Purpose The purpose of this paper is to introduce new and modified “staged combustion” cycles in the form of engineering algorithm as a possible propulsion contender for future aerospace vehicle to achieve the highest possible “total impulse” to “mass” of propulsion system. Design/methodology/approach In this regard, the mathematical cycle model is formed to calculate the engine’s parameters. In addition, flow conditions (pressure, temperature, flow rate, etc). in the chamber, nozzle and turbopump are assessed based on the results of turbo machinery power balance and initial data such as thrust, propellant mixture ratio and specifications. The developed code has been written in the modern, object-oriented C++ programming language. Findings The results of the developed code are compared with the Russian RD180 engine which demonstrates the superiority and capability of new “thermodynamic diagrams”. Research limitations/implications This algorithm is under constraint to control the critical variation of combustion pressure, turbine rpm, pump cavitation and turbine temperature. It is imperative to emphasize that this paper is limited to “oxidizer-rich staged combustion” engines with “single pre-burner”. Originality/value This study sheds light on using fuel booster turbopump and the second-stage fuel pump to moderate the effect of cavitation on pumps which reduces tank pressure and, as a consequence, decreases the propulsion system weight.