Mass fraction
Encyclopedia
In aerospace engineering
, the propellant mass fraction is a measure of a vehicle's performance, determined as the portion of the vehicle's mass which does not reach the destination. In other words, the propellant mass fraction is the ratio between the propellant mass and the initial mass of the vehicle.
In a spacecraft, this is an orbit, while for aircraft it is their landing location. A higher mass fraction represents less weight in a design. Another related measure is the payload fraction
, which is the fraction of initial weight that is payload.
And because,
it follows that:
Where:
is the propellant mass fraction
is the propellant mass
is the initial mass of the vehicle
is the final mass of the vehicle
s for a given target orbit
, a rocket's mass fraction is the portion of the rocket's pre-launch mass (fully fueled) that does not reach orbit. The propellant mass fraction is the ratio of just the propellant to the entire mass of the vehicle at takeoff (propellant plus dry mass). In the cases of a single stage to orbit (SSTO) vehicle or suborbital vehicle, the mass fraction equals the propellant mass fraction; simply the fuel mass divided by the mass of the full spaceship. A rocket employing staging
, which are the only designs to have reached orbit, has a mass fraction higher than the propellant mass fraction because parts of the rocket itself are dropped off en route. Propellant mass fractions are typically around 0.8 to 0.9.
In aircraft, mass fraction is related to range, an aircraft with a higher mass fraction can go farther. Aircraft mass fractions are typically around 0.5.
When applied to a rocket as a whole, a low mass fraction is desirable, since it indicates a greater capability for the rocket to deliver payload to orbit for a given amount of fuel. Conversely, when applied to a single stage, where the propellant mass fraction calculation doesn't include the payload, a higher propellant mass fraction corresponds to a more efficient design, since there is less non-propellant mass. Without the benefit of staging, SSTO designs are typically designed for mass fractions around 0.9. Staging increases the payload fraction
, which is one of the reasons SSTO's appear difficult to build.
For example, the complete Space Shuttle system
has:
Given these numbers, the propellant mass fraction is
.
The mass fraction plays an important role in the rocket equation:
Where
is the ratio of final mass to initial mass (i.e., one minus the mass fraction), 
is the change in the vehicle's velocity as a result of the fuel burn and 
is the effective exhaust velocity (see below).
The term effective exhaust velocity
is defined as:
where Isp is the fuel's specific impulse in seconds and gn is the standard acceleration of gravity (note that this is not the local acceleration of gravity).
To make a powered landing from orbit on a celestial body without an atmosphere requires the same mass reduction as reaching orbit from its surface, if the speed at which the surface is reached is zero.
Aerospace engineering
Aerospace engineering is the primary branch of engineering concerned with the design, construction and science of aircraft and spacecraft. It is divided into two major and overlapping branches: aeronautical engineering and astronautical engineering...
, the propellant mass fraction is a measure of a vehicle's performance, determined as the portion of the vehicle's mass which does not reach the destination. In other words, the propellant mass fraction is the ratio between the propellant mass and the initial mass of the vehicle.
In a spacecraft, this is an orbit, while for aircraft it is their landing location. A higher mass fraction represents less weight in a design. Another related measure is the payload fraction
Payload fraction
In aerospace engineering, payload fraction is a common term used to characterize the efficiency of a particular design. Payload fraction is calculated by dividing the weight of the payload by the weight of the otherwise empty aircraft when fully fueled...
, which is the fraction of initial weight that is payload.
Formulation
The propellant mass fraction is given by:And because,
it follows that:
Where:
is the propellant mass fraction is the propellant mass is the initial mass of the vehicle is the final mass of the vehicleSignificance
In rocketRocket
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...
s for a given target orbit
Orbit
In physics, an orbit is the gravitationally curved path of an object around a point in space, for example the orbit of a planet around the center of a star system, such as the Solar System...
, a rocket's mass fraction is the portion of the rocket's pre-launch mass (fully fueled) that does not reach orbit. The propellant mass fraction is the ratio of just the propellant to the entire mass of the vehicle at takeoff (propellant plus dry mass). In the cases of a single stage to orbit (SSTO) vehicle or suborbital vehicle, the mass fraction equals the propellant mass fraction; simply the fuel mass divided by the mass of the full spaceship. A rocket employing staging
Multistage rocket
A multistage rocket is a rocket that usestwo or more stages, each of which contains its own engines and propellant. A tandem or serial stage is mounted on top of another stage; a parallel stage is attached alongside another stage. The result is effectively two or more rockets stacked on top of or...
, which are the only designs to have reached orbit, has a mass fraction higher than the propellant mass fraction because parts of the rocket itself are dropped off en route. Propellant mass fractions are typically around 0.8 to 0.9.
In aircraft, mass fraction is related to range, an aircraft with a higher mass fraction can go farther. Aircraft mass fractions are typically around 0.5.
When applied to a rocket as a whole, a low mass fraction is desirable, since it indicates a greater capability for the rocket to deliver payload to orbit for a given amount of fuel. Conversely, when applied to a single stage, where the propellant mass fraction calculation doesn't include the payload, a higher propellant mass fraction corresponds to a more efficient design, since there is less non-propellant mass. Without the benefit of staging, SSTO designs are typically designed for mass fractions around 0.9. Staging increases the payload fraction
Payload fraction
In aerospace engineering, payload fraction is a common term used to characterize the efficiency of a particular design. Payload fraction is calculated by dividing the weight of the payload by the weight of the otherwise empty aircraft when fully fueled...
, which is one of the reasons SSTO's appear difficult to build.
For example, the complete Space Shuttle system
Space Shuttle program
NASA's Space Shuttle program, officially called Space Transportation System , was the United States government's manned launch vehicle program from 1981 to 2011...
has:
- fueled weight at liftoff: 1,708,500 kg
- dry weight at liftoff: 342,100 kg
Given these numbers, the propellant mass fraction is
.The mass fraction plays an important role in the rocket equation:
Where
is the ratio of final mass to initial mass (i.e., one minus the mass fraction), is the change in the vehicle's velocity as a result of the fuel burn and is the effective exhaust velocity (see below).The term effective exhaust velocity
Specific impulse
Specific impulse is a way to describe the efficiency of rocket and jet engines. It represents the derivative of the impulse with respect to amount of propellant used, i.e., the thrust divided by the amount of propellant used per unit time. If the "amount" of propellant is given in terms of mass ,...
is defined as:
where Isp is the fuel's specific impulse in seconds and gn is the standard acceleration of gravity (note that this is not the local acceleration of gravity).
To make a powered landing from orbit on a celestial body without an atmosphere requires the same mass reduction as reaching orbit from its surface, if the speed at which the surface is reached is zero.