Analysis of the two dimensional sheet debris flight equations: initial and final state

Abstract

This work presents some analytical and numerical results of a dynamic analysis of the dimensionless 2-D sheet flight equations. Two empirical models for aerodynamic forces and moments are used and compared. Results show that the initial condition of rest is always unstable, and for long times three distinct flight regimes are possible, depending on the initial angle of attack, the Tachikawa number, Ta (in fact, the parameter chosen was its inverse, <TEX>${\Omega}$</TEX>), and a mass ratio <TEX>${\Phi}$</TEX>. The final orbits in the velocity space and their maximum kinetic energy are compared with a theoretical asymptotic state of the motion equations, and some design considerations are proposed.