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).
Key Formula
I_sp = F / (m_dot * g_0) = v_e / g_0
LaTeX: I_{sp} = \dfrac{F}{\dot{m}\, g_0} = \dfrac{v_e}{g_0}
| Symbol | Meaning | Unit |
|---|---|---|
| I_{sp} | Specific impulse | s |
| F | Thrust force | N |
| \dot{m} | Propellant mass flow rate | kg/s |
| g_0 | Standard gravity (9.80665) | m/s² |
| v_e | Effective exhaust velocity | m/s |
Worked Example
Problem
A rocket engine produces 500 kN of thrust while consuming propellant at 200 kg/s. Calculate its specific impulse.
Solution
Step 1: Write the formula: I_sp = F / (ṁ × g_0). Step 2: Substitute: F = 500,000 N, ṁ = 200 kg/s, g_0 = 9.80665 m/s². Step 3: Denominator = 200 × 9.80665 = 1961.33 N·s/kg. Step 4: I_sp = 500,000 / 1961.33 = 255.0 s.
Answer
I_sp ≈ 255 s
Specific Impulse of Common Rocket Propellant Combinations
| Propellant Combination | Oxidiser | I_sp Sea Level (s) | I_sp Vacuum (s) | Application |
|---|---|---|---|---|
| RP-1 (kerosene) / LOX | Liquid oxygen | 283 | 311 | Falcon 9 first stage |
| LH2 / LOX | Liquid oxygen | 370 | 451 | Space Shuttle main engine |
| UDMH / N2O4 | Nitrogen tetroxide | 256 | 311 | ISRO PSLV second stage |
| Solid composite (APCP) | Ammonium perchlorate | 230 – 250 | 265 – 285 | Space Shuttle SRBs |
| Ion thruster (Xenon) | — | — | 1500 – 10000 | Deep space probes |
| Cold gas (N2) | — | 65 – 70 | 65 – 70 | Attitude control thrusters |
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.
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.
Orbital Mechanics
Orbital mechanics (also called astrodynamics) is the branch of aerospace engineering and applied physics that studies the motion of spacecraft, satellites, and celestial bodies under the influence of gravitational forces. It is governed by Newton's law of universal gravitation and Kepler's three laws of planetary motion, and it underpins the planning of satellite launches, orbital transfers, interplanetary trajectories, and re-entry profiles. Mastery of orbital mechanics is essential for mission design, ground-track prediction, and spacecraft manoeuvring.
From Latin specificus (of a particular kind) and Latin impulsus (a push, impulse, from impellere — to drive). The term "specific impulse" was standardised in aerospace engineering in the 1940s–1950s as a propellant-agnostic efficiency metric for comparing rocket engines.