Development of a sensitivity analysis tool for the trajectory of multistage launch vehicles

Abstract

The primary objective of this work is to create a highly accurate sensitivity analysis tool for multi-stage launch vehicle trajectories. This tool is designed to assess the impact of various parameters on the trajectory and performance of multi-stage launch vehicles. To achieve this, we have developed high-fidelity simulation software that considers all translational and angular movements by modelling the six-degrees-of-freedom (6DOF) equations of motion. The validation of this software is based on experimental data. An essential aspect of this work is the utilization of the developed sensitivity analysis tool to determine how different parameters affect the trajectory of multi-stage launch vehicles. Through the sensitivity analysis conducted using the developed tool, it is possible to identify which parameters are of critical importance during the design phase. We apply a generic mission profile for the Minotaur-I launcher to obtain parametric dependencies of the flight path. Through a comprehensive parametric study, we evaluate a range of critical parameters, including gross lift-off weight, a specific impulse of each stage, pitch-over manoeuvre initial time and angle, and ignition impulse of each stage. These parameters significantly influence the trajectory, performance, and reliability of the launch vehicle for mission design and success. The results of the sensitivity analysis underscore that even minor variations in these parameters can result in substantial deviations from the nominal insertion altitude. The acceptability of errors in specific impulse changes varies across stages, with maximum changes of 6.07%, and the fourth stage showing less sensitivity at 0.13%. However, it's important to note that variations in the parameters of the first stage tend to be challenging to rectify once they occur, with maximum changes in specific impulses reaching 75.57%. Another noteworthy discovery is that the acceptability of changes in pitch-over manoeuvre initiation times depends on the rate of change; they can be deemed either acceptable or unacceptable based on this factor, with changes ranging between 17.90% and 98.38%.