The payload ratio is defined as the mass of the payload divided by the empty mass of the structure. Because of the extra cost involved in staging rockets, given the choice, it's often more economic to use few stages with a small payload ratio rather than more stages each with a high payload ratio. When there is more than one stage, then the payload ratio should be similar in each stage. So for example if with available fuels and structures, it is found that 2.2 equal payload stages are needed to reach orbit, then both stages should have a mass ratio of a bit less than 1.0, say about about 0.9.

In cases where the empty structure has some use, for instance if the upper stage can be used as a pressure vessel for a space station, then it makes sense to use a very low payload ratio and go straight to orbit. This is barely achievable with a pumped LOX / kerosene spacecraft with the known exhaust velocity for that rocket being 3330 m / s.

In pumped rocket and rocket cost payload ratio is used to calculate final velocity, fuel mass, payload mass and tank mass.

fixed mass = engine mass + interface mass
fixed payload = payload ratio * fixed mass
relative tank mass = fuel volume ratio + oxidizer volume ratio + propellant volume ratio * tank pressure * 3.0 / effective tensile
tank payload = relative tank mass * ( 1.0 + payload ratio )
remaining mass = mass - fixed mass - fixed payload
fuel mass = remaining mass / ( 1.0 + tank payload )
tank mass = relative tank mass * fuel mass

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

payload mass = fixed payload + tank mass * payload ratio
 

In spacecraft in vacuum, atmospheric spacecraft, multi stage spacecraft and spacecraft cost payload ratio is used to calculate the duration, final acceleration, final velocity, fuel mass and payload mass.

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

payload mass = payload ratio * empty mass
 
 

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