Working mass

# Working mass

Discussion

Encyclopedia
Working mass is a mass against which a system operates in order to produce acceleration
Acceleration
In physics, acceleration is the rate of change of velocity with time. In one dimension, acceleration is the rate at which something speeds up or slows down. However, since velocity is a vector, acceleration describes the rate of change of both the magnitude and the direction of velocity. ...

.
In the case of a rocket, for example, the reaction mass is the fuel shot backwards to provide propulsion. All acceleration requires an exchange of momentum
Momentum
In classical mechanics, linear momentum or translational momentum is the product of the mass and velocity of an object...

, which can be thought of as the "unit of movement". Momentum is related to mass and velocity, as given by the formula P = mv, where P is the momentum, m the mass, and v the velocity. The velocity of a body is easily changeable, but in most cases the mass is not, which makes it important.

## Rockets and rocket-like reaction engines

In rockets, the total velocity change can be calculated (using the Tsiolkovsky rocket equation
Tsiolkovsky rocket equation
The Tsiolkovsky rocket equation, or ideal rocket equation is an equation that is useful for considering vehicles that follow the basic principle of a rocket: where a device that can apply acceleration to itself by expelling part of its mass with high speed and moving due to the conservation of...

) as follows:

Where:
• v = ship velocity.
• u = exhaust velocity.
• M = ship mass, not including the fuel.
• m = total mass ejected from the ship (working mass).

The term working mass is used primarily in the aerospace
Aerospace
Aerospace comprises the atmosphere of Earth and surrounding space. Typically the term is used to refer to the industry that researches, designs, manufactures, operates, and maintains vehicles moving through air and space...

field. In more "down to earth" examples the working mass is typically provided by the Earth, which contains so much momentum in comparison to most vehicles that the amount it gains or loses can be ignored. However in the case of an aircraft
Aircraft
An aircraft is a vehicle that is able to fly by gaining support from the air, or, in general, the atmosphere of a planet. An aircraft counters the force of gravity by using either static lift or by using the dynamic lift of an airfoil, or in a few cases the downward thrust from jet engines.Although...

the working mass is the air, and in the case of a rocket
Rocket
A rocket is a missile, spacecraft, aircraft or other vehicle which obtains thrust from a rocket engine. In all rockets, the exhaust is formed entirely from propellants carried within the rocket before use. Rocket engines work by action and reaction...

, it is the rocket fuel itself. Most rocket engines use light-weight fuels (liquid hydrogen
Hydrogen
Hydrogen is the chemical element with atomic number 1. It is represented by the symbol H. With an average atomic weight of , hydrogen is the lightest and most abundant chemical element, constituting roughly 75% of the Universe's chemical elemental mass. Stars in the main sequence are mainly...

, oxygen
Oxygen
Oxygen is the element with atomic number 8 and represented by the symbol O. Its name derives from the Greek roots ὀξύς and -γενής , because at the time of naming, it was mistakenly thought that all acids required oxygen in their composition...

, or kerosene
Kerosene
Kerosene, sometimes spelled kerosine in scientific and industrial usage, also known as paraffin or paraffin oil in the United Kingdom, Hong Kong, Ireland and South Africa, is a combustible hydrocarbon liquid. The name is derived from Greek keros...

) accelerated to super-sonic speeds. However, ion engines often use heavier elements like Xenon
Xenon
Xenon is a chemical element with the symbol Xe and atomic number 54. The element name is pronounced or . A colorless, heavy, odorless noble gas, xenon occurs in the Earth's atmosphere in trace amounts...

as the reaction mass, accelerated to much higher speeds using electric fields.

In many cases the working mass is separate from the energy
Energy
In physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems...

used to accelerate it. In a car the engine provides power to the wheels, which then accelerates the Earth backward to make the car move forward. This is not the case for most rockets however, where the rocket propellant is the working mass, as well as the energy source. This means that rockets stop accelerating as soon as they run out of fuel, regardless of other power sources they may have. This can be a problem for satellites that need to be repositioned often, as it limits their useful life. In general, the exhaust velocity should be close to the ship velocity for optimum energy efficiency. This limitation of rocket propulsion is one of the main motivations for the ongoing interest in field propulsion
Field propulsion
Field propulsion is the concept of spacecraft propulsion where no propellant is necessary but instead momentum of the spacecraft is changed by an interaction of the spacecraft with external force fields....

technology.