I. Introduction
The Unmanned Surface Vehicle is an unmanned ocean mobile observation platform powered by wave energy. It enables long-term, wide-area, all-directional, and real-time exploration of the marine environment, demonstrating broad prospects in oceanographic research and applications. The primary propulsion of a Unmanned Surface Vehicle is generated by the thrust produced by its subsurface glider. Its spring-loaded hydrofoil mechanism (HSM) converts wave energy into forward kinetic energy, serving as a critical energy conversion unit that significantly influences the overall performance of the system.

This study focuses on analyzing the dynamic performance of the spring-loaded hydrofoil mechanism in a Unmanned Surface Vehicle. The main work is summarized as follows:

First, through an analysis of numerical calculation methods for the spring-loaded hydrofoil mechanism, the simulation setup and key parameters are determined. Based on this, the motion characteristics, force conditions, and dynamic performance parameters of the mechanism are systematically analyzed.

Second, the external input conditions for simulation are defined. Two key structural parameters affecting the hydrofoil mechanism—the spring stiffness coefficient (SSC) and the limit position angle (LPA)—are investigated through simulation. The study focuses on how different values of SSC and LPA influence the dynamic performance of the hydrofoil mechanism under given sea conditions. Based on simulation results, a performance analysis of these parameters is conducted. Furthermore, vortex theory is employed to explain the mechanism by which the limit position angle enhances hydrofoil performance, and validation is carried out using performance data under varying wave heights.

II. Dynamic Performance Study of the Spring-Loaded Hydrofoil Mechanism
This study primarily employs computational fluid dynamics (CFD) software, specifically FLUENT. The kinematic model of the spring-loaded hydrofoil mechanism is implemented through User-Defined Functions (UDFs), enabling the simulation of passive hydrofoil motion. A numerical simulation model of the mechanism is established to investigate the effects of spring stiffness coefficient and limit position angle on its dynamic performance.

The analysis further examines the influence of vortex dynamics on the forward propulsion performance of the hydrofoil and elucidates the fundamental reasons why the limit position angle enhances propulsion efficiency. Finally, the validity of the conclusions is verified through simulations under different wave height conditions.

Figure 1. Simulation Model

The kinematic equations of the spring-loaded hydrofoil mechanism were implemented in FLUENT through a User-Defined Function (UDF) and compiled for numerical simulation. Since the hydrofoil undergoes both acceleration and deceleration phases during its upward and downward motions, the horizontal force experiences two variations within one motion cycle, whereas the vertical force varies only once. As a result, the hydrofoil consistently provides a forward thrust component for the Unmanned Surface Vehicle.

When the spring stiffness coefficient exceeds 3000 N/m, the moment coefficient varies significantly over time. The effective angle of attack can be calculated based on the pitch angle and the inflow velocity, while the horizontal component of thrust is determined by the lift force and the angle of attack.

For lower spring stiffness values, the forward thrust coefficient decreases with the reduction in hydrofoil lift coefficient. In contrast, at higher spring stiffness values, the thrust coefficient increases with the rise in lift coefficient.

Due to the relatively small restoring moment of a soft spring, the hydrofoil rapidly reaches its maximum angular position, resulting in a sharp variation in the pitch angle profile. Conversely, a stiffer spring generates a larger restoring moment, leading to a slower variation in pitch angle throughout the motion process.

Figure 2. (a) Forward thrust coefficient; (b) lift coefficient; (c) moment coefficient; and (d) pitch angle over one cycle under different spring stiffness coefficients.

A time-domain analysis was first conducted to investigate the influence of spring stiffness on the dynamic performance of the spring-loaded hydrofoil mechanism. To further explore the relationship between input and output responses of the system, the forward thrust coefficient was selected for frequency-domain analysis using Fourier transform, as shown in the figure.

From the frequency spectrum, it can be observed that the dominant frequency is concentrated at 0.3643 Hz, while other frequency components appear as harmonics of the fundamental frequency. The wave input period is 5.5 s, corresponding to a wave frequency of 0.182 Hz. It is therefore evident that the dominant frequency of the forward thrust coefficient is approximately twice the wave frequency.

This indicates that the forward thrust generated by the spring-loaded hydrofoil mechanism is strongly correlated with the wave input conditions, including wave height and period, and exhibits a multiple relationship with the input wave frequency. This also indirectly explains why higher wave frequencies lead to greater forward thrust generation by the hydrofoil system.

Figure 3. Fourier transform of the forward thrust coefficient under different spring stiffness coefficients.

The average thrust coefficient, average input power, propulsion efficiency, and wave energy capture efficiency of the spring-loaded hydrofoil mechanism under different spring stiffness coefficients are presented in Table 1.

Table 1. Average forward thrust coefficient, average input power, propulsion efficiency, and wave energy capture efficiency under different spring stiffness coefficients.

Based on the kinematic equations of the spring-loaded hydrofoil mechanism, a UDF program incorporating a limit position angle was implemented and compiled into the CFD software for numerical simulation. An angular constraint function was introduced to restrict the pitch angle of the hydrofoil during motion.

The average forward thrust coefficient, average input power, propulsion efficiency, and wave energy capture efficiency under different limit position angles are presented in Table 2. It can be observed that the average forward thrust coefficient first increases and then decreases with increasing limit position angle, reaching its maximum value at 25°.

Compared with the hydrofoil system without a limit position angle (as shown in Table 3.2), both the average forward thrust coefficient and the average input power are improved. This indicates that introducing a limit position angle enhances the conversion efficiency of wave energy into forward thrust for the spring-loaded hydrofoil mechanism. In addition, the propulsion efficiency increases gradually with the increase of the limit position angle.

However, the wave energy capture efficiency decreases as the limit position angle continues to increase. This is mainly because the imposed angular constraint restricts the hydrofoil motion, forcing it to overcome greater hydrodynamic resistance during the gliding process.

Table 2. Average forward thrust coefficient, average input power, propulsion efficiency, and wave energy capture efficiency under different limit position angles.

III. Sea Trial

The sea trial was conducted using two “Black Pearl” Unmanned Surface Vehicles. One was configured without a limit position angle, and the other was configured with a 25° limit position angle. The spring stiffness coefficient was set to 5000 N/m, and a three-dimensional biomimetic hydrofoil was adopted, as shown in Figure 4.

The test area was selected in the Qianliyan waters of Qingdao. The entire sea trial was divided into four stages: system burn-in testing, deployment, real-time monitoring, and recovery.

The burn-in testing phase was primarily conducted to verify the stability of the remote communication and electrical systems of the “Black Pearl” Unmanned Surface Vehicle. This included checking whether the remote data transmission system could successfully transmit and receive data, whether remote command execution was responsive, whether the power management system could properly supply energy to the battery, and whether the solar power system was operating normally.

During the deployment phase, the tested Unmanned Surface Vehicles were transported by vessel to the vicinity of the Qianliyan sea area in Qingdao. Deployment was carried out using a deployment trolley, deployment ropes, and hooks. Before deployment, AIS tracking devices were installed on both vehicles to ensure accurate positioning during the recovery phase.

The real-time monitoring phase involved remote control of the deployed “Black Pearl” Unmanned Surface Vehicles. By adjusting target waypoints and navigation modes, the performance of the two configurations (with and without limit angle) was compared. To better evaluate their speed performance, a straight-line round-trip navigation experiment was designed between two waypoints. During the experiment, the Unmanned Surface Vehicles transmitted operational data every 10 minutes via Iridium satellite communication, including GPS position, sea state parameters, and heading information. The underwater glider subsystem also provided attitude data during operation, obtained via onboard compass measurements.

In the recovery phase, the positions of the Unmanned Surface Vehicles were determined using AIS and GPS signals. The support vessel navigated to the target area, and the vehicles were recovered using onboard lifting equipment.

Figure 4. Sea navigation track of the “Black Pearl” Unmanned Surface Vehicle.

The actual velocity, fitted velocity, and average velocity curves of the Unmanned Surface Vehicle with and without a limit position angle indicate that the average speed of the non-limited configuration is 0.307 m/s, while that of the 25° limit position angle configuration is 0.3718 m/s. The difference between the two average speeds is 0.065 m/s. Compared with the non-limited configuration, the 25° limit position angle configuration achieves an approximately 30% increase in speed, demonstrating that the 25° structural configuration significantly improves the velocity performance of the Unmanned Surface Vehicle.

IV. Conclusions

First, a theoretical and modeling analysis of the spring-loaded hydrofoil mechanism was conducted. In the computational model analysis, the motion behavior, force characteristics, and dynamic performance parameters of the mechanism were systematically investigated. In the simulation strategy analysis, a numerical simulation framework for the hydrofoil mechanism was established, the key theoretical aspects of the simulation process were clarified, and a complete simulation scheme was developed.

Second, the influence of spring stiffness on the dynamic performance of the hydrofoil mechanism was studied. Under the input conditions of a sea state 2 nearshore environment in Qingdao, numerical simulations were performed. The results show that when the spring stiffness coefficient is 5000 N/m, the hydrofoil achieves its maximum forward propulsion performance. Based on this, the effect of the limit position angle on performance was further investigated. The results indicate that when the limit position angle is 25°, the hydrofoil reaches its optimal propulsion performance. Compared with the non-limited case, the average forward thrust increases by 10%, and the input power increases by 42.7%.

Meanwhile, the presence of the limit position angle eliminates the dual-peak phenomenon in both the thrust coefficient and lift coefficient curves, providing a more stable and continuous forward propulsion force for the hydrofoil motion. The numerical simulations validate the correctness of the conclusions.

Finally, to verify the overall performance improvement brought by the 25° limit position angle, sea trials were conducted using both configurations of the “Black Pearl” Unmanned Surface Vehicle. Track and velocity data were collected and analyzed during straight-line navigation segments. The results show that both track deviation and velocity follow a normal distribution. The 25° configuration demonstrates better heading stability compared with the non-limited configuration. In addition, the average speed of the 25° Unmanned Surface Vehicle is increased by nearly 30% compared with the non-limited case.