Thrust

By /

Thrust is the fundamental force produced by an aircraft engine to propel the aircraft forward. In aerothermodynamics, understanding thrust is essential because it connects the thermodynamic energy conversion within the engine to the mechanical force that overcomes aerodynamic drag and enables flight.

1. Definition of Thrust

Thrust is a reaction force described by Newton’s Third Law: for every action, there is an equal and opposite reaction. When an engine accelerates air (or exhaust gases) backward, it generates an equal and opposite force that pushes the aircraft forward.

Mathematically, for a control volume with mass flow:

F = \dot{m}(V_{exit} - V_{inlet})

Where:

  • F = thrust (N)
  • \dot{m} = mass flow rate (kg/s)
  • V_{exit} = velocity of exhaust gases (m/s)
  • V_{inlet} = inlet air velocity relative to the engine (m/s)

2. Control Volume Approach

Consider an engine as a control volume. Air enters at velocity V_0 and exits at higher velocity V_{exit}:

  • The engine accelerates airflow by adding energy (via combustion).
  • The change in momentum of the flow produces thrust.

For air-breathing engines:

F = \dot{m}<em>a (V</em>{exit} - V_0) + \dot{m}<em>f V</em>{exit}

If \dot{m}_f (fuel mass flow rate) is small compared to \dot{m}_a (air mass flow rate), it can be simplified:

F \approx \dot{m}<em>a (V</em>{exit} - V_0)

3. Gross Thrust and Net Thrust

  • Gross thrust: The total momentum thrust at the nozzle exit, measured relative to the engine.

F_{gross} = \dot{m} V_{exit}

Net thrust: The useful thrust that propels the aircraft, accounting for the inlet velocity.

F_{net} = \dot{m} (V_{exit} - V_0)

Net thrust is the actual force available to overcome drag and accelerate the aircraft.

4. Specific Thrust

Specific thrust is thrust per unit mass flow rate of air:

\text{Specific Thrust} = \frac{F}{\dot{m}_a}

This metric is useful for comparing engine types:

  • Turbojets: high specific thrust
  • Turbofans (especially high-bypass): lower specific thrust but higher efficiency

5. Alternative Thrust Equation (with Pressure Difference)

In addition to momentum change, pressure forces at the nozzle exit contribute to thrust if there’s a mismatch with ambient pressure:

F = \dot{m}(V_{exit} - V_0) + (p_{exit} - p_{ambient}) A_{exit}

Where:

  • p_{exit} = nozzle exit pressure
  • p_{ambient} = ambient pressure
  • A_{exit} = nozzle exit area

This is important for:

  • Under-expanded or over-expanded nozzles.
  • Supersonic flight conditions.

6. Thrust in Different Engine Types

  • Turbojet: Produces thrust primarily via high-velocity jet exhaust. High specific thrust, suitable for supersonic flight.
  • Turbofan: Combines jet exhaust thrust with fan-generated bypass flow. Lower exhaust velocity, higher mass flow for better efficiency in subsonic flight.
  • Ramjet: No moving compressors or turbines. Relies on high-speed airflow compression, suitable for supersonic speeds.
  • Rocket: Carries its own oxidizer. Thrust is independent of atmospheric air.

7. Factors Affecting Thrust

  • Flight speed: As inlet velocity V_0 increases, net thrust generally decreases for constant exit conditions.
  • Altitude: Lower air density at higher altitude reduces mass flow rate, affecting thrust.
  • Temperature: Higher inlet air temperature reduces air density, also lowering thrust.
  • Engine design: Nozzle geometry, bypass ratio (for turbofans), compressor and turbine efficiencies.

8. Example Calculation

Consider a turbojet engine with:

  • Air mass flow rate: 50 , \text{kg/s}
  • Inlet velocity: 250 , \text{m/s}
  • Exit velocity: 600 , \text{m/s}

Thrust:

F = \dot{m}<em>a (V</em>{exit} - V_0)

F = 50 \times (600 - 250) = 17,500 , \text{N}

9. Importance of Thrust in Aircraft Performance

Thrust must overcome drag for steady, level flight. It also determines:

  • Rate of climb
  • Acceleration
  • Maximum speed
  • Takeoff distance

A propulsion system is designed to provide sufficient thrust across all required phases of flight while optimizing fuel efficiency and emissions.

10. Summary

Thrust is the essential output of an aircraft propulsion system, converting thermal energy into mechanical force. It is governed by:

  • Mass flow rate of air and fuel
  • Change in flow velocity
  • Pressure differences at the nozzle exit

A clear understanding of thrust is the foundation for analyzing engine efficiency, range, and the thermodynamic cycles that drive modern aircraft engines.

Shopping Cart
Scroll to Top