This paper studies the estimation of added resistance of ships in both head and oblique waves using an asymptotic formula in short waves. The enhanced asymptotic formula, which was introduced only for head waves by Yang et al. (2018), is extended for oblique waves. A new correction term due to the finite draught of the ship is derived based on different control surface compared with the previous formula. The local steady velocity that was proposed in the previous modification is applied only for the bow region and the original local steady velocity is used for the ship part after the mid-ship. The bluntness coefficients are also modified taking into account the incident wave angle. The results of added resistance in short head and oblique waves are compared to experimental results, other empirical formula, and/or numerical computation.


Due to the regulation for evaluating an energy efficiency design index (EEDI) for newly built ships to restrict greenhouse gas emissions, the added resistance of ships in seaway is an important issue in seakeeping and ship resistance communities. The additional resistance due to incoming waves is the main contribution to determine the weather factor, which is the ratio of ship speed in a real sea condition to that in calm water. Thus, an accurate and efficient method to predict the added resistance in waves is required for early stage ship design (Yang et al., 2018).

A significant amount of research has been performed on this issue over the last several decades based on experimental, numerical, and simplified approaches (Seo et al., 2013, references are therein). Because modern merchant ships are much larger than in the past, the waves encountered are of relatively short wavelength. The asymptotic formula (Faltinsen et al., 1980) and empirical formulae (Tsujimoto et al., 2008; Sea Trial Analysis JIP, 2006; see also International Standard Organization, 2015) of added resistance in waves are fundamental tools for predicting the added resistance of ships in short waves.

The asymptotic formula of added resistance in short waves shows fair agreement with experimental data for blunt ships at low forward speeds, whereas underestimation of results can be observed for slender ships at relatively high forward speeds. The modification was made in the original asymptotic formula introducing refraction of incident waves near the ship bow based on the conservation of wave action (Ohkusu, 1984). However, Ohkusu's method tends to overestimate the added resistance in short waves for blunt ships at low speed, while it still provides underestimated added resistance for slender ships.

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