Modeling the Transverse Roll Dynamics of a Small-Scale Ship Model and a Passive Internal-Pendulum Stabilization Concept

Transverse stability governs the safety and operability of ships, and roll—the rotation about the longitudinal axis—produces the largest lateral oscillations, affecting crew comfort, cargo safety and structural loads. Reduced-scale nautical models offer a low-cost route to study this behavior, yet quantitative roll models and simple, space-constrained stabilization solutions for competition models remain scarce. This work models the free roll of the Jaraqui nautical model as a linear second-order (mass–spring–damper) system, valid for small heel angles (sin φ ≈ φ). The equation of motion was cast in state-space form and integrated in MATLAB with the ode45 (Runge–Kutta 4/5) solver. A parametric study varied the damping ratio ζ from 0.02 to 0.50 at a natural frequency ωn = 1 rad/s and an initial heel of 10°; the damped period, 2% settling time and logarithmic decrement were computed. The simulated response reproduced the expected exponentially decaying oscillation. Increasing ζ from 0.02 to 0.50 shortened the 2% settling time from ≈200 s to 8 s and raised the logarithmic decrement from 0.13 to 3.63, while the damped period grew only 16%. A passive internal-pendulum stabilizer was then sized conceptually: the central hull region near the longitudinal center of gravity was identified as the installation site, with a 90–110 mm arm, a 150–250 g mass and ±20° travel, subject to a tuning condition ωpendulum ≈ ωroll for effective energy transfer. The linear model captures the essential roll physics and provides a design-oriented basis for a low-cost passive stabilizer; experimental identification of the true roll frequency and prototype testing are the next steps.