ANALYTICAL OPTIMIZATION OF ROCKET NOZZLE EXPANSION RATIOS FOR ENHANCED PROPULSIVE EFFICIENCY ACROSS VARIABLE ATMOSPHERIC ALTITUDES

Abstract

This study investigates the analytical optimization of rocket engine nozzle expansion ratios to maximize thrust efficiency across varying atmospheric altitudes. While traditional bell-nozzle designs are optimized for a specific ambient pressure, their performance significantly degrades under off-design conditions, leading to flow separation or underexpansion. We present a comprehensive mathematical model based on isentropic flow relations and the Method of Characteristics to evaluate the pressure-area relationship within the supersonic regime. By formulating a multi-objective optimization function that considers mass flow rate (m), exit Mach number (M_e), and ambient pressure fluctuations, this research identifies the critical expansion coefficients () that minimize losses in specific impulse (I_sp). The results demonstrate that a dual-contour optimization approach can enhance vacuum thrust by up to 4.2% compared to static conical designs, without increasing the engine's structural mass. These findings provide a theoretical framework for the development of next-generation adaptive nozzle systems in multi-stage aerospace vehicles.