The linear relationship between the pressure and the relative wave elevation on the hull surface is a prominent factor to be reconsidered in relation to the uncertainty of the added resistance. An evaluation method is proposed to access the nonlinear relationship between the hull pressure and the relative wave elevation, which has a decisive influence on the added resistance evaluation. This method is used to experimentally investigate the effect of bow-wave breaking of the fast displacement ship in waves. The results show that the nonlinearity between relative wave elevation and hull surface pressure due to the plunging breaking of a bow wave is intuitively detected using the proposed analytical tool. The effect of bow-wave breaking is deduced by comparing the integral of the local pressure. This study provides important insight into the nonlinear relationship between relative wave elevation and added resistance. In addition, the findings provide a better understanding of the process of plunging breaking of bow waves. The procedure of plunging type of bow-wave breaking is defined in three stages considering the relationship between pressure and wave height: bow-wave developing stage, pile-up and breaking stage, and bow-wave absent stage.

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The publication of the Energy Efficiency Design Index (EEDI) by the International Maritime Organization (IMO) has recently stimulated the accurate assessment of actual sea performance of ships, which is evaluated as added resistance in waves. However, a satisfactory consensus on the evaluation method has not yet been reached owing to uncertainty in wave added resistance. This uncertainty can be improved by developing analytical methods that recognize nonlinearities. A typical factor contributing to the uncertainty of added resistance is the breaking of the bow wave. In this study, an evaluation method is developed to explain the nonlinearity of added resistance due to the uncertainty of bow-wave breaking. The accuracy of evaluation of added resistance can be improved by considering the speed of the ship, which affects the stability of the bow wave. This study also confirms that the breaking of the bow wave causes a violation of the linear relation between the pressure and the relative wave elevation of the bow wave. In order to express the nonlinearity of added resistance due to the breaking of the bow wave, a transfer function including the speed of the ship is proposed because the speed of the ship affects the stability type of bow-wave breaking. By analyzing the results of the added resistance measured in a fast ship series test, it was confirmed that the added resistance should be evaluated by considering the ship’s speed. In addition, hull pressures and relative wave elevations are measured for the mother ship of the series test, and analysis tools are developed to represent the nonlinearity between these two signals. This analysis confirms that the nonlinear relationship between the hull pressure and the relative wave elevation, which significantly contributes to the added resistance, is greatly influenced by the speed of the ship. This study provides important insight into the violation of the linear relation by using the proposed analysis tools. The results show that the nonlinearity due to the plunging breaking of a bow wave is intuitively detected. The nonlinearity is shown to vary with the ship’s speed. The findings provide a better understanding of the process of plunging breaking of bow waves. Based on the above findings, a correction model is proposed to improve the accuracy of numerical calculation performed using the linear potential theory. The calculation of the fast ship is compared with the experimental results. The results reveal that the accuracy of added resistance estimation can be improved through the physics-based correction. Furthermore, a method for improving the reliability of the added resistance estimation is proposed by identifying the nonlinearity of the plunging breaking of the bow wave on a fast displacement ship.@en

A bow wave breaking is one of the most prominent factors to be considered regarding the nonlinearity of added resistance for a ship. Considering the stability of the bow wave breaking, which is mostly influenced by the ship speed and the waterline entrance angle, can enhance understanding of the nonlinearity. Understanding of the nonlinearity can be improved by considering the stability of the bow wave breaking, which is mostly influenced by the ship speed and the waterline entrance angle. New transfer function containing the ship speed is proposed to make a better representative of the nonlinearity. This method is evaluated with the model test data of the Fast Displacement Ship (FDS) under the short waves condition (λ/L= 0.4). This study has shown that new transfer function can be an efficient analysis method of the ship performance prediction offering intuitive consistency with proposed residual resistance concept. The findings lead to better understanding the nonlinearity considering bow wave breaking.@en