Development of a Mathematical Model and Difficulty Index for Bulk Carrier Jetty Approach under Adverse Meteorological Conditions

Abstract

Adverse meteorological and oceanographic conditions can significantly increase the difficulty of low-speed jetty approaches. However, wind, current, tug assistance, vessel response, and under-keel clearance are often assessed separately. This study develops a non-dimensional Jetty-Approach Difficulty Index (J) that integrates these factors into a single quantitative measure. The model was applied to a loaded bulk carrier approaching Kapar Power Station during strong winds, currents, a spring tide, and a squall. Time-resolved operational and environmental data were analysed and compared with an independent marine pilot assessment. The calculated index was J = 4.481, representing Difficulty Level 4, classified as Challenging, and was consistent with the pilot’s rating of 4/5. Environmental sway and yaw loading contributed approximately 84.5% of the total index. The proposed framework provides a practical basis for quantifying approach difficulty, although further cases are required for calibration and validation.