# Numerical Simulation of Seakeeping Performance on the Preliminary Design of a Semi-Planing Craft
## 1 Introduction  
Because of the increasing amount of attention being paid to maritime traffic safety, navigation safety has become a major concern that must be addressed. Ships must not only display favorable efficiency and offer optimal comfort that meets the requirements of owners but also demonstrate excellent seakeeping performance and structural strength. Thus, modern ships must exhibit favorable propulsion efficiency and navigational safety. Ships navigating the sea are subject to the effects of marine environments, and the effects of these environments are even more pronounced in high-speed crafts such as most yachts and military fast attack crafts. [PERSON] et al. [1] indicated that high-speed crafts may employ any of three motion modes for all Froude numbers (\(F_{r}=\frac{V}{\sqrt{gt}}\)). These modes are the displacement mode, transition mode, and planing mode. At moderate to high speeds, high-speed crafts experience dynamic lift that causes changes in their hull trim angles, thus seriously compromising their seakeeping performance. When analyzing the seakeeping performance of a craft, most studies have referenced related experimental research or performed numeral calculations. As technology and computer equipment become increasingly advanced, people regularly perform numerical calculations to design modern ships; several studies have adopted numerical methods to investigate ships' seakeeping performance. Generally, two primary methods are used to evaluate such responses, the two-dimensional strip theory and three-dimensional panel method. [PERSON] [2] used the two-dimensional strip theory to calculate the heaving and pitching motion of slender vessels in regular waves. [PERSON] [3] used the two-dimensional strip theorypresented by [PERSON] [2] as the basis to calculate wave loads such as vertical shear and vertical bending moments. [PERSON] et al. [4] proposed the use of the potential theory to calculate the motion responses of a vessel under regular wave conditions as well as the shear and bending moments created by such waves. This method, also called the new strip theory, is an improved version of the two-dimensional strip theory. In 1980, [PERSON] et al. [5] used the diffraction theory to calculate the hydrodynamic force and motion responses in oblique waves. In 1993, [PERSON] [6] combined strip theory in the time-domain to analyze the problem of nonlinear motion responses experienced by vessels under large-amplitude wave conditions. [PERSON] et al. [7] utilized two-dimensional strip theory to solve hydrodynamic force-related problems and developed a set of mathematical models to predict the influence of the bank effect on ship motion in waves. Because two-dimensional strip theory does not consider the interaction and speed effects between strips, its prediction and analysis accuracy for swaying and rolling motion is relatively poor. Accordingly, the three-dimensional panel method was developed to resolve these problems. [PERSON] [8; 9] proposed the use of three-dimensional frequency-domain Green functions to analyze ship motion. However, because of the technological limitations of computer hardware at that time, no major developmental breakthroughs were made until after 1970. [PERSON] [10] employed the three-dimensional singularity distribution method to investigate the motion, wave-exciting force, and moment of forward-moving vessels. [PERSON] [11] used three-dimensional pulsating sources to calculate the velocity potentials of ship motion. [PERSON] and [PERSON] [12] adopted the three-dimensional source distribution method to examine the diffraction and radiation situations of forward-moving vessels under the constraint of various water depth limits. [PERSON] et al. [13] utilized a three-dimensional time domain approach to study ship motion; [PERSON] and [PERSON] [14] developed a three-dimensional time-domain method to analyze large-amplitude ship motion.