Investigating the Effect of Bilge Keel Geometry on Roll Damping Using a Simplified Pendulum Model

Ship roll motion is a critical aspect of maritime stability and safety, influencing vessel performance, cargo integrity, and passenger comfort. Understanding the dynamic behavior of ships during roll decay is essential for optimizing design and operational safety. This study investigates the roll dynamics of three distinct vessel types—a Fishing Vessel, a Small Cargo Ship, and a Large Tanker—to analyze how size, displacement, and bilge keel configurations influence roll decay, angular velocity, and energy dissipation. The problem lies in understanding how these parameters affect stability across different ship classes. Using numerical simulations, roll motion was modeled for each vessel over a 60-second decay period. Results showed that smaller vessels, such as the Fishing Vessel, exhibited faster roll decay with stabilization occurring within approximately 30 seconds, owing to their lower mass and more efficient energy dissipation (final energy near 0 J). In contrast, the Tanker required over 50 seconds to stabilize, reflecting slower energy dissipation rates and significant inertia (initial energy of ~2.5 × 10⠶ J). The phase diagrams further demonstrated the gradual convergence of roll motion trajectories toward equilibrium for all vessels, highlighting the influence of vessel-specific dynamics. This study provides actionable insights into the effects of vessel design on roll stability, offering recommendations for enhanced bilge keel configurations and supplemental damping systems for larger vessels. These findings contribute to the development of safer and more efficient ship designs, ensuring operational stability across various vessel types.