Simplified Mathematical Modelling of Wing Tip Vortices

A following aircraft may experience sudden loads due to encounter of wingtip vortices generated by a leading aircraft. Many techniques of various complexity have been used to model the effect of the trailing vortices on an encountering aircraft with varying levels of success in terms of predicting the overall effects. Three levels of modelling are usually implemented. The first is used to discriminate acceptable and unacceptable encounters, the second for hazard characterization and the third for evaluation of vortex hazard. The first level uses a 1-DOF aircraft model with 2-DOF vortex model. The second level of modelling uses a 3-DOF aircraft model with a vortex model which includes atmospheric effects. The third level is a 6-DOF aircraft model with a 3-DOF viscous vortex model. However, a combination of all models and methods have been used. The purpose of this paper is to establish a simplified mathematical model of wing tip vortices which can aid in the investigation of: various patterns of aircraft responses to a vortex encounter, significant parameters, induced loads, vortex severity, and also in determining the set of parameters that affect the vortex-aircraft aerodynamic interaction. Mathematical modeling was done to derive the two most important vortex parameters, i.e. velocity and circulation. However, this was done qualitatively only to study the relative effect of the various parameters and not the exact quantities.