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Working mass

Working mass

Overview
Working mass is a mass against which a system operates in order to produce acceleration
Acceleration
In physics, and more specifically kinematics, acceleration is the change in velocity over time. Because velocity is a vector, it can change in two ways: a change in magnitude and/or a change in direction. In one dimension, i.e. a line, acceleration is the rate at which something speeds up or slows...

. All acceleration requires an exchange of momentum
Momentum
In classical mechanics, momentum is the product of the mass and velocity of an object . For more accurate measures of momentum, see the section "modern definitions of momentum" on this page...

, 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.

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 a mathematical equation that relates the delta-v with the effective exhaust velocity and the initial and end mass of a rocket....

) 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.
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Encyclopedia
Working mass is a mass against which a system operates in order to produce acceleration
Acceleration
In physics, and more specifically kinematics, acceleration is the change in velocity over time. Because velocity is a vector, it can change in two ways: a change in magnitude and/or a change in direction. In one dimension, i.e. a line, acceleration is the rate at which something speeds up or slows...

. All acceleration requires an exchange of momentum
Momentum
In classical mechanics, momentum is the product of the mass and velocity of an object . For more accurate measures of momentum, see the section "modern definitions of momentum" on this page...

, 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 a mathematical equation that relates the delta-v with the effective exhaust velocity and the initial and end mass of a rocket....

) 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 which is able to fly by being supported by 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 An aircraft is a vehicle which is able to fly by being supported...

 the working mass is the air, and in the case of a rocket
Rocket
A rocket or rocket vehicle is a missile, spacecraft, aircraft or other vehicle which obtains thrust by the reaction of the rocket to the ejection of a jet of fast moving fluid exhaust from a rocket engine. Chemical rockets create their exhaust by the combustion of rocket propellant...

, 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. At standard temperature and pressure, hydrogen is a colorless, odorless, nonmetallic, tasteless, highly flammable diatomic gas with the molecular formula H2...

, oxygen
Oxygen
Oxygen Oxygen Oxygen (acid, literally "sharp", from the taste of acids) and -γενής (-genēs) (producer, literally begetter) is the element with atomic number 8 and represented by the symbol O...

, or kerosene
Kerosene
Kerosene, sometimes spelled kerosine in scientific and industrial usage, also known as paraffin, 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 represented by the symbol Xe. Its atomic number is 54. 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 a scalar physical quantity that describes the amount of work that can be performed by a force, an attribute of objects and systems that is subject to a conservation law...

 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 fuel 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, rocket fuels can provide more energy than they can use, which leads to a number of techniques designed to provide external working mass in order to carry a smaller fuel load. These air-augmented rocket
Air-augmented rocket
Air-augmented rockets use the supersonic exhaust of some kind of rocket engine to further compress air collected by ram effect during flight to use as additional working mass, leading to greater effective thrust for any given amount of fuel than either the rocket or a ramjet...

s are only useful on rockets that travel through the atmosphere, and have not been used in service.