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# Rocket Propulsion Systems | Rocket Engine Work | Rocket Engine Thrust

## Rocket propulsion Systems

A rocket engine is defined as an engine that expands thrust by ejecting a stream of matter (i.e. exhaust gas) backwards. Since the reaction (i.e. thrust force) principle involved assumes a self enclosed supply of energy. A rocket engine can operate in any medium including space (i.e. Outside the earth’s atmosphere), where there is no oxygen to support combustion.

### Rocket Engine work

The working principles of rocket engines are primarily governed by Newton’s law of motion. Newton’s first law states that there is no change in the motion of body unless a resultant force acts on it. The governing action such as gravitational force, lift force, drag force and the thrust force of the rocket engine all proceed on the vehicle to cause the resultant motion. The net amount of the resultant force and its directions decide the acceleration on the vehicle and the path of the flight trajectory, in accordance with Newton’s second law.

### Rocket Engine Thrust

A rocket engine develops its thrust by ejecting a mass backward. The mass is accelerated backward by combustion that accelerates its velocity from 0 to 1000 m/s. The Newton’s Second law states that, the force for this acceleration is proportional to the mass of the exhaust gases. The force acting on the accelerating mass and the resultant exhaust gases, produce a thrust in accordance with Newton’s third law, which states that for every action, there is an equal and opposite reaction. So the thrust force in the rocket engine is developed by internal fluids within the rocket which accelerates equal but opposite external force.

The force vector (i.e. thrust), can be determined by investigating the change of momentum in the design and the sum of the forces that act on a closed duct in a control volume. The internal flow to the rocket experiences a change of momentum that is equal to the mass flow rate and the change in velocity of the gases. When the inlet velocity is low the change in momentum considered as negligible.

### Force of a Rocket:

The sum of all pressures on the surfaces perpendicular to the flow axis of the device reduces to a resultant force. Due to the pressure differential between the pressure at the nozzle exit plane and the ambient pressure that acts on the exit area of the nozzle.

Net pressure force = (Pexit – P ambient) A exit

The sum of the forces that acts on a rocket is equal to the change of momentum in accordance with Newton’s second law.

Thrust = m Vexit + (Pexit – Pambient) A exit

• When Pexit equals Pambient expansion is optimum and performance is good.
• When the nozzle exit pressure is less than ambient, the nozzle is said to be over-expanded.
• When exit pressure is greater than ambient, the nozzle is said to be under-expanded.

Generally the rocket flies through the atmosphere; it experiences variations in the ambient pressure. So it operates at optimum expansion at only one altitude. Resultant design and flight conditions based on the rocket exit areas in different altitudes.