Fuel mass ratio is the mass of fuel divided by the total mass of fuel, oxidizer and propellant. The fuel mass ratio is low if the fuel is high in hydrogen, which has one reducing electron and a molecular weight of one. The fuel mass ratio is higher if the fuel is high in carbon, which has four reducing electrons and a molecular weight of twelve. The fuel mass ratio is really high if the fuel is high in oxygen, which has minus two reducing electrons and a molecular weight of sixteen. So hydrogen gives the lowest fuel mass ratio and methanol gives the highest fuel mass ratio.

A typical fuel mass ratio is one quarter. This is why there have been many attempts to power high speed craft with atmospheric oxygen. However, this is not practical above about mach three because the equipment needed to use dilute, gaseous oxygen at that speed weighs more than an onboard liquid oxidizer. In general for orbital craft, it is useful to have a first stage operating up to about mach three to use atmospheric oxygen and the second stage to use rockets. Given the combustion efficiency, fuel molar, mixture, mixture oxidizer mix and mixture oxidizer mix, the fuel molar ratio can be calculated which in turn with fuel molecular and oxidizer mix molecular is used to calculate the fuel mass ratio.

fuel molar ratio = 1.0 - mixture
mixture oxidizer mix = 1.0 + mixture

unreacted fuel = 0.0
if ( fuel molar ratio > mixture oxidizer mix ) {
    unreacted fuel = fuel molar ratio - mixture oxidizer mix
}

If the combustion isn't ideal:

if ( combustion efficiency < 1.0 ) {

Then the quadratic equation is used to determine the part of each reactant that combines chemically:

    ratio = 9999999.9
    if ( fuel molar ratio != 0.0 ) {
    ratio = mixture oxidizer mix / fuel molar ratio
    }
    unreactability = 1.0 / ( 1.0 - combustion efficiency )
    a = 2 * unreactability * unreactability
    b = a * ( ratio - 1.0 )
    c = ratio + 1.0
    unreacted = 0.5 / a * ( sqrt( b * b + 4.0 * a * c ) - b )
    unreacted fuel = fuel molar ratio * unreacted
}

fuel molar ratio *= fuel molar
mixture oxidizer mix *= oxidizer mix molar
mixture molar = fuel molar ratio + mixture oxidizer mix
fuel molar ratio /= mixture molar

fuel mass ratio = fuel molar ratio * fuel molecular
oxidizer mix mass ratio = mixture oxidizer mix * oxidizer mix molecular
mixture mass = fuel mass ratio + oxidizer mix mass ratio
fuel mass ratio /= mixture mass
 
 

This is used in bipropellant rocket, tripropellant rocket, pumped rocket and rocket cost.
 
 

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