Mass fraction

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In aerospace engineering, the mass fraction is an important measure of a rocket's efficiency. 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 vehicle the mass fraction is simply the fuel mass divided by the mass of the full spaceship, but with a rocket employing staging, which is the vast majority of them, the mass fraction is higher because parts of the rocket itself are dropped off enroute. Mass fractions are typically around .8 to .9, with lower numbers being better.

For example, the complete Space Shuttle system has:

weight at liftoff: 2,041,166 kg (4.5 million lbs.),
weight at end of mission: 104,326 kg (230,000 lbs.), and
maximum cargo to orbit: 28,803 kg (63,500 lbs.).

Given these numbers, the mass fraction is <math>1-(133,000/2,041,000) = 0.935<math> 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 133,000 should be a little higher.

A lower mass fraction for the rocket means that it uses fuel efficiently, reserving a larger portion of its mass as payload. Without the benefit of staging, SSTO designs are typically designed for mass fractions around .9. Staging increases the mass fraction, which is one of the reasons SSTO's appear difficult to build.

For individual stages, however, a higher mass fraction is better, meaning that there is less non-propellent mass.

The mass fraction plays an important role in the rocket equation:

<math>\Delta v = -v_e ln (m_f / m_0)<math>

Where <math>m_f/m_0<math> is the ratio of final mass to initial mass (i.e., one minus the mass fraction), <math>\Delta v<math> is the change in the vehicle's velocity as a result of the fuel burn and <math>v_e<math> is the effective exhaust velocity (assuming a perfectly efficient nozzle), then

where I_sp is the fuel's specific impulse.

In theory, a mass fraction of less than 0.5 would allow a spacecraft to carry enough fuel to orbit that it could make an entirely powered landing, avoiding the need for extensive aerobraking, and the difficulties associated with the intense heat generated.