This post covers some basic calculations of internal combustion engine volumetric efficiency, and compares at theoretical vs rated shaft-power outputs for some notable engines.
Composition of Air
Atmospheric air is comprised primarily of Nitrogen, Oxygen, and Argon, making up 78.08%, 20.946%, and 0.934% respectively by molar composition (and by volume if an ideal gas is assumed). Negligible quantities of CO2 and various noble gasses are also present.
From the respective molar masses of the components, m(N2) = 28g/mol, m(O2) = 32g/mol, and m(Ar) = 39.95g/mol, the %wt of oxygen can be found to be 23.16%.
Taking the density of air at sea level to be 1.225kg/m3 , the oxygen density is thus 0.28371kg/m3 , or 8.66mol/m3.
Stoichiometric Mixture Ratio of Petrol
For simplicity of calculation the composition of petrol will be assumed to be entirely comprised of Octane (C8).
Complete combustion of one mole of Octane with a molar mass of 114.23g/mol produces 8mol of CO2 and 9mol H2O molecules, consuming 12.5mol of O2 in the process, with a total mass of 400g at 32g/mol. The stochiometric mixture ratio of oxygen to petrol is thus 3.5017:1 by weight.
A cubic meter of air will thus fully combust 0.081021kg of petrol.
Theoretical Maximum Power Output
Using the 44.40MJ/kg LHV specific energy of petrol, a cubic meter of air thus has a potential energy of 3.59732MJ under stochiometric conditions, or 3.59732J/cc, which can be expressed as a maximum thermal power as a function of RPM and displacement.
$$Max\ Thermal\ Power (4\ stroke) = 3.59732 \cdot displacement(cc) \cdot RPM \div 120 = 0.03W/RPM/cc$$
$$Max\ Thermal\ Power (2\ stroke) = 3.59732 \cdot displacement(cc) \cdot RPM \div 60 = 0.06W/RPM/cc$$
From here we have no easy way to calculate volumetric efficiencies for different engines, without knowing the exact thermal efficiency under the test conditions. Instead we will compare the rated shaft power to the maximum thermal power, in order to find the projected efficiency under an assumption of 100% volumetric efficiency operation.
https://www.thermalfluidscentral.org/encyclopedia/index.php/Heat_of_Combustion
