Mass fraction
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In aerospace engineering, the 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 a spacecraft, this is an orbit, while for aircraft it is their landing location. A higher mass fraction represents less weight in a design. Its inverse is the mass ratio. Another related measure is the payload fraction, which is the fraction of initial weight that is payload.
In rockets 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. In the cases of a single stage to orbit (SSTO) vehicle the mass fraction is simply the fuel mass divided by the mass of the full spaceship, but with a rocket employing staging, which are the only designs to have reached orbit, the mass fraction is higher because parts of the rocket itself are dropped off en route. 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 further. Mass fractions are typically around 0.5.
When applied to a rocket as a whole, a higher mass fraction is desirable (everything else being equal), since it gives a higher delta-v. A higher 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 0.88-0.95. Staging helps increase the mass fraction, which is one of the reasons SSTO's appear difficult to build.
For example, the complete Space Shuttle system has:
- weight at liftoff: 4,500,000 lb (2,040,000 kg)
- weight at end of mission: 230,000 lb (104,000 kg), and
- maximum cargo to orbit: 63,500 lb (28,800 kg)
Given these numbers, the mass fraction is 1 − (293,500 / 4,500,000) = 0.935 or perhaps a little less because of the fuel brought to orbit for use when returning: this may not have been counted as cargo, in which case the figure 293,500 should be a little higher.
The mass fraction plays an important role in the rocket equation:
- Δv = − veln(mf / m0)
Where mf / m0 is the ratio of final mass to initial mass (i.e., one minus the mass fraction), Δv is the change in the vehicle's velocity as a result of the fuel burn and ve is the effective exhaust velocity (see below).
The term effective exhaust velocity is defined as:
- ve = gnIsp
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.
