Modelling of flight dynamics of an airplane encountering trailing vortices generated by another airplane

This paper presents method of flight dynamics modelling for aircraft encountering trailing vortices generated by other airplane. The mathematical model of 6-DOF spatial motion was applied. Aerodynamic forces produced by a wing were calculated using strip theory method – the wing was divided into a series of chordwise strips and contribution of each strip in these forces was determined. Local angle of attack for each strip was determined taking into account an influence of trailing vortices. Exemplary results of simulations for the case of two straight vortices encountered by aircraft are shown. Incremental contributions to aerodynamic forces and moments of all strips are summed. Model and description of trailing vortices, induced velocity inside the vortex, induced velocity outside the vortex, model of motion dynamics, equations of motion, airplane forces, moments acting on the airplane, aerodynamic forces and moments, trailing vortex effect on the airplane are presented in the paper. In particular, pair of straight trailing vortices, induced velocity for Rankine vortex, strip model of the wing, angle of attack for the strip, airplane pitch angle, bank angle, altitude, trajectory are illustrated.