Specific impulse Guide, Meaning , Facts, Information and Description

The specific impulse of a rocket (commonly abbreviated I_sp) 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 fuel that has not yet been spent.

For a delta-v that is much smaller than the specific impulse, the fuel required is approximately proportional, but for a delta-v that is larger than the specific impulse, 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).

where

I_sp is the specific impulse, as defined above, and measured in metre per second.

v_e is the exhaust velocity measured in metres per second.

See spacecraft propulsion for the details.

Table of contents

1 Alternative definition 2 Summary 3 See also

Alternative definition

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:

where

I_sp is the alternative definition of specific impulse measured in seconds

g₀ is the acceleration at Earth's surface (9.81 m/s²)

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 for example 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 existing 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.

Summary

The specific impulse is:

• in m/s:
  • the effective exhaust speed
  • the impulse (increase or decrease in momentum) per unit mass of propellant used
  • the thrust per unit propellant mass flow rate
  • 100 times the delta-v that can be produced with a propellant mass of 1 % of the current total mass (100 times the delta-v that reduces the mass with 1%)
  • the delta-v that can be produced with a propellant mass of 63.2 % of the initial total mass (the delta-v that reduces the total mass by a factor e, to 36.8 %)
  • twice the power per unit thrust
• in s:
  • 100 times the time an acceleration of g can be produced (i.e. a thrust equal to the weight on Earth of the current mass) with a propellant mass of 1 % of the current total mass (100 times the time it takes in this case to reduce the total mass with 1 %)
  • the time an acceleration of g can be produced with a propellant mass of 63.2 % of the initial total mass (the time it takes in this case to reduce the total mass by a factor e, to 36.8 %)
  • the net power to produce an acceleration of 1 to a mass which at Earth has a weight of 1 N

For example for hydrogen/oxygen:

• in m/s:
  • the effective exhaust speed is 4,500 m/s
  • the impulse produced per unit mass of propellant used is 4,500 kgm/s per kg
  • the thrust is 4,500 N if the propellant mass flow rate is 1 kg/s
  • the delta-v that can be produced with a propellant mass of 1 % of the current total mass (the delta-v that reduces the mass with 1%) is 45 m/s
  • the delta-v that can be produced with a propellant mass of 63.2 % of the initial total mass (the delta-v that reduces the total mass by a factor e, to 36.8 %) is 4,500 m/s
  • the power-thrust ratio is 2,250 W/N
• in s:
  • an acceleration of g (i.e. a thrust equal to the weight on Earth of the current mass) during 4.6 seconds can be produced with a propellant mass of 1 % of the current total mass (that is the time it takes in this case to reduce the total mass with 1 %)
  • an acceleration of g (i.e. a thrust equal to the weight on Earth of the current mass) during 460 seconds can be produced with a propellant mass of 63.2 % of the initial total mass (it is the time it takes in this case to reduce the total mass by a factor e, to 36.8 %)
  • the net power to produce an acceleration of 1 to a mass which at Earth has a weight of 1 N is 230 W.

The power to produce an acceleration of g is 23.5 kW/kg

See also

• Impulse
• Tsiolkovsky rocket equation

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