Thrust

Author: Tianjiang Shuo
Website: https://cislunarspace.cn

Definition

Thrust is the propulsive force generated by a rocket engine, composed of momentum thrust (reaction force) and static thrust. Thrust is the fundamental force that enables a rocket to overcome gravity and aerodynamic drag for accelerated flight. Its magnitude is:

P = \dot{m} u_e + S_e(p_e - p_H)

where $\dot{m}$ is the propellant mass flow rate, $u_e$ is the exhaust velocity, $S_e$ is the nozzle exit area, $p_e$ is the static pressure of the exhaust gas at the nozzle exit, and $p_H$ is the ambient atmospheric pressure.

Core Elements

Components of Thrust

Component	Expression	Physical Meaning
Momentum thrust (reaction force)	$\dot{m} u_e$	Reaction force from the expelled gas; the dominant component of thrust
Static thrust	$S_e(p_e - p_H)$	Force produced by the pressure difference across the nozzle exit

Momentum thrust is derived from the fundamental principle of variable mass mechanics: a rocket expels mass at rate $\dot{m}$ with exhaust velocity $u_e$ , producing a reaction force of $-\dot{m}u_e$ .

Effective Exhaust Velocity

Introducing the effective exhaust velocity $u_e'$ , thrust can be expressed more concisely:

u_e' = u_e + S_e \frac{p_e}{\dot{m}}

P = \dot{m} u_e' - S_e p_H

The effective exhaust velocity is independent of ambient atmospheric pressure and is an intrinsic characteristic of the engine.

Vacuum Thrust and Sea-Level Thrust

Condition	Expression	Description
Vacuum thrust	$P_v = \dot{m} u_e'$	Maximum thrust, no atmospheric pressure loss
Sea-level thrust	$P_0 = \dot{m} u_e' - S_e p_0$	Thrust at sea level
General formula	$P = P_0 + S_e(p_0 - p_H)$	Thrust at any altitude

Engine Operating Process

The operating process of a rocket engine: propellant (fuel + oxidizer) is fed into the combustion chamber for a chemical reaction, producing high-temperature, high-pressure gas. The gas expands and accelerates through the nozzle, generating thrust as it is expelled at high velocity. Different propellant types (liquid, solid, hybrid) correspond to different engine configurations.

Application Value

Thrust is the sole source of propulsion during a rocket's powered flight phase. The magnitude and direction of thrust directly affect the vehicle's acceleration, velocity increment, and flight trajectory. Thrust varies with altitude (due to changing atmospheric pressure), reaching its maximum in vacuum. For cislunar space missions, thrust determines launch capability, orbital transfer velocity increment ( $\Delta v$ ), and mission feasibility.

Specific Impulse

References

Zheng Wei, An Xueying, Zhou Xiang, He Ruizhi. Aerospace Flight Mechanics (空天飞行力学)[M]. National University of Defense Technology, 2026.
Jia Peiran, Chen Kejun, et al. Long-Range Rocket Ballistics (远程火箭弹道学)[M]. National University of Defense Technology Press.