# Research on the Hydrodynamic Performance of a Pentamaran in Calm Water and Regular Waves
## 1 Introduction  
Global climate change may be one of the most challenging environmental problems facing society [1; 2]. Freight merchant ships and containerships are among the largest maritime emitters of CO\({}_{2}\). The scarcity of fossil fuels and rising concern about global warming have prompted international organizations to improve vessel efficiency and push the development of ship energy technologies such as wing systems, propeller boss cap fins, reaction rudders, and high-performance ships [3; 4]. The pentamaran is a new type of high-performance ship developed at the end of the 20 th century. Its structure consists of a slender main hull and four side hulls distributed on both sides of the main hull. Due to its advantages of low high-speed resistance, good stability, and high seaworthiness, the pentamaran has good application prospects in both commercial and military ships [5]. It is believed that a pentamaran can carry more cargo compared to traditional commercial containerships, thereby increasing cargo volume and reducing polluting gas emissions. At the same time, the speed range of the pentamaran varies widely and is also suitable for speed variations from low to high. This also has a positive effect on environmental protection [6]. Since it was proposed, many scholars have studied the hydrodynamic performance of the pentamaran. [PERSON] et al. [7] and [PERSON] [8; 9] completed the preliminary design of a transatlantic pentamaran container ship with a loading weight of up to 8000 tons and aservice speed of 40 knots, carrying out model tests and optimization of the pentamaran. The pentamaran designed by [PERSON] et al. is shown in Figure 1. This was a relatively early pentamaran design proposal. Most subsequent studies were conducted on the basis of this design. [PERSON] and [PERSON] [10] conducted nonlinear time-domain simulations of ship motion and load effects on a same pentamaran container ship under different sea conditions. The results showed that when the ship's hull was treated as a rigid body, the predicted wave-induced design vertical sagging and hogging bending moments amidships were comparable to the rule values. The structural dynamic effects, mainly whipping, would increase the design values by 30% to 50% in the numerical prediction. [PERSON] et al. [11] explored the resistance characteristics of the pentamaran using experiments and studied the influence of parameters of rear side hulls including the shape line, position, and displacement on the resistance characteristics. The results showed that the rear side hulls should use a conventional molded line. [PERSON] [12,13] and [PERSON] [14] studied the hydrodynamic performance of the pentamaran in calm water. Through the research, it was shown that the computational fluid dynamics (CFD) method could be used to calculate and simulate the hydrodynamic characteristics of the multi-hull ship with free surface. Combined with the classical linearized free surface conditions, [PERSON] [15] proposed a boundary element method based on the potential flow theory to predict the hydrodynamic performance of a pentamaran in unbounded water at a constant speed. He came to the conclusion that when Froude number \(F_{n}\) was greater than 0.8, the wave-making interference between the main hull and side hulls was small, which could significantly reduce the wave-making resistance. [PERSON] et al. [16, 17, 18] studied the resistance characteristics of the pentamaran with variable side hull spacing and position using the towing tests, finding that the influence of the side body position on the resistance was closely related to \(F_{n}\). In recent years, [PERSON] and his team have been active in the research of the pentamaran, covering the overall arrangement of side hulls [19], the installation layout of symmetrical and asymmetrical side bodies [20,21], drag reduction of X-shaped pentamarans [22], and the optimization of main and side hulls profiles [23,24]. [PERSON] et al.