Engine Thrust
Engine thrust is the reaction force produced by a jet or rocket engine as it expels mass (exhaust gases) at high velocity, propelling the vehicle in the opposite direction in accordance with Newton's third law of motion. For air-breathing jet engines, thrust depends on the mass flow rate of air through the engine and the velocity increase imparted to it; for rocket engines, thrust depends on propellant mass flow and exhaust velocity. Thrust must exceed aerodynamic drag for acceleration and must balance it during steady flight.
Key Formula
F = m_dot * (v_e - v_0) + (p_e - p_0) * A_e
LaTeX: F = \dot{m} (v_e - v_0) + (p_e - p_0) A_e
| Symbol | Meaning | Unit |
|---|---|---|
| F | Thrust force | N |
| \dot{m} | Mass flow rate of exhaust | kg/s |
| v_e | Exhaust velocity at nozzle exit | m/s |
| v_0 | Inlet (freestream) velocity | m/s |
| p_e | Exit plane pressure | Pa |
| p_0 | Ambient pressure | Pa |
| A_e | Nozzle exit area | m² |
Worked Example
Problem
A turbojet engine ingests air at 60 kg/s, accelerating it from 0 m/s (static test) to an exhaust velocity of 600 m/s. The nozzle exit pressure equals ambient pressure. Calculate the thrust.
Solution
Step 1: Since the test is static, v_0 = 0 m/s, and p_e = p_0, so the pressure term vanishes. Step 2: F = ṁ × (v_e − v_0) = 60 × (600 − 0). Step 3: F = 60 × 600 = 36,000 N.
Answer
F = 36,000 N (36 kN)
Thrust Values for Representative Aerospace Engines
| Engine | Type | Max Thrust (kN) | Application | Notable Feature |
|---|---|---|---|---|
| CFM56-7B | Turbofan | 121 | Boeing 737 NG | High bypass ratio |
| General Electric GE90-115B | Turbofan | 513 | Boeing 777-300ER | World's largest turbofan |
| Rolls-Royce Merlin | Piston | ~7.5 | Spitfire / Lancaster | WWII warbird |
| SpaceX Merlin 1D | Rocket (kerosene-LOX) | 845 | Falcon 9 (sea level) | Reusable booster |
| Space Shuttle Main Engine | Rocket (LH2-LOX) | 1860 | Space Shuttle | Throttleable 67–109% |
| ISRO Vikas Engine | Rocket (UDMH-N2O4) | 799 | PSLV second stage | Indian space programme |
Interactive Tools
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Related Terms
Tsiolkovsky Rocket Equation
The Tsiolkovsky rocket equation (also called the ideal rocket equation) describes the relationship between the change in velocity (Δv) of a rocket and the logarithmic ratio of its initial to final mass, scaled by the exhaust velocity of the propellant. Derived by Russian scientist Konstantin Tsiolkovsky in 1897, it reveals the fundamental challenge of rocketry: achieving large Δv requires either very high exhaust velocities or carrying propellant many times the mass of the payload. It is the foundational equation for mission planning and launch vehicle design.
Specific Impulse
Specific impulse (I_sp) is a measure of the propellant efficiency of a rocket or jet engine, defined as the thrust produced per unit weight flow rate of propellant consumed; it is expressed in seconds and is independent of gravity field when defined in this way. A higher specific impulse indicates that the engine generates more thrust for each kilogram of propellant burned per second, making it the key figure of merit for comparing propulsion systems. Specific impulse directly relates to exhaust velocity: I_sp = v_e / g_0, where g_0 is standard gravity (9.80665 m/s²).
Aerodynamic Drag
Aerodynamic drag is the resistive force exerted on a body moving through a fluid (such as air), acting parallel and opposite to the direction of motion. It consists of pressure drag (form drag), skin friction drag, and induced drag, all of which dissipate kinetic energy and reduce vehicle efficiency. Minimising drag is a primary goal in the aerodynamic design of aircraft, rockets, and high-speed ground vehicles.
From Old Norse þrysta (to push, thrust). In engineering, "thrust" specifically denoting propulsive force came into standard use with the development of jet propulsion in the 1930s and 1940s.