Stoichiometry

Stoichiometry is an important concept in combustion and hybrid launchers, since they use the energy from combustible fuels. A stoichiometric mixture is one where the ratio of fuel and oxygen molecules is balanced, so all the fuel and oxygen in the chamber is (in optimal conditions) consumed in the reaction. A fuel meter system is usually designed to achieve this mixture, which will yield the most power out of the combustion reaction.

Calculations

The stoichiometric ratio for gaseous fuels can easily be calculated. When the hydrogen and carbon in a fuel burns, it combines with oxygen as follows:

C + O₂ --> CO₂
2H₂ + O₂ --> 2H₂O
C_xH_x + O₂ --> CO₂ + H₂O

If the fuel molecule contains oxygen atoms, they will replace oxygen atoms from the air in the reaction. So for each oxygen atom the fuel contains, one less atom of atmospheric oxygen is needed. To begin calculating the stoichiometric ratio of a fuel, first find the chemical formula for the fuel, and count how many hydrogen, carbon and oxygen (if any) atoms it contains.

Since hydrogen combines with oxygen to make water (H₂O), and two hydrogen atoms combine with every oxygen atom, four hydrogen atoms will consume one O₂ molecule. Conversely, it can be said that one hydrogen atom will consume 0.25 O₂ molecules.

Carbon atoms combine with oxygen to form CO₂, so each carbon atom will consume one entire O2 molecule.

Any oxygen in the fuel will lead to one less oxygen atom being consumed from the air. Two oxygen atoms will prevent one O₂ molecule from being consumed, so each oxygen atom "saves" 0.5 O₂ molecules.

Now we need to find how many O₂ molecules are consumed by each fuel molecule, which is calculated as follows:

• for each hydrogen atom, add 0.25 to the amount of oxygen molecules needed
• for each carbon atom, add 1
• for each oxygen atom, subtract 0.5

The resulting number is the oxygen to fuel ratio. To find the fuel to oxygen ratio, divide 1 by this number. The amount of oxygen in air is 21%, so to find the fractional fuel to air ratio, the fuel to oxygen ratio is multiplied with 0.21. To find the ratio in percent, multiply this value by 100.

To find the volume of fuel needed for a particular chamber, the fractional ratio is multiplied by the chamber volume.

Concrete example

Formula of propane: C3H8

• number of carbon molecules: 3
• number of hydrogen molecules: 8
• number of oxygen molecules: 0

number of oxygen molecules needed = 3*1 + 8*0.25 = 5 molecules
the actual combustion reaction is as follows: C3H8 + 5O₂ --> 3CO₂ + 4H₂O

fuel/oxygen ratio = 1/5 = 0.2
fuel/air ratio = 0.2*0.21 = 0.042, or 4.2%
fuel volume in a 3000 cc chamber = 3000*0.042 = 126 cc

Single formula for fractional fuel to air ratio: (1/(C+(H/4)+(O/2)))*0.21