Specific Impulse

Author: Tianjiang Shuo

Website: https://cislunarspace.cn

Definition

Specific impulse (ISPI_{SP}) is the core metric for evaluating rocket engine performance. It is defined as the ratio of engine thrust to propellant weight flow rate (or mass flow rate). The higher the specific impulse, the greater the thrust produced per unit mass of propellant, and the more efficient the engine.

Core Elements

Two Dimensional Definitions

DefinitionFormulaUnitDescription
Weight-specific impulseISP=Pm˙g0I_{SP} = \frac{P}{\dot{m} g_0}seconds (s)Most commonly used in engineering
Mass-specific impulseISP=Pm˙I_{SP} = \frac{P}{\dot{m}}m/sEquivalent to effective exhaust velocity

where g0=9.80665g_0 = 9.80665 m/s2^2 is the standard sea-level gravitational acceleration. The two definitions are interconvertible.

Relationship with Effective Exhaust Velocity

Substituting the thrust formula P=m˙ue′−SepHP = \dot{m} u_e' - S_e p_H into the specific impulse definition:

ISP=ue′g0−SepHm˙g0I_{SP} = \frac{u_e'}{g_0} - \frac{S_e p_H}{\dot{m} g_0}

ConditionSpecific Impulse
Vacuum specific impulseISP,v=ue′g0I_{SP,v} = \frac{u_e'}{g_0} (maximum value)
Sea-level specific impulseISP,0=ue′g0−Sep0m˙g0I_{SP,0} = \frac{u_e'}{g_0} - \frac{S_e p_0}{\dot{m} g_0}

Typical Engine Specific Impulse

Engine TypePropellantVacuum Specific Impulse (s)
Liquid engineLH2_2 + LOX430--460
Liquid engineUDMH + N2_2O4_4300--340
Solid engineComposite propellant240--290
Electric propulsionXenon1000--5000

Specific Impulse and the Tsiolkovsky Equation

Specific impulse directly determines a rocket's velocity increment capability. From the Tsiolkovsky equation:

Δv=ISPg0ln⁡m0mf\Delta v = I_{SP} g_0 \ln\frac{m_0}{m_f}

A 10% increase in specific impulse yields a 10% increase in velocity increment for the same mass ratio.

Application Value

Specific impulse is the primary parameter for rocket engine selection and mission analysis. Higher specific impulse means greater propulsion efficiency and larger velocity increment capability. For cislunar space missions, specific impulse directly affects payload capacity, the propellant mass required for orbital transfers, and overall mission feasibility. Deep space exploration missions favor high-specific-impulse engines (such as electric propulsion) to reduce propellant mass.

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.
  • Sutton G P, Biblarz O. Rocket Propulsion Elements[M]. 9th ed. Wiley, 2016.