Specific impulse

The specific impulse defines the efficiency of an engine. It is linked to the thrust and fuel consumption. The unit is either meters per second or only seconds.

Formula

Failed to parse (syntax error): {\displaystyle '"`UNIQ--math-00000000-QINU`"'}

Where:

• $I_{sp}$ is the specific impulse in meters per second
• $F_{T}$ the thrust in newtons
• ${\dot {m}}$ the fuel consumption in kg/s

By multiplying this value with g₀ it is possible to change the unit to only seconds. The value g₀ behaves like a conversion factor and doesn't change when the gravity for the craft is changing. Usually both values are called specific impulse and are abbreviated by I_sp and the name I_sp,g0 is used here only to clarify that both values aren't the same. This value is sometimes called weight specific impulse.

Failed to parse (syntax error): {\displaystyle '"`UNIQ--math-00000005-QINU`"'}

Where:

• $I_{sp,g_{0}}$ is the specific impulse in seconds
• $g_{0}$ is the surface gravity in the required unit (usually 9.81 meters per second squared)

The formula using the it (e.g. for Δv) has to specify what unit it does expect and if the value is defined in the one it has to be converted.

Physical background

In KSP the fuel consumption on most engines depend on the atmospheric pressure with the lowest consumption in vacuum. So the specific impulse is at the highest point in the vacuum. This is loosely the same behaviour as in the real world, but the reason is different. The fuel consumption is always the same but the thrust is increasing over time. Because the a higher thrust with the same fuel consumption is more efficient the specific impulse also rises.

To convert the specific impulse between the handy weight specific impulse and the physical usable specific impulse it had to be converted with g₀. It appears that this value isn't the real world 9.81 m/s²; instead it is a little higher value of 9.82 m/s² making the engines a bit more efficient than expected.

Although the unit of the specific impulse is a velocity, it usually isn't the exhaust speed. Because some of the fuel consumed isn't used for propelling directly, but runs the turbopumps to fuel the engine.

See also

• Terminology
• Specific impulse on Wikipedia