760 kg/m³).

SI units & wing loading

Definition — Wing loading (W/S)

Aircraft weight divided by wing area. Unit: N/m². Higher wing loading → higher stall speed and steeper approach.

Key fact

Mean geometric chord = wing area ÷ wing span. MAC (mean aerodynamic chord) — chord of a rectangular wing with the same moment and lift characteristics as the actual wing. Relative thickness is expressed as % chord.

Wing geometry

Definition — Aspect ratio (AR)

AR = span² / wing area or span / average chord. High AR = long thin wing; low AR = short stubby wing.

Definition — Taper ratio

CT / CR (tip chord ÷ root chord). Sweep angle — angle between a line at 25% chord (root to tip) and a line perpendicular to the root chord.

Key fact

Gross wing area includes the portion cut out for the fuselage. Net wing area excludes the fuselage portion. Dihedral — angle between the wing plane and the horizontal in unbanked level flight (also: angle between 0.25 chord line and the lateral axis).

Aerofoil types

Definition — Symmetrical aerofoil

At 0° AoA: no lift, no pitching moment, CP stationary with AoA increase. Drag only.

Definition — Positively cambered

At CL = 0: negative AoA, pitching moment down.

Definition — Negatively cambered

At CL = 0: positive AoA, pitching moment up (used on tailplane/elevator for downforce).

Angles — do not confuse

Term	Definition
Wing AoA	Angle between chord line and relative airflow
Aircraft AoA	Angle between longitudinal axis and speed vector (FSA)
Angle of incidence	Fixed angle between longitudinal axis and wing root chord
Pitch angle	Angle between longitudinal axis and horizontal
Wing AoA	Aircraft AoA + incidence angle

Exam trap

Pitch angle ≠ AoA. Same AoA can exist at different pitch angles (climb vs level). AoA is unaffected by density — at constant IAS in level flight, AoA stays the same as altitude increases and TAS rises.

Pressure, Bernoulli & continuity

Key fact

Dynamic pressure q = ½ρV² (TAS). q = 0 when speed = 0. Total pressure = static + dynamic (PT = PS + q). Streamlines converge → velocity increases, static pressure decreases. Streamlines diverge → opposite.

Formula — Equation of continuity (incompressible, below M0.4)

A₁ × V₁ = A₂ × V₂   (mass flow constant)

When cross-sectional area reduces, velocity must increase.

Definition — Stagnation point

Where relative velocity = 0; static pressure at maximum (= total pressure). Moves forward/up as AoA decreases; moves down as AoA increases until critical AoA.

Centre of pressure & aerodynamic centre

Definition — Centre of pressure (CP)

Point on chord where total aerodynamic reaction acts. On symmetric airfoils CP does not move. On cambered wings CP moves forward as AoA increases until stall, then moves aft to ~50% chord at stalling angle.

Definition — Aerodynamic centre (AC)

Fixed point at approximately 25% chord — pitching moment coefficient constant with AoA (assuming no flow separation). Do not confuse AC with CP.

Airspeed definitions

Key fact

IAS — indicated on ASI. CAS/RAS — IAS corrected for position and instrument error. EAS — CAS corrected for compressibility (above ~300 kt). TAS — EAS corrected for density. Mnemonic: ICE-T.

Key fact

At constant IAS in level flight (no compressibility): TAS increases with altitude, CL constant, AoA constant. Double IAS → lift × 4, CL = 1/ratio².