A Novel Methodology and Modelling for the Calculation of the Ship’s Pivot Point Making Use of a Full-Mission Bridge Simulator

In recent years, both the number and the size of ships have increased considerably, whereas port areas have expanded much more slowly. As a result, port manoeuvres are increasingly performed in restricted waters, which increases navigational risk during ship operations. For this reason, ship-handlers must know the instantaneous position of the pivot point (PP) at any time. The aim of this paper is to propose novel mathematical models to determine the PP’s position and to identify the most relevant variables influencing it. For this purpose, a full-mission bridge simulator was used to generate a dataset based on multiple simulations performed under different combinations of rudder angles and engine telegraph orders. First, a new trigonometric formulation is proposed to determine the instantaneous position of the PP using only directly measurable variables, namely the speed through water and the transverse velocities at the bow and stern. Subsequently, additional predictive models were developed using Design of Experiments (DOE) and response surface techniques. These models achieve high predictive accuracy while remaining simple enough to be applied in practical ship-handling scenarios. The resulting models can assist ship-handlers in anticipating PP behaviour and improving manoeuvring safety, particularly in restricted waters. Original 3D charts showing the combination of several input variables are included to identify the map of the whole process.