Analysis of two-stage endo-atmospheric separation using statistical methods

In this paper, selection and analysis of an atmospheric two stage separation system is discussed. The main purpose of this system is to test a supersonic parachute projectile, where a stage separation occurs after the burn out. Subsequently, the parachute is ejected from the payload after a minimum elapsed time. The separation times, for the supersonic parachute ejection, as well as the time needed for a safe clearing distance between the two stages are two critical issues in the separation process. In this respect, the knowledge of the relative position between the two stages is necessary to assure a safe distance and in order to adjust the required system parameters. In addition, as the nature of the parameters involved in the separation process is not deterministic, it would be useful to utilize the concept of random variables in the dynamic modeling of the separation process. In this paper, the modeling and simulation of the separation process is initially performed and partially verified. Subsequently, an approximate statistical method is utilized to acquire some probabilistic information about the relative distances at the two critical times. According to the simulation results, the relative distance between the two stages falls in a safe region. Finally, Monte Carlo simulation is also performed for comparison and verification of the statistical results that indicated a small and acceptable deviation between the two approaches. Thus, it can be concluded that the simpler approximate statistical approach is also valid for uncertainty analysis and can provide valuable knowledge needed in the preliminary design phase of the separation system.