This work describes a simulation program suitable for predicting the behavior of the boomerang in function of its geometrical characteristics, of the throw parameters and of the environmental conditions, taking into account any non-stationary states corresponding to some motion steps (throw, transition from helicopter mode to autogyro mode, landing). These phases certainly have a significant effect on the characteristics of the trajectory. Boomerang has been treated as a lifting rotor and the nonlinear Pitt-Peters dynamic inflow model has been used, even at very high values of the advancing ratio. The mathematical model is strongly nonlinear and thus greatly dipendent on the initial condition. The influence of different environmental conditions as well as different geometric and throw parameters have been shown through the graphical comparison of the geographical trajectories. Each qualitative trend has been experimentally verified and this is a preliminary confirmation of the reliability of the numerical code. Finally a whole flight has been described and analysed in each aspect and the necessity to use an unsteady model has been shown through a time-topographical analysis of the advancing blade angles of attack.