Characteristic Curve of Closed-Cycle Liquid Rocket Engines

Teaching liquid rocket engine systems at the university or technical level often relies on simplified approaches that enable clear visualization of the fundamental principles and parameters relevant to design. In contrast, detailed design requires advanced methods that progressively incorporate the complexity of the engine subsystems. Although software for high-fidelity analysis is widely available, a sound understanding of basic concepts remains essential for rapid identification of system characteristics, for educational purposes, and for the preliminary assessment of potential concepts. Within this framework, several textbooks provide comprehensive resources on rocket science, particularly regarding the architecture of pump-fed liquid rocket engines. As a complement, the present study examines closed-cycle configurations through a unifying feature: the characteristic curve, which relates chamber pressure to the turbine temperature ratio—or, equivalently, to the turbine inlet pressure—based on the turbomachinery power balance. While simplified, this approach allows general considerations of practical relevance and, despite its limitations, provides insight into the chamber pressures attainable for different closed-cycle and propellant combinations.