Mass fraction

In aerospace engineering, the mass fraction of a rocket is an important measure of its efficiency. The mass fraction measures the total amount of mass delivered to orbit to the weight of the fully-fueled vehicle prior to launch. In the cases of a single stage to orbit vehicle the mass fraction is simply the weight of the spaceship empty compared to full, 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. The Space Shuttle is .82 for instance, considered to be fairly good. 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 a single stage rocket operating in a vacuum, in a regime where gravity can be neglected (i.e., in orbit, in free fall, or over a very short time span), the following formula applies:

Where is the ratio of final mass to initial mass (i.e., the mass fraction), is the change in the vehicle's velocity as a result of the fuel burn and is the effective exhaust velocity (assuming a perfectly efficient nozzle, then

where Isp is the fuel's specific impulse.)