Analysis of minimum safe approach distances based on vessels navigation safety domain

This article presents an analytical study of changes in the critical allowable approach distance between converging vessels, taking into account the shape of the vessel's safety zone. The research aims to address the important issue of ensuring maritime navigation safety by developing a mathematical approach for precise modeling of vessel domains under various approach scenarios. Analytical expressions are proposed and derived for calculating minimum safe distances for both elliptical zones and zones of complex configuration, allowing flexible assessment of approach situations depending on the relative motion of vessels. The analysis shows that although elliptical and complex-shaped domains differ geometrically, the nature of changes in critical approach distance in both cases remains similar, indicating the possibility of effective application of either model in practical conditions depending on the required level of detail and available computational resources. Graphical representation of the results clearly illustrates the dynamics of distance changes as a function of the angle between the courses of approaching vessels, which can be used in the development of software for navigation systems. The obtained dependencies allow not only quantitative assessment of allowable approach distances but also account for the influence of the approach aspect, which significantly affects the decision-making process by both navigators and automated collision avoidance systems. The results create a foundation for further improvement of collision avoidance algorithms and contribute to increasing the level of automation in navigation processes and overall maritime safety, especially in conditions of heavy traffic or restricted waterways.