Specific impulse

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Specific impulse (commonly abbreviated I_sp) is the impulse (change in momentum) per unit mass for rocket fuels. In other words, the specific impulse is a measure of how much push can be obtained from a fixed mass of fuel.

A rocket must carry all its fuel with it, so the mass of the unburned fuel must be accelerated along with the rocket itself. Thus minimizing the mass of fuel required to achieve a given push is crucial to building effective rockets. Using Newton's third law it is not difficult to verify that for a fixed mass of fuel, the total change in velocity (in fact, momentum) it can accomplish can only be increased by increasing the exhaust velocity.

It follows that the faster the speed at which propellant is thrown out the back of the rocket, the faster the rocket can travel or the more cargo it can carry. The specific impulse of a rocket propellant is a measure of how fast the propellant is ejected out of the back of the rocket. A rocket with a high specific impulse doesn't need as much fuel as a rocket with low specific impulse to reach a given velocity.

The specific impulse as defined above is equal to the exhaust velocity u_eq.

An alternative way of defining the specific impulse is also sometimes used. In this sense, sepcific impulse is defined as the change in momentum per unit weight:

where g_e = acceleration at Earth's surface (9.8 m/s²).

In this case I_sp is measured in seconds.

This second definition is valuable because accelerations are often measured in terms of g_e (for example, astronauts should not be subjected to more than a few times the earth's gravity). Then if an engine has a specific impulse of 10000 seconds, one kilogram of fuel can produce the same impulse as a one-earth-gravity thrust acting for 10000 seconds. Of course, depending on the engine, this might take much more than 10000 seconds (in fact the only known rockets with this kind of specific impulse can only provide small fractions of an earth gravity, so it would take much longer to do this).

The specific impulse for various means of propulsion are given in the entry for spacecraft propulsion.