Approximation of the wave profile for simplified calculation of the waterplane area of a container ship in waves

The article proposes a stepwise approximation method for the wave profile to simplify the calculation of the waterplane area of a container ship in waves. The specific hull form of container ships, characterized by fine bow and stern shapes and a full midship section, leads to significant variations in the waterplane area when operating in waves, which directly affects stability and, consequently, navigational safety. Calculating the waterplane area under wave conditions is a complex problem that is difficult for navigation officers to solve in practical shipboard conditions. To facilitate this task, a simplified calculation method based on stepwise approximation of the wave profile and the use of waterplane section fullness coefficients is proposed. This method makes it possible to determine changes in the waterplane area depending on the position of the wave along the ship’s hull. The study employs the characteristics of a real large container ship for the calculations. A quasi-static positioning of the ship on a wave whose length is equal to the ship’s length between perpendiculars is considered, and two wave crest position scenarios along the hull are analyzed: at the bow and stern, and at the midship section. Waterplane profiles for specified draughts are obtained from measurements taken from the ship’s design drawings. The areas of the waterplane sections and their fullness coefficients are determined, and the waterplane areas in waves are calculated for the two selected scenarios. The calculation results demonstrate sufficient accuracy of the proposed method, which justifies its practical application by navigation officers. It is noted that further research based on the results obtained in this study may be aimed at identifying dangerous wavelengths not equal to the ship length and at assessing changes in container ship stability as a function of variations in the waterplane area in waves. The application of the research results by navigation officers will enable improved control of container ship behavior in waves and will significantly contribute to enhancing navigational safety.