Spatial Parameterization of Blunt Body Dynamics under Parachutes

Abstract

The dynamics of blunt bodies under parachutes is complex. The designer must balance translational requirements to slow down rapidly and over short distance, without violating rotational requirements to avoid high rates, flipover, and riser recontact. The designer’s effectors are: parachute drag area, the timing of reefing stages, timing of chute cutaway, and timing of next stage deployment. In the time domain, the equations of motion are non-linear and time varying, which has limited their solution to the most idealized cases, among them the steady state flight at constant dynamic pressure. The steady state dynamic pressure assumption is quite limiting as the whole purpose of parachutes is to reduce the dynamic pressure in a series of highly transient events. This paper explores the body/chute system dynamics with distance as an independent variable, rather than time. We find in the spatial coordinates, the differential equation for dynamic pressure becomes linear and yields a simple closed form solution. But the main finding here is that translational dynamics alter the rotational stability during the velocity transient period. This effect is a strong function of the difference in drag area between the previous stage and the next, and decays to zero as the system approaches steady state velocity. The transient term is found to be stabilizing at cutaway (reducing drag area) and destabilizing for reefed systems (increasing drag area).