Identify the four forces of flight, apply equilibrium conditions to steady level flight, climbs and descents, and calculate net force and acceleration during accelerated phases

What this dot point is asking

NESA wants you to identify the four forces of flight, apply equilibrium in steady level flight, climb and descent, and find net force and acceleration when the forces are unbalanced.

The answer

The four forces

• Lift (L). Aerodynamic force on the wings perpendicular to the airflow. Always pointing approximately upward in level flight.
• Weight (W). Gravitational force on the aircraft, $W = mg$, directed toward the centre of the Earth.
• Thrust (T). Propulsive force from the engines, along the engine axis (approximately aligned with the flight direction for cruise).
• Drag (D). Aerodynamic resistance, parallel to the airflow and opposite to the flight direction.

Steady level flight

In steady level flight (constant altitude, constant airspeed, no acceleration), both pairs of forces balance:

A typical airliner cruises with $L/D \approx 15$ to 20. Higher $L/D$ means lower fuel burn per kilometre.

Steady climb

In a climb at angle $\theta$ at constant airspeed, the forces along the flight path and perpendicular to it must each balance:

Along the flight path:

Perpendicular to the flight path:

In a climb, lift is less than weight (because the weight component perpendicular to the flight path is $W\cos\theta < W$), and thrust is more than cruise thrust (to lift the aircraft against gravity).

Steady descent

In a descent at angle $\theta$ at constant airspeed:

If thrust is zero (glide), the descent angle is determined by the lift-to-drag ratio:

A glider with $L/D = 40$ descends at $\tan^{-1}(1/40) = 1.4$ degrees, travelling 40 m horizontally per 1 m of altitude lost.

Accelerated flight

If forces are not balanced, Newton's second law gives:

For takeoff acceleration along the runway: $T - D - \mu (W - L) = ma$, where $\mu$ is the rolling friction coefficient and $W - L$ is the normal force on the gear (which decreases as lift builds up with airspeed).

Australian context

Qantas operates Boeing 737s on domestic routes and Boeing 787, Airbus A330 and Airbus A380 on international routes. The new Boeing 787-9 has a quoted cruise $L/D$ of about 21 (composite wing, advanced aerofoil design). The Royal Australian Air Force operates Boeing F/A-18F Super Hornets and Lockheed F-35A Lightning II, which trade $L/D$ for supersonic capability and manoeuvrability.