Modelling of wreckage trajectories following in-flight breakup

The study of ballistic trajectories is well-­established, with work dating back to the 1940s. More recently, ballistic trajectory analysis has been used by air accident investigators in an attempt to understand events leading up to an accident, with notable examples including the investigation into the Lockerbie bombing. Building on the history of a previous model, this thesis offers an enhanced model for the calculation of ballistic trajectories incorporating altitude dependence for wind, density and gravity. Attempts to solve the model analytically were unsuccessful, and therefore, the model was solved numerically using an implicit scheme, to deal with the inherent stiffness of the equations, and an extrapolation technique. Cubic splines were used to accurately represent the wind proUile in an analytical way. The numerical solution was veriUied against a simpliUied analytical case and results are presented for two simulated breakup cases. Four key parameters were then varied to provide information about the sensitivity of Uinal wreckage location to variation in system parameters. The results indicate that for simulated large aircraft breakups, low ballistic coefUicient items are most heavily affected by breakup altitude, wind magnitude and wind angle whereas large ballistic coefUicient items are most heavily affected by breakup velocity, although to a much lesser extent (around 15% of the distance of low ballistic coefUicient). For small aircraft breakups, wind angle and breakup altitude have the largest effect on low ballistic coefUicient items, with velocity and altitude affecting high ballistic coefUicient items to a larger extent (around 50% of low ballistic coefUicient items). The results will allow investigators to understand better the factors which affect items of differing ballistic coefUicient in different situations. The project as a whole provides a new solution engine for the trajectory problem which can form the basis of a new software package for investigators.