State Bernoulli's principle, describe how an aerofoil generates lift, and apply the lift equation to calculate the lift on a wing at different speeds and altitudes

What this dot point is asking

NESA wants you to state Bernoulli's principle, describe how an aerofoil produces lift, apply the lift equation to find lift force at a given speed and altitude, and explain how lift coefficient varies with angle of attack.

The answer

Bernoulli's principle

For a streamline of an incompressible, inviscid, steady flow, the total pressure is constant:

where $P$ is the static pressure, $\rho$ is the fluid density, $v$ is the local flow speed and $h$ is the height. For aerodynamic problems at constant altitude, the gravitational term cancels:

Higher local flow speed produces lower static pressure. This is the central observation behind aerofoil lift.

How an aerofoil produces lift

An aerofoil has an asymmetric or angled cross-section. As air flows around it:

• Air accelerates over the upper (longer) surface; static pressure on top decreases.
• Air on the lower surface decelerates relative to free stream; static pressure on the bottom increases.
• The net pressure difference (lower pressure on top minus higher pressure on bottom) integrated over the wing area produces an upward force, the lift.

The flow over the upper surface is curved by the aerofoil and accelerated by the Coanda effect; the rear edge sheds vorticity that satisfies the Kutta condition (smooth flow leaves the trailing edge). The full mathematical theory (circulation theory by Kutta-Joukowski) reduces to a clean engineering equation.

The lift equation

where:

• IMATH_9 is air density (kg/m^3)
• IMATH_10 is true airspeed (m/s)
• IMATH_11 is wing area (m^2)
• IMATH_12 is the lift coefficient (dimensionless), a function of aerofoil geometry and angle of attack

Lift coefficient versus angle of attack

For a typical aerofoil:

• At zero angle of attack, $C_L$ is around 0.2 to 0.4 (depending on camber).
• Increasing angle of attack increases $C_L$ linearly at about $0.1$ per degree, up to a stall angle of 15 to 18 degrees.
• At stall, flow separates from the upper surface; $C_L$ drops sharply and the aircraft loses lift.

Aircraft adjust angle of attack to keep $C_L$ matched to the required lift at the current airspeed and density.

Air density and altitude

Air density falls with altitude (approximately 1.225 kg/m^3 at sea level, 0.74 kg/m^3 at 5000 m, 0.41 kg/m^3 at 10{,}000 m). For the same lift, an aircraft at altitude must fly faster (true airspeed). The pilot reads indicated airspeed, which already accounts for density via the pitot static system; indicated airspeed is roughly constant for a given $C_L$ regardless of altitude.

Australian context

The Royal Australian Air Force PC-21 trainer aircraft and the F/A-18F Super Hornet use modern aerofoils with leading-edge devices and trailing-edge flaps to vary $C_L$ across the flight envelope. Civil airliners (Boeing 737, Airbus A320) use supercritical aerofoils that delay shock formation at high subsonic Mach numbers, raising the practical cruise speed.