Towing simulation in wind through a nonlinear 4-DOF model: Bifurcation analysis and occurrence of fishtailing

Towing dynamics is investigated by means of a simplified mathematical model that approximates the tug as a point particle with prescribed motion, while the tow is modelled as a 4-DOF (surge/sway/yaw/roll) nonlinear dynamical system. Manoeuvring forces and moments are calculated via a model capable of dealing with high drift angles; aerodynamic effects are also taken into account and the connection between the tug and the tow is simulated by means of a single elastic towline. A numerical bifurcation analysis is carried out to determine the equilibria of the system when a relevant parameter (such as wind direction/speed) is modified. Time-domain simulations are performed wherever necessary. An example application is proposed, in which the behaviour of two vessels under towing is examined. It is shown that multiple stable/unstable towing equilibria may exist and that the response of the system is deeply affected by the wind direction and speed; in the absence of stable equilibrium solutions, a potentially dangerous fishtailing phenomenon takes place, sometimes leading to evident roll oscillations and large snap-loads in the towing line. Two different towing speeds are examined, in order to analyse how such an important operational parameter can affect the equilibria of the system and their stability.