Specific impulse
The specific impulse of a rocket (commonly abbreviated Isp) is the impulse (change in momentum) per unit mass of its fuel. It is a measure of how much push can be obtained from a fixed mass of fuel. Essentially it is simply the exhaust velocity.
A rocket must carry all its fuel with it, so the mass of the unburned fuel must be accelerated along with the rocket itself. Minimizing the mass of fuel required to achieve a given push is crucial to building effective rockets. Using Newton's laws of motion 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.
A spacecraft without propulsion follows an orbit determined by the gravitational field. Deviations from the corresponding velocity pattern (these are called delta-v) are achieved by sending exhaust mass in the direction opposite to that of the desired velocity change.
Due to the law of conservation of momentum, to change the speed of the spacecraft with an amount equal to 1% of the exhaust speed, requires an exhaust mass equal to 1% of the mass of the spacecraft, including the the fuel that has not yet been spent.
For a small delta-v the fuel required is approximately proportial, but for a large delta-v this requirement of carrying the fuel and spending much of the fuel on accelerating the fuel, gives rise to an exponential increase in fuel requirement (and larger tanks which also add to the mass) with the exhaust velocity (specific impulse) as crucial parameter.
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.
- <math>I_{\rm sp}=v_{\rm e} \,<math>
The specific impulse as defined above is equal to the exhaust velocity ve.
In free fall, the exhaust velocity determines how much the engine can change the velocity of the spacecraft without heroic measures — for changes in velocity that are large compared to the exhaust velocity, the amount of fuel required is exponential in the change in velocity needed. See spacecraft propulsion for the details.
An alternative way of defining the specific impulse is also frequently used. In this sense, specific impulse is defined as the change in momentum per unit weight:
- <math>I_{\rm sp}=\frac{v_{\rm e}}{g_{\rm 0}}<math>
where g0 is the acceleration at Earth's surface (9.8 m/s2).
In this case Isp is measured in seconds.
This second definition is valuable because accelerations are often measured in terms of g0 (for example, astronauts should not be subjected to more than a few times the earth's gravity).
The specific impulse in seconds is the time one kilogram of fuel lasts if a one-earth-gravity thrust (including e.g. a hypothetical hovering over the Earth) is applied to a mass of one kilogram. The concept is also used for engines not capable of such a thrust, e.g. the only known rockets with a specific impulse of 10,000 seconds can only provide small fractions of an earth gravity. Then specific impulse is e.g. the time one kilogram of fuel lasts if 0.01 g thrust is applied to a mass of 100 kilogram.
The specific impulses for various means of propulsion are given in the entry for spacecraft propulsion.
