# Specific Impulse by weight - with mass flow rate

## Description

Specific impulse (usually abbreviated Isp) is a measure of the efficiency of rocket and jet engines. By definition, it is the impulse delivered per unit of propellant consumed, and is dimensionally equivalent to the thrust generated per unit propellant flow rate. If mass (kilogram or slug) is used as the unit of propellant, then specific impulse has units of velocity. If weight (newton or pound force) is used instead, then specific impulse has units of time (seconds). The conversion constant between these two versions is the standard gravitational acceleration constant (g0). The higher the specific impulse, the lower the propellant flow rate required for a given thrust, and in the case of a rocket, the less propellant needed for a given delta-v, per the Tsiolkovsky rocket equation.

Specific impulse is a useful value to compare engines, much like miles per gallon or liters per 100 kilometers is used for cars. A propulsion method and system with a higher specific impulse is more propellant-efficient. While the unit of seconds can seem confusing to laypeople, it is fairly simple to understand as “hover-time”: how long a rocket can “hover” before running out of fuel, given the weight of that propellant/fuel. Of course, the weight of the rocket has to be taken out of consideration and so does the reduction in fuel weight as it’s expended; the basic idea is “how long can any given amount of x hold itself up”. Obviously that must mean “...against Earth’s gravity”, which means nothing in non-Earth conditions; hence Isp being given in velocity when propellant is measured in mass rather than weight, and the question becomes “how fast can any given amount of x accelerate itself?”

Note that Isp describes efficiency in terms of amount of propellant, not the engine (or engine/propellant design/combination). Higher Isp means less propellant needed to impart a given momentum, but it says nothing about the overall system’s ability to supply needed thrust, especially with respect to time. Some systems with very high Isp (cf. ion thrusters) may have relatively very heavy/massive power generators, and/or produce thrust over a long period; thus, while “efficient” in terms of propellant mass carried, they may actually be quite poor at delivering high thrust quickly vs. “less efficient” engine/propellant designs.

Another number that measures the same thing, usually used for air breathing jet engines, is specific fuel consumption. Specific fuel consumption is inversely proportional to specific impulse and effective exhaust velocity. The actual exhaust velocity is the average speed of the exhaust jet as it leaves the vehicle. The effective exhaust velocity is the exhaust velocity that the propellant would need to produce the same thrust. The two are identical for an ideal rocket working in vacuum, but are radically different for an air-breathing jet engine that obtains extra thrust by accelerating air. Specific impulse and effective exhaust velocity are proportional.

For all vehicles specific impulse (impulse per unit weight-on-Earth of propellant) in seconds can be defined by the equation shown here.

Related formulas## Variables

I_{spm} | specific impulse by weight (s) |

F | thrust (N) |

ṁ | fuel mass rate (kg/s) |

g_{0} | standard acceleration due to gravity(for an object in a vacuum near the surface of the Earth : 9.80665 m/s^2) (m/s^{2}) |