Methods to Alleviate Processing Requirements of High-Fidelity Multibody Parachute Simulations Involving a Confluence Mass

Abstract

Methods designed to reduce the numerical stiffness and processing requirements of high fidelity entry trajectory models involving parachutes are explored. Parachute deployment systems have often been simulated using rigid body dynamic models. The system is comprised of a parachute rigid body attached to the vehicle via a confluence mass with flexible lines. The simulations incorporating the confluence mass often take excessive amounts of processing time due to the relatively small mass of the confluence point and the resulting high frequency motion. The two methods investigated here seek to simplify the equations of motion to be integrated in the simulation, removing the numerical stiffness and increasing the required time step. Initially an analytic solution is derived from previous work on the subject and is used to linearize the confluence point equations of motion about an equilibrium point. The motion of the confluence point about the equilibrium point can then be reduced to that of a simple harmonic oscillator, resolved analytically and averaged over a larger time step than required for integration of the original set of equations of motion. This procedure allows the removal of the equations of motion of the confluence mass from the system, replacing them with analytic solutions for its position and velocity. The numerically stiff portion of the simulation is thus removed, significantly improving processing time. The second method developed is entitled the singular perturbation method, and involves suppressing the small inertia of the confluence mass responsible for high frequency motion. The singularly perturbed system allows simplification of the equations of motion by removing the confluence point velocity state equations. The velocity state vector may be estimated by taking the limit of the equations of motion of the confluence point as its mass approaches zero. The stiffness of the equations is again removed, thereby increasing the integration time step and decreasing overall processing time. The singular perturbation method is applied to parachute entry models of the Mars Exploration Rover mission as well as the Crew Exploration Vehicle abort mode. Results from both methods are compared to models in which a confluence point with mass is used with integration of the full set of equations of motion. Performance is evaluated in each case by way of comparing integration time step to measure the benefits of application of the methods. Necessary assumptions and the resulting implications for each approach are defined and evaluated to assess the convenience and application of the methods.