Scale effects on the wave-making resistance of ships sailing in shallow water

The conventional extrapolation of ship resistance from model tests to full scale presumes that the coefficient of wave-making resistance (C_w) depends on the Froude number only. This leads to the assumption that C_w of a ship is identical to C_w of its scaled model. However, this assumption is challenged in shallow water due to viscous effects, which are represented by the Reynolds number (Re). In this study, different scales (different Re) of the Wigley hull and the KCS hull are used to investigate the scale effects on C_w numerically. After verification and validation, systematic computations are performed for both ships and their scaled models in various shallow-water conditions. Based on the results, significantly larger values of C_w are found for the KCS at model scale in very shallow water, suggesting that the conventional extrapolation has to be reconsidered. Additionally, this study reveals the relationship between the changes in frictional resistance coefficient (C_f) and the changes in C_w caused by shallow water, which benefits the prediction of shallow water effects on C_w. Finally, use of a larger ship model, where the Re is also higher, is recommended for resistance tests in shallow water to reduce scale effects on C_w.