Numerical Evaluation of Post-Deck-Flooding IMO Criteria for a Low-Freeboard Harbor Tugboat

Abstract

Low-freeboard harbour tugboats often work in quartering seas where a single boarding wave can leave water sloshing on deck and erode their transverse stability. This paper evaluates how much of that erosion a 28 m tug can tolerate before it breaks the intact-stability limits of IMO MSC 267(85). Using only the vessel’s trim-and-stability booklet, the study superimposes thin sheets of retained water—0 to 0.35 m deep, with drainage coefficients K = 0.50–0.90—on three loading states: fully laden, half-load and lightship. For every depth and K pair the corrected righting-arm curve, metacentric height and righting-area reserves are recomputed; a limiting-KG curve and a K–depth PASS/FAIL heat-map are then produced, and wave data from BMKG (2020–2024) are used to estimate the yearly probability of exceeding the IMO limits. Calculations show that in the full-departure condition the first IMO criterion fails when only 0.12 m of water is trapped at K = 0.70, whereas the threshold rises to 0.24 m at half-load and 0.31 m in lightship. Lowering K to 0.55—achievable by higher bulwarks or larger freeing ports—moves the failure boundary rightward by nearly 50 % and cuts the annual exceedance probability below 10^-3.