Analysis of Ship Stability Using Longitudinal and Transverse Equilibrium Equations: A Practical Application on the Libyan Vessel ANWAAR AFRQYA

Abstract

Load distribution within ships, particularly oil tankers, is a fundamental factor that directly impacts their stability and navigational safety, especially in light of the ongoing changes in shipping patterns and modern marine designs. Despite the existence of general regulatory standards, maritime accidents still indicate gaps in understanding the precise relationship between longitudinal and transverse mass distribution and its impact on the dynamic and static stability of ships. Based on this problem, this study aimed to; analyze the stability of marine vessels by applying mathematical modeling of longitudinal and transverse equilibrium equations, using the Libyan oil tanker ANWAAR AFRQYA as a real-world case study. The metacentric height (GM) and the righting arm (GZ) are key indicators used to assess a ship's ability to resist heeling and capsizing under various maritime forces. Based on the vessel's actual specifications, the submerged volume and transverse moment of inertia were estimated to calculate the metacentric radius and GM under different loading conditions. The results showed that a ship is unstable when the center of gravity is significantly higher than the center of buoyancy. The center of gravity is higher than the metacenter (M), and the GM value becomes negative, indicating a tendency to capsize, which increases the possibility of a rollover, especially at angles of inclination exceeding 15°. When the center of gravity was lowered to more appropriate levels, the stability improved significantly, with GZ values remaining within safe limits. This study highlights the importance of load distribution and dynamic ballast systems, particularly for deep-draft, longitudinally structured tankers. It also emphasizes the value of mathematical models in supporting engineering decisions during both design and operational phases