Rocket Engine Nozzle - Specific Impulse

Specific Impulse

Thrust is the force which moves a rocket through the air, and through space. Thrust is generated by the propulsion system of the rocket through the application of Newton's third law of motion: "For every action there is an equal and opposite reaction". A gas or working fluid is accelerated out the rear of the rocket engine nozzle and the rocket is accelerated in the opposite direction. The thrust of a rocket engine nozzle can be defined as:

and for perfectly expanded nozzles, this reduces to:

The specific impulse, is the ratio of the amount of thrust produced to the weight flow of the propellants. It is a measure of the fuel efficiency of a rocket engine. It can be obtained from:

where:
	= gross rocket engine thrust, N
	= mass flow rate of exhaust gas, kg/s
	= exhaust gas velocity at nozzle exit, m/s
	= exhaust gas pressure at nozzle exit, Pa
	= external ambient pressure, Pa (also known as free stream pressure)
	= cross-sectional area of nozzle exhaust exit, m²
	= equivalent (or effective) exhaust gas velocity at nozzle exit, m/s
	= specific impulse, s
	= Gravitational acceleration at sea level on Earth = 9.807 m/s²

In certain cases, where equals, then:

In cases where this may not be the case since for a rocket nozzle is proportional to, then it is possible to define a constant quantity which is the vacuum for any given engine thus:

and hence:

which is simply the vacuum thrust minus the force of the ambient atmospheric pressure acting over the exit plane.

Essentially then, for rocket nozzles, the ambient pressure acting over the engine largely cancels but effectively acts over the exit plane of the rocket engine in a rearward direction, while the exhaust jet generates forward thrust.