Mass fraction

From Academic Kids

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 0.8 to 0.9, with lower numbers being better.

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 <math>1-(293,500/4,500,000) = 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 293,500 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 0.9. 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).

The term specific impulse is defined as:

<math>v_e = g_n I_{sp}<math>

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).

See also Payload fraction, Mass ratio.

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