The debris flight equations

This paper presents a mathematical analysis of the equations of debris flight. In particular the two-dimensional motions of two types of debris are considered—compact and sheet debris. The equations of motion for debris flight are derived in a generalised dimensionless form that reveals the fundamental controlling parameters of the problem. Simplified forms of the equations are then derived for compact and sheet debris, and the large time asymptotic solutions derived for velocities and energies. Numerical solutions of the equations of motion are presented for a range of the controlling dimensionless parameters that are typical of full-scale conditions. The results are compared as far as possible with experimental data. The results for compact debris are well defined and the predicted dimensionless velocities and trajectories are a function of a single dimensionless parameter. For the sheet debris, however, the situation is much more complex, and the results show a level of sensitivity to boundary conditions and the values of the controlling parameters that is typical of chaotic systems. For such objects debris flight can take a number of forms with clockwise, anti-clockwise or no rotation taking place. The resulting dimensionless trajectories and velocities are widely spread. The effect of simulating atmospheric turbulence on the flight of both types of object was also considered, and it was shown that if the gust wind speed during the course of the debris flight is used as the normalising velocity, the variations in trajectory, although noticeable, are not particularly large. A discussion of how this analysis could be used in the design process is then presented, conclusions are drawn and suggestions made for further work.