Empty mass ratio is the gross mass of the craft on takeoff divided by the mass of the craft without fuel or payload. Typical empty mass ratios range from about five to one for reusable pressure fed hydrogen rockets, to about seventeen to one for pumped hydrogen peroxide rockets.

In pumped rocket and rocket cost the empty mass ratios are calculated ultimately from the liquids, materials and machinery involved. The figures in the table above are typical values for use in the spacecraft set of scripts, which look at all stages of a spacecraft in an atmosphere, rather than the rocket set of scripts, which look in detail at one stage of a spacecraft. Given empty mass, mass and payload mass, empty mass can be calculated which is in turn used to calculate final velocity.

empty mass ratio = ( mass - payload mass ) / empty mass

final velocity = exhaustvelocity * log( empty mass ratio / ( 1.0 + payload ratio ) )
 

In spacecraft in vacuum, atmospheric spacecraft, multi stage spacecraft and spacecraft cost the empty mass ratio is chosen. In the table above, H2O2 stands for hydrogen peroxide, a dense oxidizer which is a liquid at room temperature. LOX stands for liquid oxygen stored at about 90K, this requires some insulation which lowers the mass ratio of the spacecraft. Methane and ozone have densities and melting points close to that of oxygen so their tank masses are similar. LH2 stands for liquid hydrogen stored at about 20K which requires considerable insulation and large fuel tanks because it has a low density, which further lowers the mass ratio of the spacecraft.

These mass ratios assume no payload. They're ultimately derived from the fact that a pumped LOX / kerosene rocket took off from Florida and barely made it to orbit with no payload. Putting that back into the atmospheric spacecraft with the known exhaust velocity for that rocket being 3,330 m / s gives a mass ratio of 13.8. From there LH2 spacecraft are assumed to have a mass ratio 0.75 times as high; H2O2 spacecraft are assumed to have a mass ratio 1.2 times as high. Reusable spacecraft are assumed to have a mass ratio 0.62 times as high as expendable spacecraft. Rockets engines without pumps which have pressurized fuel tanks are assumed to have a mass ratio 0.8 times as high.

These are typical values for medium technology structures, with more expensive technology and lower safety margins, mass ratios can be higher. This is used to calculate the duration, empty mass, final acceleration, final velocity and fuel mass.

duration = exhaust velocity / liftoff acceleration * ( 1.0 - ( 1.0 + payload ratio ) / empty mass ratio )

empty mass = mass / empty mass ratio

final acceleration = liftoff acceleration * empty mass ratio / ( 1.0 + payload ratio )

final velocity = exhaust velocity * log( empty mass ratio / ( 1.0 + payload ratio ) )

fuel mass = mass * ( 1.0 - ( 1.0 + payload ratio ) / empty mass ratio )
 
 

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