Subsonic Aerodynamics | Basics, Laws and Definitions | PPL(A) Principles of Flight

Subsonic aerodynamics basics, laws & definitions for PPL(A) candidates

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Basics, Laws and Definitions

Newton’s Laws of Motion

First Law (Inertia): An object stays at rest or moves at constant velocity unless acted on by an external force.

Second Law: Acceleration of a body is proportional to the net force and inversely proportional to its mass.

F = m × a

Newton’s Second Law — Applied

Use F = m × a to find acceleration when force and mass are known:

a = F ÷ m

Example: F = 100 N, m = 5 kg → a = 100 ÷ 5 = 20 m/s²

Third Law: If one body exerts a force on another, the second exerts an equal and opposite force on the first. Forces between two bodies are equal in size and opposite in direction.

Bernoulli’s Theorem

In a stream tube with negligible friction, vorticity, and Coriolis effects:

Static pressure + Dynamic pressure = Constant total pressure

This is the frictionless form. Real flows have friction losses, so an extended form of Bernoulli is required in practice.

Key relationships:

If velocity (V) increases → dynamic pressure (½ρV²) rises → static pressure drops
If velocity decreases → dynamic pressure falls → static pressure rises
Lower velocity → lower dynamic pressure → higher static pressure

Law of Continuity

For incompressible flow, mass flow rate remains constant along a stream tube:

A × V = constant → A₁ × V₁ = A₂ × V₂

A = cross-sectional area
V = flow velocity

Area change	Velocity effect
Smaller area	Higher velocity
Larger area	Lower velocity

The Venturi tube is a practical application of this law — a tube with decreasing then increasing cross-sectional area:

The throat is the narrowest section, where velocity is highest
At the throat: dynamic pressure is maximum, static pressure is minimum

Streamlines

In steady flow, a streamline is the same as a pathline or streakline. Streamlines are lines tangent to the local velocity vectors and can be visualised by particles moving with the flow.

Density and the ISA

The internationally recognised symbol for density is the Greek letter ρ (rho)
SI unit of density: kg/m³
ISA (International Standard Atmosphere) standard sea-level density: ρ₀ = 1.225 kg/m³

Airspeed and Pressure Measurement

Pitot-Static System

Airspeed is measured using a Pitot-static system:

Pitot tube → measures total pressure
Static ports → measure static pressure
Dynamic pressure = total pressure − static pressure

The airspeed indicator uses this difference to calculate airspeed.

Stagnation Point

Total pressure is measured at the point where airflow comes to a complete stop — the stagnation point.

At the stagnation point, air velocity is zero; all dynamic pressure converts fully to static pressure, causing maximum pressure at this point
On an airfoil, the stagnation point is near the leading edge, slightly below the chord line, due to airflow splitting around the wing
Aircraft use a Pitot tube facing the airflow to capture this total pressure

Indicated Airspeed (IAS) vs True Airspeed (TAS)

Basic airspeed indicators show Indicated Airspeed (IAS), calculated assuming standard sea-level density ρ₀ = 1.225 kg/m³.

True Airspeed (TAS) uses actual air density (ρ).

IAS is directly proportional to dynamic pressure and therefore directly relates to aerodynamic forces — making it the operationally important speed.

Effect of altitude:

As altitude increases → ρ decreases
To maintain the same IAS (same dynamic pressure), TAS must increase
As altitude decreases → density increases → TAS must reduce to keep IAS constant

Rule of thumb:

TAS ≈ IAS + (2% × IAS × altitude in thousands of feet)

Aerodynamic Forces

The Aerodynamic Force Formula

All aerodynamic forces — lift and drag — are calculated using the same general formula:

F = C × ½ × ρ × V² × S

Symbol	Meaning
C	Dimensionless coefficient (cL for lift, cD for drag)
ρ	Air density (kg/m³)
V	Velocity (m/s)
S	Reference surface area (m²)
F	Force in Newtons

The resultant aerodynamic force from the wing’s pressure distribution splits into two components:

Lift — acts perpendicular to the undisturbed airflow
Drag — acts parallel to the airflow, opposing motion

Resultant force = vector sum of lift and drag

Lift

Lift is the aerodynamic force component acting perpendicular to the undisturbed airflow.

Lift depends on wing shape, angle of attack, and aircraft speed
Lift direction is relative to the airflow — it is not always strictly upward

Drag

Aerodynamic drag opposes motion through a fluid.

Acts parallel to the airflow, opposite to the direction of motion
Caused by air resistance and surface friction

Airfoil Geometry

Chord Line and Chord

Chord line: straight line from the leading edge to the trailing edge
Chord: the length of the chord line — usually larger at the root than at the tip
Leading edge: the front point where the mean camber line meets the airfoil
Trailing edge: the rear point where the mean camber line meets the airfoil

Angle of Attack (AoA)

The angle of attack is the angle between the airfoil’s chord line and the undisturbed (freestream) airflow.

The lift coefficient (cL) depends on angle of attack and airfoil shape (camber and thickness)
When only angle of attack varies, it becomes the primary factor affecting cL and lift

Camber

Camber: the distance between the mean camber line and the chord line
Relative camber: maximum camber ÷ chord length
Maximum camber: the point of greatest distance between the mean camber line and the chord line
Mean camber line: a curved line equidistant from the upper and lower wing surfaces

Airfoil type	Mean camber line
Cambered airfoil	Curved; does not coincide with chord line
Symmetrical airfoil (zero camber)	Straight; coincides with chord line

Relative Thickness

Relative thickness = maximum thickness ÷ chord length, expressed as a percentage of chord
Maximum thickness = the largest distance between the upper and lower airfoil surfaces

Wing Geometry

Taper Ratio

Taper ratio = wing tip chord ÷ wing root chord (dimensionless)

Most wings have shorter tip chords than root chords for better aerodynamics and structural efficiency.

Wing type	Taper ratio
Tapered wing	< 1
Rectangular wing	= 1

Aspect Ratio

AR = wingspan² ÷ wing area (dimensionless)

For a rectangular wing (constant chord): AR = wingspan ÷ chord

Mean chord = wing area ÷ wingspan
For a rectangular wing, chord is constant, so mean chord = chord

Aspect ratio	Wing shape
High AR	Long, narrow wings
Low AR	Short, wide wings

Wing Planform Types

Rectangular wing: constant chord from root to tip — no tapering
Tapered wing: chord length decreases from root to tip
Swept-back wing: wings angle backward from root to tip (like a pointing arrow)

2D vs 3D Flow

2D flow: motion confined to a single plane — as with an infinite-span wing profile
3D flow: motion extends in all three spatial directions — as with a finite-span wing

Almost all real flows are 3D.

2D flow is used in wind tunnel testing to eliminate wing tip vortex effects, isolating the airfoil profile geometry alone. This is achieved by using a model with an effectively infinite wingspan.

Finite wings produce wing tip vortices, which require full 3D flow analysis.

Unit Conversions

Distance

To convert	Multiply by	Result
Nautical miles → km	× 1.852	1 NM = 1.852 km
Feet → metres	× 0.3048	1 ft = 0.3048 m
Metres → feet	× 3.28	1 m = 3.28 ft

Speed

To convert	Factor	Notes
Knots → km/h	× 1.852	1 kt = 1.852 km/h
Knots → m/s	× 0.5144	1 kt = 0.5144 m/s
km/h → knots	÷ 1.852	—

Mass

To convert	Multiply by	Result
Pounds → kg	× 0.454	1 lb = 0.454 kg
kg → pounds	÷ 0.454	—