Ballistics Model for Particles on a Horizontal Plane in a Vacuum Propelled by a Vertically Impinging Gas Jet

Abstract

In previous work, a time-stepped numerical algorithm to compute particle trajectories consisting of lunar soil blown by the engine exhaust of a lunar lander was developed. The time-stepped integration method relies on the gas density, velocity, and temperature fields, calculated by computational fluid dynamics simulations, to compute the forces and accelerations acting on single noninteracting particles. In this paper, a computationally efficient particle ballistics model is presented where the trajectory is estimated by computing the vertical position (axial coordinate x) as a function of the horizontal position (radial coordinate y) using a constant horizontal velocity and a vertical acceleration approximated as a power-law. The unknown parameters of the model are determined by fitting the ballistics trajectory path to a matrix of trajectories generated by the time-step integration method using the rocket exhaust gas properties predicted by computational fluid dynamics software. Also in previous work, a strictly empirical trajectory model was developed to satisfy the need for a computationally efficient method of computing particle trajectories. This new model (like the previous model) is expressed as a time-independent trajectory path function. However, the method of this current work is based on physical laws of motion, unlike the previous empirical model.