Numerical Study on the Influence of Catamaran Hull Arrangement and Demihull Angle on Calm Water Resistance

Abstract

This study investigates the WAM-V (Wave Adaptive Modular Vessel) catamaran configuration, focusing on the hydrodynamic interaction between its articulated hulls. The unique hinged connection mechanism induces a relative angular displacement between the demihulls during operation, significantly modifying the calm water resistance characteristics. Such resistance variations critically influence both vessel maneuverability and the operational effectiveness of onboard acoustic detection systems. This study using computational fluid dynamics (CFD) technology, the effects of varying demihull spacing and the angles of the demihulls on resistance were calculated. Numerical simulations were performed using STAR-CCM+, employing the Reynolds-averaged Navier–Stokes equations (RANS) method combined with the k-epsilon turbulence model. The study investigates the free surface and double body viscous flow at different Froude numbers in the range of 0.3 to 0.75. The analysis focuses on the effects of the demihull spacing ratio (B_S/L_PP, Demihull spacing/Length between perpendiculars) on calm water resistance. Specifically, the resistance coefficient at B_S/L_PP = 0.2 is on average 14% higher than that at B_S/L_PP = 0.5. Additionally, the influence of demihull angles on resistance was simulated at B_S/L_PP = 0.42. The results indicate that inner demihull angles result in higher resistance compared to outer angles, with the maximum increase in resistance being approximately 9%, with specific outer angles effectively reducing resistance. This study provides a scientific basis for optimizing catamaran design and offers valuable insights for enhancing sailing performance.

1. Introduction

The Wave Adaptive Modular Vessel (WAM-V) is distinguished by its remarkable adaptability, enabling efficient operations in the highly variable marine environment. It is suitable for a wide range of applications, including environmental monitoring and marine scientific research. The unique flexible structure of the vessel enhances the stability of the upper platform, which is extremely beneficial for many observational instruments. However, the flexible structure implies a variable flow field around the hull, which can affect the vessel’s resistance. Therefore, it is necessary to conduct resistance studies on different hull forms.

With the continuous advancement of computer technology and the optimization of computational performance, an increasing number of researchers have adopted CFD (Computational Fluid Dynamics) methods to investigate hydrodynamic characteristics of marine vessels, particularly in analyzing the influence of physical factors such as hull geometry, fluid–structure interaction, and viscous effects on hydrodynamic performance. Islam et al. [1] employed a RANS-based solver to predict the resistance of a container ship in calm water, comparing the results with experimental data. Similarly, Julianto et al. [2] investigated the structural response of a catamaran in waves using fluid–structure interaction (FSI) analysis. Li et al. [3] coupled aerodynamics and hydrodynamics using the RANS method to simulate the self-propulsion performance of an unmanned sailing boat, while Maki et al. [4] performed a numerical study on the calm water resistance of surface effect ships, comparing outcomes across different numerical methods. Mousaviraad et al. [5] conducted a URANS (Unsteady Reynolds-Averaged Navier–Stokes equations) analysis to explore the multibody dynamics of a flexible catamaran in calm water and waves. Chen et al. [6] carried out a systematic investigation into the hydrodynamic performance of a small unmanned catamaran, and Bekhit [7] performed unsteady RANS simulations to study ship resistance, heave, and pitch in regular waves. Broglia et al. [8] explored the interference effects in high-speed catamarans using numerical simulations, while Davis and Holloway [9] discussed the impact of ship shape on the motions of high-speed vessels in waves. These studies highlight the broad applicability of CFD technology in analyzing ship resistance performance and underscore its value as a critical tool for ship design and optimization. Zhao et al. [10] systematically investigated the hydrodynamic performance of a pentamaran in calm water and regular waves using finite volume methods, revealing how side hull arrangements influence resistance components and wave-making interference. Doğrul et al. [11] numerically analyzed the Delft 372 catamaran, quantifying interference factors (IF) in vertical motions and added resistance under head waves, emphasizing the significance of hull spacing in hydrodynamic interactions. Mittendorf and Papanikolaou [12] developed a simplified panel method based on thin-ship theory, integrated with surrogate models, to optimize a zero-emission high-speed catamaran. Their approach demonstrated computational efficiency comparable to advanced Rankine panel methods while capturing aerodynamic contributions from tunnel flow. Wang et al. [13] experimentally and numerically investigated the resistance characteristics of a high-speed planing catamaran, highlighting the tunnel’s aerodynamic lift—equivalent to 26% of the vessel’s weight at high speeds—as a key mechanism for resistance reduction. Nursal et al. [14] investigated the resistance characteristics of catamarans through towing tests and CFD analysis using the Realizable k-ε turbulence model, validating the accuracy of numerical simulations and finding that optimizing hull spacing and shape can significantly reduce resistance. Ozturk et al. [15] further studied the seakeeping performance of a new Double-M craft in regular waves using the Realizable Two-Layer k-ε turbulence model for full-scale CFD analysis. They found that the Double-M craft exhibited significantly reduced added resistance and motion responses in waves, with a 10.34% reduction in added resistance and 72.5% and 35.5% reductions in heave and pitch motion responses, respectively, at a wavelength-to-ship length ratio of 1.5. Farkas et al. [16] conducted a CFD investigation on the Series 60 catamaran, revealing that narrow separation distances (s/L = 0.226) at intermediate Froude numbers (Fn = 0.4–0.5) maximize interference resistance, where wave effects dominated and viscous interference was associated with crossflow. Subsequently, Farkas et al. [17] demonstrated for the Delft 372 catamaran that narrow spacing (s/L = 0.167) peaks the interference factor (IF) at Fr = 0.5, requiring overset mesh techniques to capture dynamic trim effects, while wider spacing (s/L = 0.3) significantly reduces resistance. Recent studies by Martić et al. [18] have revealed that total resistance of catamarans in shallow water conditions (h/T = 2) can increase by up to 40%. Through the integration of Enhanced Free-Form Deformation (FFD) with Particle Swarm Optimization (PSO), Guo et al. [19] achieved automated hull optimization, demonstrating the effectiveness of CFD in advanced hull form design.

Prior research on catamaran hydrodynamics has predominantly focused on rigidly connected hull configurations, with limited exploration of articulated systems such as the WAM-V. Peterson [20] conducted foundational studies on WAM-V dynamics, revealing that its suspension system significantly isolates payloads from wave-induced vibrations, CFD-MBD FSI validations studies by Conger et al. [21] have demonstrated the necessity of two-way coupling to resolve coupled hydroelastic phenomena, yet the hydrodynamic coupling between articulated hulls remains underexplored.

The numerical method using the unsteady Reynolds-averaged Navier–Stokes (RANS) model in conjunction with the Volume of Fluid (VOF) method and the k-ε turbulence model, is capable of accurately simulating hydrodynamic interactions and free surfaces and is applicable to a variety of catamaran configurations. However, it performs poorly in predicting complex flow phenomena.

This study focuses on a WAM-V for marine surveying, which employs a hinge-connected suspension damping system between the hulls. While enhancing equipment stability, this design introduces two critical hydrodynamic challenges: (1) Variable demihull angles formed during navigation significantly alter resistance characteristics. (2) Inter-hull flow disturbances directly affect the detection accuracy of acoustic surveying equipment. Addressing the research gap in systematic studies on small unmanned catamarans with variable angles identified in current catamaran hydrodynamics literature, this paper employs CFD methods to illustrate the influence mechanisms of demihull angle variations on resistance.

2. Numerical Method

2.1. Governing Equations

The unsteady Reynolds-averaged Navier–Stokes (RANS) model in STAR-CCM+ (v. 18.06.007-R8) software was employed for this study. The Volume of Fluid (VOF) method was employed to simulate free surface. The governing equations include the continuity Equation (1) and the momentum Equation (2), expressed as follows:

$$\nabla \cdot u=0$$

(1)

$${\displaystyle \frac{\partial u}{\partial t}} +(u\cdot \nabla )u=-{\displaystyle \frac{1 }{\rho }}\nabla p+\nu {\nabla }^{2}u+f$$

(2)

where u is the velocity vector, p is the pressure, ρ is the density, ν is the kinematic viscosity coefficient, and f is the volume force.

The standard k-ε model is widely recognized for its stability and high computational accuracy, making it a common choice for simulating high Reynolds number turbulence. In this study, the governing equations of the standard k-ε model are utilized, expressed as follows:

$${\displaystyle \frac{\partial (\rho k)}{\partial t}} +{\displaystyle \frac{\partial (\rho u_j k)}{\partial x_j }} ={\displaystyle \frac{\partial }{\partial x_j }}\left[\left(\mu + {\displaystyle \frac{{\mu }_t}{{\sigma }_k}}\right) {\displaystyle \frac{\partial k}{\partial x_j }}\right] +P_k +G_b -\rho \epsilon +Y_{M }$$

(3)

where P_k is the turbulent kinetic energy generated by the mean velocity gradient, G_b is the turbulent kinetic energy generated by buoyancy, and μ_t is the turbulent viscosity coefficient, usually denoted by ${\mu }_t=\rho C_{\mu }{\displaystyle \frac{k^2}{\epsilon }}$.

$${\displaystyle \frac{\partial (\rho \epsilon )}{\partial t}} +{\displaystyle \frac{\partial (\rho u_j\epsilon )}{\partial x_j }} ={\displaystyle \frac{\partial }{\partial x_j }}\left[\left(\mu + {\displaystyle \frac{{\mu }_t}{{\sigma }_{\epsilon }}}\right) {\displaystyle \frac{{\partial }_{\epsilon }}{\partial x_j}}\right] +C_{\epsilon 1}{\displaystyle \frac{\epsilon }{k}} (P_k +C_{\epsilon 3} G_b )-C_{\epsilon 2} \rho {\displaystyle \frac{{\epsilon }^2}{k}}$$

(4)

where C_ε1, C_ε2, and C_ε3 are empirical constants.

Using the VOF method to define the free surface, the phase distribution and position at the cross-interface are described by the field of the phase volume fraction α_i. The volume fraction of phase i is defined as follows:

$${\alpha }_i ={\displaystyle \frac{V_i}{V}}$$

(5)

where Vi is the volume of phase i in the grid cell and V is the volume of the grid cell. The sum of the volume fractions of all phases in the grid cell must be one:

$${\displaystyle \sum _{i=1}^N{\alpha }_i} =1$$

(6)

where N is the total number of phases. Depending on the value of the volume fraction, it is possible to distinguish the presence of different phases or fluids in the grid cell:

α_i = 0, the grid cell has no phase at all i;

α_i = 1, the grid cell is completely filled by phase i;

0 < α_i < 1, the value between the two limits indicates the presence of an interface between the phases.

2.2. Discretized Method

The flow governing equations, including the turbulence model, are solved using the Finite Volume Method implemented in the commercial software STAR-CCM+. The semi-implicit method for pressure-linked equations (SIMPLE) is employed as the solution algorithm.

In this approach, the continuity and momentum equations are first solved sequentially and then coupled through a predictor–corrector scheme. Spatial discretization is performed using a second-order accurate scheme, while temporal discretization employs a first-order Euler implicit scheme. Due to the implicit format of the time term, the calculation is unconditionally stable.

3. Numerical Calculations for Catamarans

3.1. Geometric Model and Principal Dimensions

The computational mesh generation was constructed based on a WAM-V model, specifically designed for a compact observation unmanned surface vehicle (USV), as shown in Figure 1.

Since WAV-M only has the pontoon interacting with water, the model is simplified to a double demihulls model. Its main parameters are shown in

Table 1. The main dimensions of the catamaran.

Dimension	Symbol	Value
Length between perpendiculars	LPP	3.5 m
Demihull spacing ratio	BS/LPP	0.42
Draft	T	0.12 m
Displacement	Δ	98 kg
Wetted surface area	S	2.3 m2

. The model parameters used to study the effects of B_S/L_PP are listed in

Table 2. Different values of B_S/L_PP considered.

Dimension	Symbol	Value
Demihull spacing ratio	BS/LPP	0.2
		0.3
		0.42
		0.5

.

Due to the flexible hinge connection of the demihulls, there will be an angle of the demihulls during navigation. The schematic of the model used to study the angle of the demihulls is shown in Figure 2. This study will study several parameters, with specific data shown in

Table 3. Different values of demihull angle considered.

Dimension	Symbol	Value
Angle of demihull (inner)	Ainner	2 deg
		4 deg
		6 deg
Angle of demihull (outer)	Aouter	2 deg
		4 deg
		6 deg

.

3.2. Computational Domain and Boundary Conditions

This calculation considers only the heave and pitch motions of the ship. To facilitate this, it is essential to establish a local coordinate system for the ship to define its motion directions. The origin of the local coordinate system is positioned at the center of gravity of the ship, with the x-axis pointing forward toward the bow and the z-axis oriented perpendicular to the ship, pointing upwards.

The computational domain is represented by a rectangular region, as shown in Figure 3 and Figure 4. An overview of the computational domain is shown in Figure 5.

The inlet boundary is positioned approximately 1.5L_PP from the hull, while the outlet boundary is located about 3L_PP from the hull. The vertical boundaries extend about 1.5L_PP above the water surface and below the hull. The left side boundary is set approximately 2L_PP from the hull. The velocity inlet is positioned at the bottom, 2.5L_PP below the water surface. The right side is symmetrical. The outlet boundary is defined as a pressure outlet, the hull surfaces are treated as walls, and all other boundary conditions are defined as velocity inlets.

The velocity setting of the velocity inlets is based on Equation (7):

$$v=Fr\cdot \sqrt{g\cdot L}$$

(7)

When Fr = 0.3, 0.4, 0.5, 0.6, 0.75, the corresponding velocity v = 1.76, 2.34, 2.92, 3.52, 4.39 m/s.

The wall boundary condition is treated using the Two-layer All Y+ Wall Treatment function in STAR-CCM+, and the no-slip wall condition is adopted.

The pressure outlet is initialized using the Hydrostatic Pressure of Heavy Fluid of Flat VOF Wave as the initial condition.

3.3. Mesh Generation and Time-Step Verification

When performing calculations using STAR-CCM+, selecting an appropriate computational domain and generating accurate meshing are critical steps. In this study, the Trim grid technique is primarily employed to handle the meshing of the catamaran.

To further enhance computational accuracy, mesh refinement is applied to critical regions, including areas around the hull, the upper and lower regions of the free surface, and zones where the hull geometry exhibits significant variation. This meshing strategy ensures high accuracy in essential regions while maintaining overall computational efficiency.

Specifically, the fixed grid cannot accurately track the dynamic trim and sinkage of the model, which critically affects free surface resolution and leads to inadequate representation of wave patterns. To address this, an overset mesh approach is employed, dividing the domain into two regions: the overset region (enclosing the ship) and the background region (Figure 6). The overset region moves with the ship across the stationary background grid covering the entire computational domain.

Before performing the calculations, it is essential to determine a suitable grid to balance calculation accuracy and computational efficiency. In this study, grid independence analysis is conducted by calculating the calm water resistance of a catamaran at Fr = 0.5. The numerical uncertainty analysis follows the recommendations of the International Towing Tank Conference (ITTC). The grid-scale refinement ratio (r_i), defined as $\sqrt{2}$, is expressed as follows:

$$r_i={\displaystyle \frac{\Delta x_{i,2}}{\Delta x_{i,1}}}={\displaystyle \frac{\Delta x_{i,3}}{\Delta x_{i,2}}}={\displaystyle \frac{\Delta x_{i,m}}{\Delta x_{i,m-1}}}$$

(8)

where Δx_i is the basic size of the grid and Δx_i,m is the mth Grid. Convergence was finally reached for the ship’s resistance at all three grid scales under the condition of constant density in calm water. The grid convergence was verified for the resistance coefficients, which are defined by the following equations:

$$C_T={\displaystyle \frac{R_T}{0.5\rho S{U}^2}}$$

(9)

where R_T is the resistance on the catamaran, ρ is the density of the water, S is the wet surface area for the catamaran, and U is the advance speed. The calculation results for the three grid scales are shown in

Table 4. Resistance coefficients for different numbers of grids.

Dimension	Symbol	Number of Grids	RT (N)	CT
Grid 1	${\phi }_{i,1}$	644,903	91.6	0.009279
Grid 2	${\phi }_{i,2}$	1,736,555	86.4	0.008752
Grid 3	${\phi }_{i,3}$	4,527,109	86.0	0.008712

.

When the calculation is performed, it is considered to converge when the change in resistance is less than 5%, as shown in Figure 7.

Particular attention is paid to boundary layer discretization to maintain a non-dimensional wall distance (y+) between 30 and 300, as wall functions are employed. The resulting y+ distribution meets the requirements. The specific distribution of y+ values can be found in Figure 8.

According to the ITTC Uncertainty Analysis in CFD Verification and Validation Methodology and Procedures, the determination of convergence needs to be based on a specific convergence parameter, and at least three solutions of different finenesses (m = 3) are required to evaluate the convergence of the input parameters. The convergence criteria defined in the guide are as follows:

$$R_i={\displaystyle \frac{{\epsilon }_{i,32}}{{\epsilon }_{i,21}}}$$

(10)

where ${\epsilon }_{i,32}={\phi }_{i,3}-{\phi }_{i,2}$ is the variation between the fine grid (Grid 3) and the medium grid (Grid 2), and ${\epsilon }_{i,21}={\phi }_{i,2}-{\phi }_{i,1}$ is the variation between the medium grid (Grid 2) and the coarse grid (Grid 1).

After calculation, the obtained coefficients show monotonic convergence. Under the condition that the numerical results satisfy the monotonic convergence, the uncertainty of the mesh can be simulated using Richardson’s [22] extrapolation. The order of the discretization error is defined using the following equation:

$$p_i={\displaystyle \frac{\ln (1/R_i)}{\ln (r_i)}}$$

(11)

Finally, the convergence of the grid is verified using the grid convergence index (GCI), in which

$$GC{I^{32}}_i=F_S{\displaystyle \frac{{\epsilon }_{i,32}}{{r_i}^{p_i}-1}}$$

(12)

where F_S denotes the safety coefficient, which is set to 1.25 for the case of three or more grids. The lower the GCI value, the less sensitive the numerical results are to grid changes. The calculated GCI value is 0.004%, which indicates that the effect of mesh refinement on numerical predictions decreases gradually as the number of meshes increases. These findings are summarized in

Table 5. Convergence ratio, discretization order, and GCI of grids.

${\mathit{R}}_{\mathit{i}}$	${\mathit{p}}_{\mathit{i}}$	$\mathit{G}\mathit{C}{\mathit{I}}_{\mathit{i}}$
0.077	7.4	0.004%

. Therefore, to utilize the computational resources more efficiently, a medium fineness grid (Grid 2) was selected for subsequent computations and a conservative grid selection strategy was adopted for the selection of the safety factor F_S. Grid 2 is shown in Figure 9 and Figure 10.

Three different time steps (0.02, 0.01, 0.005) were set to verify the calm water resistance of the catamaran under the above conditions, and the results are shown in

Table 6. Resistance coefficients for different time steps.

Time Step (s)	Symbol	RT (N)	CT
0.02	${\phi }_{i,4}$	85.7	0.00868
0.01	${\phi }_{i,5}$	86.4	0.00875
0.005	${\phi }_{i,6}$	86.4	0.00876

.

According to ITTC Uncertainty Analysis in CFD Verification and Validation Methodology and Procedures, the uncertainty analysis of time step can follow the same steps as the grid uncertainty analysis. Based on the steps mentioned above, the relevant parameters are obtained as shown in

Table 7. Convergence ratio, discretization order, and U_i of Time steps.

${\mathit{R}}_{\mathit{i}}$	${\mathit{p}}_{\mathit{i}}$	Ui
0.0606	8.088	10−4%

below, where U_i represents uncertainty, and its expression is the same as that in Equation (12).

The calculation U_i value is close to 0, which indicates that the effect of reducing the time step on the numerical calculation results is diminishing. This suggests that the numerical solution is becoming less sensitive to the time step size; therefore, a time step of 0.01 (s) is used for this study.

4. Effect of B_S/L_PP on Resistance

The effect of different hull spacings on the calm water resistance of the catamaran is analyzed first. This study focuses on the ratio B_S/L_PP, where B_S is the demihull spacing and L_PP is the length between perpendiculars. The analysis considers B_S/L_PP values of 0.2, 0.3, 0.42, and 0.5, and the corresponding calm water resistance is calculated at Froude numbers of 0.3, 0.4, 0.5, 0.6, and 0.75.

The simulations were performed using STAR-CCM+, with the application time set to 0.1 s, a buffer time of 0.5 s, and a maximum of 1200 iteration steps. The time step was set to 0.01 s, with a maximum of 10 iterations per time step. The calculations provided resistance values, and the resulting waveforms are shown in Figure 11. The resistance values were made dimensionless using Equation (9), and the results were compared with those of Mousaviraad [5]. The comparison curve is presented in Figure 12.

As shown in Figure 12, when B_S/L_PP = 0.2, the wave interference between the demihulls is the most intense. As shown in Figure 11, the darkest color intensity at B_S/L_PP = 0.2 indicates the highest peak wave elevation, resulting in the maximum wave-making resistance. Figure 13 further demonstrates that the wave-making resistance (R_W) at B_S/L_PP = 0.2 is significantly higher than in other cases, while the viscous resistance (R_V) exhibits nearly identical growth trends across all configurations. Consequently, the pronounced wave interference is the primary factor contributing to the elevated total resistance observed at B_S/L_PP = 0.2.

Furthermore, as shown in Figure 12, the C_T initially increases before decreasing with a rising Froude number, peaking at Fr = 0.4.

This phenomenon is in accordance with the Chengyi [23] and is caused by the fact that the first bow transverse wave of a single demihull already causes unfavorable interference for its own resistance, and the two demihulls of a catamaran deepen this interference within the critical spacing. When the speed increases, the first trough of the bow transverse wave moves further and further away from the stern with increasing speed, which is presented in Figure 14 marking part (the red circle), and the wave surface at the stern gradually rises, so the unfavorable interference between the demihulls gradually changes to favorable interference.

In this section, the resistance of different spacings was analyzed using numerical calculations, and it was found that changing the spacing within a certain range has a small effect on the resistance, and the reasonableness of the numerical model was verified by comparing it with Mousaviraad [5], which lays the foundation for the subsequent calculations.

5. Effect of the Demihull Angle on Resistance

The effect of the demihull angle on calm water resistance is analyzed in this study. Numerical calculations are conducted with B_S/L_PP = 0.42 under the conditions of Fr = 0.4 and Fr = 0.6.

The calculated waveforms are presented in Figure 15 and Figure 16, while Figure 17 illustrates the variation in resistance for Fr = 0.4 and Fr = 0.6.

From the results in Figure 17, it can be observed that the resistance on the catamaran with inner angles is greater than that with outer angles under identical speed conditions. For inner angles, the resistance of the catamaran increases as the angle increases. Notably, when the demihull outer angle is 2°, the resistance is lower than at 0°. However, as the outer angle increases beyond 2°, the resistance gradually rises and eventually surpasses the resistance at 0°. To further investigate the underlying mechanisms of this phenomenon, Figure 18 and Figure 19 present the variation curves of wave-making resistance and viscous resistance.

It is noted that for both Fr = 0.4 and Fr = 0.6, the variation amplitude of wave-making resistance is significantly greater than that of viscous resistance as shown in Figure 18 and Figure 19. The trend of wave-making resistance aligns closely with the total resistance, indicating that wave-making resistance dominates the variation in total resistance. When the demihull outer angle is 2°, the total resistance is lower than that at 0°, suggesting that this angle mitigates adverse wave interference between the demihulls. However, as the angle increases further, the wave interference induced by the demihull angle transitions into detrimental interactions, leading to elevated wave-making resistance. The lower resistance observed for outer angles compared to inner angles can be analyzed from Figure 20.

Examining the free surface waveforms of the demihull angle at 6°, shown in Figure 20, especially the red checkmarks (the red boxes), reveals a noticeable difference in ship wave interference patterns. In the case of inner angles, significant wave interference occurs in the forward part of the middle region, with pronounced rising waves affecting the inner angle demihull. In contrast, for outer angles, although rising waves are also present, the interference is primarily concentrated in the rear part of the middle region, resulting in a less pronounced impact on the catamaran’s resistance. Despite the streamlined shape of the catamaran at internal angles, wave interference between the demihulls is a major factor in generating resistance.

6. Conclusions

This study employs an overset grid technique to accurately capture free-surface flow patterns and wave profiles. A systematic investigation was conducted on the effects of demihull angle and spacing configuration on calm-water resistance characteristics. By analyzing wave-making phenomena and comparatively evaluating wave-making resistance versus viscous resistance components, the underlying mechanisms of resistance variation are elucidated with unprecedented clarity. These findings advance the fundamental understanding of hydrodynamic interactions in multihull systems. The specific conclusions are as follows.

Effect of demihull spacing ratio (B_S/L_PP) on resistance: When the demihull spacing ratio (B_S/L_PP) is 0.2, intense flow field interference between the two hulls generates additional resistance. As B_S/L_PP increases, this interference diminishes, suggesting that optimal hull spacing should be considered in catamaran design to reduce resistance and enhance performance.

Effect of demihull angle on resistance: The angle of the demihulls has a notable impact on calm water resistance. For inner angles, resistance increases as the angle grows. In contrast, at an outer angle of 2°, resistance decreases compared to that at 0°, attributed to favorable wave interference effects. However, as the outer angle increases further, the interference becomes less favorable, leading to higher resistance.

Impact of rising wave interference on resistance: Rising wave interference significantly affects the catamaran’s resistance at different angles. The inner angle experiences stronger wave interference, especially at higher Froude numbers (Fr = 0.6), resulting in a more pronounced resistance increase compared to the outer angle at the same angles.

These results provide a scientific basis for optimizing catamaran designs, particularly in terms of hull spacing and demihull angles, contributing to improved sailing performance and energy efficiency. Future research could further investigate the dynamic response of catamarans in various sea states and examine the effects of complex fluid–structure interactions on ship performance. Such studies would contribute to a more comprehensive understanding of catamaran optimization.