Surge Force Research Articles

Automatic unberthing for underactuated unmanned surface vehicle: Model-based planning and control approaches in constricted harbors

Due to limitations in maneuverability, Unmanned Surface Vehicle (USV) often struggles to achieve automatic unberthing through a single cohesive operation in constricted harbors. To address this problem, this paper proposed a novel Two-Layer Trajectory Planning Method (TL-TPM) and two Model Predictive Control (MPC) methods. Throughout the trajectory planning process, the TL-TPM considers the USV dynamic constraints along with the cumulative risk in viable areas. It incorporates the residual velocity and yaw angle deviation from the backward phase to derive the USV’s retreating trajectory and optimizes sailing time in the forward phase for a smooth forward trajectory, forming a complete automatic unberthing trajectory. The Efficiency-Priority MPC (EP-MPC) and Accuracy-Priority MPC (AP-MPC) are designed for trajectory tracking, considering tracking positional deviations, yaw angle deviations and surge force variations. The proposed EP-MPC demonstrates high computational efficiency and robustness, while AP-MPC shows superior control accuracy under various environmental disturbances. Extensive simulations validate the effectiveness of these methods in achieving automatic unberthing under wind and current impacts.

Oblique wave interaction with dual submerged oscillating buoy as WEC near a partially reflecting wall

The hydrodynamic performance of a submerged dual cylindrical wave energy converter (WEC) in front of a partially reflecting vertical wall is investigated within the framework of linear wave theory. The double cylinders are fully submerged and are constrained only in heave motion. The conversion of wave action into usable power occurs by the coordinated motion of two buoy systems viz. a power take-off mechanism (PTO). The numerical solution for the boundary value problem comprising of wave diffraction and radiation by submerged dual cylinders is obtained using the Boundary Element Method (BEM). The study is devoted to investigating the influence of various factors, the effect of cylinder dimensions, cylinder-cylinder spacing, partially reflecting wall-cylinder distance, angle of wave attack, and its submergence. The compelling results are presented by examining the heave force, surge force, response amplitude operator (RAO), damping factor, and particular interest in the WEC energy capture efficiency under distinct seawall reflections. The study reveals that there is an increase in the WEC efficiency by ≈12% in the case of a dual cylinder compared to a single cylinder. Besides, the amplification of the WEC efficiency is ≈78% for the case of a fully reflecting wall compared to the WEC in the open fluid domain. The present study will further help to understand the dynamics of WECs integrated into protecting shore structures such as breakwaters, groins, and seawalls.

CFD analysis of wave loading on a 10 MW TLP-type offshore floating wind turbine in regular waves

This paper aims to study the higher-harmonics wave-induced surge force on the CENTEC-TLP platform in regular head waves with non-breaking assumptions, using a CFD-based numerical wave tank model, which is a useful tool for the analysis of the nonlinear interaction of waves and structures. Moreover, the influence of change in the wave diffraction and the incident wave angle on the surge force subject to operational and extreme wave conditions is investigated. The numerical analysis is conducted using the CFD toolbox OpenFOAM. The link between Secondary Load Cycle and the wave scattering Type2 is apparent and it is concluded that they are all inertia-driven and that 2nd harmonics play an important role.

Experimental Study on Adaptive Backstepping Synchronous following Control and Thrust Allocation for a Dynamic Positioning Vessel

Cargo transfer vessels (CTVs) are designed to transfer cargo from a floating production storage and offloading (FPSO) unit into conventional tankers. The dynamic positioning system allows the CTV to maintain a safe position relative to the FPSO unit using a flexible cargo transmission pipe, and the CTV tows the tanker during operating conditions. The operation mode can be considered a synchronization tracking control problem. In this paper, a synchronization control strategy is presented based on the virtual leader–follower configuration and an adaptive backstepping control method. The position and heading of the following vessel are proven to be able to globally exponentially converge to the virtual ship by the contraction theorem. Then, the optimization problem of the desired thrust command from the controller is solved through an improved firefly algorithm, which fully considers the physical characteristics of the azimuth thruster and the thrust forbidden zone caused by hydrodynamic interference. To validate the effectiveness of the presented synchronous following strategy and thrust allocation algorithm, a scale model experiment is carried out under a sea state of 4 in a seakeeping basin. The experimental results show that the CTV can effectively maintain a safe distance of 100 m with a maximum deviation of 3.78 m and an average deviation of only 0.99 m in the wave heading 180°, which effectively verifies that the control strategy proposed in this paper can achieve safe and cooperative operation between the CTV and the FPSO unit. To verify the advantages of the SAF algorithm in the thrust allocation, the SQP algorithm and PSO algorithm are used to compare the experimental results. The SAF algorithm outperforms the SQP and PSO algorithms in longitudinal and lateral forces, with the R-squared (R2) values of 0.9996 (yaw moment), 0.9878 (sway force), and 0.9596 (surge force) for the actual thrusts and control commands in the wave heading 180°. The experimental results can provide technical support to improve the safe operation of CTVs.

Experimental Investigation on the Motion Characteristics of Air-Floating Tripod Bucket Foundation during Free Floating

In recent years, multi-bucket foundations have been studied and gradually adopted in engineering practices as a novel foundation for offshore wind turbines within a range of water depth of 30 to 50 m. This study investigated the motion characteristics of air-floating tripod bucket foundation (AFTBF) through a series of experiments during free air-floating. The experimental results show that the surge force appears to be the most important factor influencing pitch moment and motion, whether it is a change in water depth or a draft for AFTBF. The maximum amplitudes of surge acceleration and pitch angle show a trend of increasing with narrower spacing and decreasing with wider spacing, while the heave acceleration shows an opposite trend. The added mass and damping of heave motion for AFTBF increase with shallower water due to the increasing pressure difference between the inside and bottom of bucket foundation. The shallower the water depth and the larger the draft, the longer the resonance period of heave.

Influence of scale effect on flow field offset for ships in confined waters

To investigate the flow field characteristics of full-scale ships advancing through confined waters, the international standard container ship (KRISO Container Ship) was considered as a research object in this study. Using the RANS equation, the volume of fluid method and the body force method were selected to investigate the hydrodynamic characteristics of a model-scale ship (the model-scale ratio λ=31.6) and a full-scale ship advancing through confined waters at low speed. A virtual disk was used in the full-scale model to determine the influence of the propeller on the ship’s flow field. First, the feasibility of the numerical calculations was verified. This proves the feasibility of the numerical and grid division methods. The self-propulsion point of the full-scale ship at Fr=0.108 is determined. The calculation cases of model-scale and full-scale ships (with or without virtual disks) at different water depths and distances between the ship and the shore were calculated, and the changes in the hull surface pressure, the flow field around the ship, and the wake fraction near the ship propeller disk in different calculation cases were determined and compared. The variations in the surge force, sway force, and yaw moment between the model- scale and full-scale ships were generally consistent. In very shallow water (H/T=1.3), the non-dimensional force and moment coefficients for model-scale ships increase more rapidly with decreasing distance from shore, suggesting that using model-scale ships to investigate the wall effect in very shallow water will result in predictions that are biased towards safety. By comparing full-scale ships with and without propellers, it was discovered that the surge force, sway force, and yaw moment were marginally greater in the propeller-equipped ship due to the suction effect, and the accompanying flow before and after the propeller was slightly smaller, with less asymmetry.

Research on dynamic response prediction of semi-submersible wind turbine platform in real sea test model based on machine learning

The motion response of floating offshore wind turbine (FOWT) platform is closely related to its safety, and model test is the most direct method to fully study its dynamic characteristic behavior. In this paper the dynamic response of intermediate-scale physical semi-submersible FOWT model test under real sea environmental loads is studied and compared with the numerical model dynamic response, demonstrating that some limitations of small-scale physical model tests can be overcome, such as the catenary effect of mooring lines. It is found that the nonlinear dynamic characteristics of the physical model under actual marine environmental loads can be captured by the numerical model, which can improve the fidelity of model test data for semi-submersible FOWT structures in the existing literature. The dynamic response database of semi-submersible FOWT under complex wind, wave and current loads was established by using a numerical model with high accuracy, and was used in the prediction research of different machine learning algorithm models such as Genetic Algorithm optimization Back Propagation neural network (GA-BP), Support Vector Machine (SVM) and Gaussian Process (GP). The research shows that the relationship between the environmental load and the dynamic response of FOWT can be established by using the machine learning model, in which the number of samples has a significant impact on the prediction of the mooring line tension, and the research on the three algorithm models shows that GP performs significantly better than GA-BP and SVM in predicting the mean value of surge, pitch and mooring line force. For the dynamic response prediction of mooring line tension, GP model can get better results. In the future, this method will become an important method to predict and monitor the dynamic response of FOWT.

Hydrodynamic characteristics of an Asian sea bass-inspired underwater body

A novel underwater body geometry inspired from the morphology of Asian sea bass (Lates calcarifer) fish is developed, and its hydrodynamic coefficients for different combinations of angle of attack and drift angle are investigated using RANS-based CFD methods. The six degrees of freedom manoeuvring performance is evaluated by the calculation of surge, sway and heave forces and roll, pitch and yaw moments at Reynolds number 3.7 × 106. The numerical model is validated using experimental results for DARPA SUBOFF model. The sea bass sectional geometry has an inherent asymmetry about the horizontal plane, and this is observed in the force and moment coefficients. A detailed study for pressure coefficient and skin friction coefficient is presented, both along the length and circumferentially at specified locations for varying angles of attack and drift angles (-15° to 15°). Due to transverse pressure gradient, cross-flow structures are observed resulting in vortices from the mid-body that grow downstream, the strength depending on the angle of manoeuvre. It is observed that the sea bass-inspired body generates greater roll and pitch moments and heave force as compared to a symmetric tuna-inspired body for drift angles greater than 10°. The differences show the influence of asymmetry in underwater vessel geometry on its stability and performance during horizontal and vertical plane manoeuvres. The study of the hydrodynamic characteristics will aid the design of control surfaces and development of estimation of manoeuvring and propulsion performance for fish-inspired autonomous underwater vessels.

Failure of 24 Inches Blowdown Tower Inlet Nozzle Due to Cyclic Surge Forces

Blowdown tower is one of the equipment in closed blowdown system (CBS) in Delay Coker unit in petroleum refinery. The primary intended function of the CBS is to flush out hydrocarbon vapours from coke drum using high pressure steam into blowdown tower. The system is operating in batches and cycles, due to constant operation at various temperature, pressure, and conditions, components are susceptible to various of failures including thermal fatigue, crack, corrosion, and others. Crack incident was observed on the welding of blowdown tower nozzle that connected to closed blowdown system (CBS) piping after 11 years of operation. This paper aims to study the structural integrity and risk level of the CBS system in relation to liquid level in receiving tower (blowdown tower). Dynamic piping stress analysis and Finite Element Analysis (FEA) was conducted on this line and blowdown tower nozzle to evaluate the overall material behaviour and assessed the risk of failure. The acceptance criteria of the analysis were set to be based on ASME VIII-Division 2 part 5.2.2 (Elastic Stress Analysis Method) and ASME II-part D. Findings from FEA shows that the failure occurred on the blowdown tower nozzle was due to surge pressure impact from high pressure steam flow to obstructed high liquid elevation at the inlet nozzle. The high surge pressure that happened near the nozzle has caused the stress to exceed allowable level thus initiated the crack in cyclic/ batch service. It is recommended that petroleum refinery to continuously maintain the blowdown tower level below nozzle to prevent similar phenomenon to happen in future.

Effect of body motion on the wave loads computed with CFD on the INO-WINDMOOR floater

CFD simulations were carried out on the 1:40 model of the INO WINDMOOR floater in regular waves to extract hydrodynamic loads, both on the structure, the single columns and sections from each column. Three different approaches for the platform motion were used, (i) fixed, i.e., restrained from motion, (ii) prescribed, i.e., forcing the floater to follow the motion recorded during model tests and (iii) 6 DOF, i.e., allowing the floater to move according to external forces from waves and anchor lines. The obtained results show the effect of the free surface on the local drag forces at sections with different submergences, which are important to include when modelling the motion with simplified methods based on pre-computed force coefficients. A comparison of the surge force shows that the amplitudes of the loads obtained with moving platform are reduced compared to the corresponding fixed case. The mean total surge force computed on the single columns and the whole platform show small quantitative differences between the different methods. The motion responses of the platform for surge and heave obtained with CFD are in fair agreement with the experiments.

Three-dimensional shape optimization of a submerged body under wave diffraction

This study explores the use of shape optimization to reduce wave forces on a submerged floating body subjected to wave diffraction. To this end, gradient-based shape optimization is adopted, in which dimensionless wave excitation forces are the optimization objective. A shape parameterization method based on the Fourier-series expansion is developed that permits the representation of an arbitrary three-dimensional floating body. The discrete adjoint method is utilized to calculate the gradient of the objective function with respect to the shape parameters. Using three-dimensional shape optimization, taking the initial shape to be a hemisphere, a significant reduction in surge, heave, and pitch wave forces is achieved, with a maximum reduction of 48.40%, 68.43%, and 46.22%, respectively. Furthermore, optimization effectively suppresses wave run-up, with a maximum reduction of 15.62%. A comprehensive analysis of parameters is performed to reveal the effects of wave number, incident angle, and shape parameters on the final optimized shape and wave load characteristics. This study provides a solid guide to the optimization of floating offshore platforms and the development of innovative structural systems.

Estimation of steady wave forces and moment acting on an obliquely moving ship in short waves, and its application in a manoeuvring simulation

In this study, we propose a prediction method for steady wave forces acting on an obliquely moving ship in short waves. Particularly, we enhance an existing method that focuses on refraction of flow and waves in the vicinity of ship's waterline, in terms of the wave amplitude in the near region of the ship and the flow velocity. The former is theoretically modified by deriving an advection equation for wave energy on a ship-fixed frame, and the latter is improved by reflecting the results of computational fluid dynamics that automatically includes viscous effects. A comparison between the prediction and published captive model test results shows that the present method can more adequately capture the variation of the steady wave forces owing to the ship advancing speed and lateral drift than the original method, although the prediction accuracy is not necessarily improved under all conditions. To confirm the applicability of the present method for steady wave forces to ship manoeuvring problems, we predict course-keeping manoeuvres of a ship in regular short waves through a numerical simulation that considers only the steady wave forces in the equation of motion in calm water. The manoeuvring simulation results are validated using previously published free-running model test results, involving various rudder effectiveness conditions for the ship model and full-scale ships, both with and without engine limits. The comparison shows that the present method for steady wave forces is effective in predicting the course-keeping manoeuvres under rudder effectiveness conditions for a ship model in regular short waves. Nonetheless, the present method is insufficiently practical in terms of the manoeuvring simulation under rudder effectiveness conditions for a full-scale ship that is relatively more susceptible to waves. We confirm that an empirical correction for the computed steady wave surge forces based on the discrepancy between the measured and computed values under the ship resting enables the approximate prediction of the course-keeping manoeuvres even under the rudder effectiveness conditions for the full-scale ship.

Survival of young planted mangroves in a calm bay environment during a tropical cyclone

The efforts of mangrove plantations are not always successful, and the reasons for their failure remain unclear. In this study, the growth of planted mangroves (Kandelia sp.) was monitored in a mangrove forest on Amami Island, Japan, to investigate their survival over the first three years. A strong typhoon passed near the island 16 months after planting. Although the mangroves were planted at the frontal edge of the intertidal zone, most of young mangroves survived without visible damage. The external forces acting on the plants, such as wave forces, storm surge forces, wind drag forces, and oscillatory acceleration, were estimated by applying an integrated analysis model for tropical cyclones, storm surges, wind waves, and plant kinematics. These analyses yielded three main results. First, although large waves over 10 m in height were generated offshore, the mangrove forest was located in the innermost part of the bay, resulting in considerable wave attenuation. Second, the wave period in the bay was much shorter than that in the open ocean, which may have promoted resonance between waves and mangrove plants. The oscillatory acceleration of the young mangroves was estimated to have approximately the same magnitude as that of the gravitational force. Third, the young mangroves could withstand a fairly strong typhoon, but this may have been fortuitous because the timing of the adverse wind wave conditions coincided with low tide. It is estimated that if the tides had been higher, the oscillatory acceleration would have been five times that of the gravitational acceleration. Although this study only presents examples of specific mangrove species in a particular location, the findings can be used to improve the attempts to restore mangrove forests and thereby protect coastal settlements from the adverse effects of tropical cyclones.

Estimating hurricane-induced vertical surge and wave loads on elevated coastal buildings based on CFD simulations and ensemble learning

This study focuses on developing Machine Learning models based on CFD simulations to estimate hurricane induced vertical wave and surge forces on elevated coastal buildings caused by regular waves. In particular, this study aims at addressing the existing gap in designing elevated coastal buildings, which stems from lack of a generalizable equation for estimating vertical hurricane wave and surge forces for a variety of building geometries and wave conditions. To this end, based on a validated Computational Fluid Dynamics (CFD) model, six key variables that affect the wave forces on buildings are considered, which include building dimensions (length and width of rectangular plan buildings) and wave characteristics. In addition, the effect of building length in relation to wave length on the resulting vertical forces is explicitly considered, while the effect of building width is considered implicitly. Subsequently, a Latin Hypercube Sampling (LHS) strategy is implemented for generating 256 random samples, each representing a unique building geometry with a rectangular plan and wave condition scenario. A pipeline is then developed for generating CFD models corresponding to each sample, which are then deployed on a high-performance computing (HPC) cluster, creating a dataset of vertical surge and wave forces. Based on the key design variables, an ensemble of Machine Learning (ML) models is developed to predict vertical wave forces. For the purpose of design and risk assessment, different force levels may be of interest. Therefore, different models were trained to predict multiple levels of forces on elevated buildings, including maximum, average, 25th, 75th, and 99th percentiles of peak forces. The developed model for each of these force levels is then investigated to identify the main building geometry and wave conditions features that affect the resulting forces, which can inform the decisions of the designers in the early-stage phases. For further assistance in the early-stage design, based on a subset of identified important features, a simple expression for each force level is provided to narrow down the design space to top performing early design candidates, while the main estimators can be used for the final design of elevated buildings. Results show that based on CFD simulations, highly accurate and generalizable predictive models with error rates of about 4% on the test set can be developed.

Experimental hydrodynamic assessment of a cylindrical-type floating solar system exposed to waves

In this paper, an experimental investigation on the wave loads and structural motions of two semi-fixed semi-immersed horizontal cylinders type rafts in the free surface zone is conducted. The physical models are tested at the 1:4.5 scale and exposed to a range of regular and irregular waves in a wave flume at Queen's University Belfast. The physical models and experimental setup are discussed alongside an investigation of the hydrodynamic phenomena, surge forces, and dynamic responses that each structure exhibits in the coastal wave climates. Furthermore, an investigation into the wave attenuation by both models is carried out. The results show that the surge forces have a positive correlation with wave steepness for both models. Hydrodynamic phenomena such as wave runup and overtopping, radiative damping and reflected waves, constructive interference, diffraction and flow separation were identified during the experiments. A negative mean heave displacement is observed during the monochromatic sea states which could result in impact loading and submergence of the superstructure components and photovoltaic panels at full-scale. The results presented in this paper may be used to calibrate and verify numerical models that calculate the global responses and hydrodynamic forces. It may also benefit the design processes of geometrically similar floating solar technologies by providing data on surge loads, motion responses and hydrodynamic observations.

Underactuated Source Seeking by Surge Force Tuning: Theory and Boat Experiments

We extend source seeking algorithms, in the absence of position and velocity measurements, and with the tuning of the surge input, from velocity-actuated (unicycle) kinematic models to force-actuated generic Euler–Lagrange dynamic underactuated models. In the design and analysis, we employ a symmetric product approximation, averaging, passivity, and partial-state stability theory. The proposed control law requires only real-time measurement of the source signal at the current position of the vehicle and ensures semi-global practical uniform asymptotic stability (SPUAS) with respect to the linear motion coordinates for the closed-loop system. The performance of our source seeker with surge force tuning is illustrated with both numerical simulations and experiments of an underactuated boat.

Selection strategies and finite-time target tracking of multiple unmanned surface vehicles with mode uncertainty and disturbances

In this paper, the finite-time coordinated target tracking problem of multi-unmanned surface vehicles (USVs) with model uncertainty, underactuation and disturbances based on distributed coordinated control is studied. Firstly, from the point of view of practical application, the select tracking scenario is proposed to protect monitoring area. Three new initial selection strategies are proposed to shorten the total time for the whole tracking system. Secondly, based on sliding mode control, the surge force finite time tracking controller and the yaw moment finite time tracking controller are proposed. And the novel continuous function is introduced to eliminate the singularity. Finally, the Lyapunov stability criterion proves that the designed controllers can realize multi-USVs coordinated finite-time tracking. Simulation results show the effectiveness of the designed distributed coordinated controllers, and verify the correctness of the initial selection strategies.

The Effect of a Linear Free Surface Boundary Condition on the Steady-State Wave-Making of Shallowly Submerged Underwater Vehicles

Near-surface simulation methods for shallowly submerged underwater vehicles are necessary for the population of a variety of free-surface-affected, coefficient-based maneuvering and seakeeping models. Simulations vary in complexity and computational costs, often sacrificing accuracy for simplicity and speed. One particular simplifying assumption, the linearization of the free surface boundary conditions, is explored in this study by comparing the steady-state wave-making characteristics of a shallowly submerged prolate spheroid using two different simulation methods at several submergence depths and forward speeds. Hydrodynamic responses are compared between a time-domain boundary element method that makes use of a linearized free surface boundary condition and an inviscid, volume of fluid Reynolds-Averaged Navier–Stokes computational fluid dynamics code that imposes no explicit free surface boundary condition. Differences of up to 22.6%, 32.5%, and 33.3% are found in the prediction of steady state surge force, heave force, and pitch moment, respectively. The largest differences between the two simulation methods arise for motions occurring at small submergences and large wave-making velocities where linear free-surface assumptions become less valid. Nonlinearities that occur in such cases are revealed through physical artifacts such as wave steepening, wave breaking, and high-energy waves. A further examination of near-surface viscous forces reveals that the viscous drag on the vessel is depth dependent due to the changing velocity profile around the body.

Accelerated second-order hydrodynamic load calculation on semi-submersible floaters

A rapid method for calculation of second-order hydrodynamic wave loads on semi-submersible platforms is developed and validated against radiation–diffraction theory. The method is based on slender-body theory and builds on modal truncation of the quadratic transfer function (QTF). The semi-submersible floater is split into individual members and the existing theory for vertical cylindrical columns is extended to include the heave force. Further expressions for the surge, heave and pitch load on the horizontal pontoons are derived and implemented. The accuracy of the method is assessed by comparison to radiation–diffraction results using the Pinkster approximation. We find that the slender-body approximation for the column surge force is most accurate for small values of the diameter-to-draft ratio. For the three sea states considered, this error is below 10% for diameter-to-draft ratios less than 0.2.Error analysis is provided for the column heave and pitch and the pontoon loads. For all members, application of 128 modes in the QTF approximation is found sufficient to accurately represent the full slender-body QTF solution.Next, the first- and second-order loads on the full floater under different sea state conditions are compared to radiation–diffraction theory. With 128 modes, the second-order loads are obtained 2500 times faster than with conventional approaches with error levels of 22% for surge, 10% for pitch and zero error for heave. The surge error is discussed and linked to the small draft of the columns. The numerical efficiency of the method allows the consideration of second-order loads in the first stages of the design and optimisation of semi-submersible floaters.

Towards the effects of load condition on ship manoeuvrability by a system simulation method with hydrodynamic derivatives from RANS computations

The effects of load condition on ship manoeuvrability are investigated by means of system simulation method. To this end, a MMG-type mathematical manoeuvring model is applied to simulate the standard turning and zigzag rudder manoeuvres for a KVLCC2 ship model in six load conditions (two drafts × three trims). In order to determine the needed hydrodynamic derivatives, the forces and moments on the hull in a range of combined static drift and circle motions are computed by using the own expanded RANS (Reynolds-Averaged Navier-Stokes) solver on OpenFOAM. However, the coefficients of hydrodynamic interaction among hull, propeller and rudder are obtained from available experiments. The computed surge forces, sway forces and yaw moments agree fairly well with the experimental data, suggesting a promising prospect for the used RANS solver in the application of ship manoeuvring prediction. By regressing the hydrodynamic forces and moments, the hydrodynamic derivatives are obtained. Turning and zigzag rudder manoeuvres are simulated by solving ship motion equations in line with the acquired derivatives and coefficients. Comparing the simulated results between the full and ballast load condition without trim, a small draft (i.e. the ballast load condition) improves turning performance, but weaken course stability. For the three full load conditions or ballast load conditions, trim by bow improves turning ability, but deteriorates yaw-checking ability. The simulated results for two load conditions show satisfactory agreement with available experimental data, which suggests that the present procedure for ship manoeuvring prediction is effective. The course stability indexes are analysed as well. The load condition will affect significantly the manoeuvrability of a ship, at least for KVLCC2. It may be quite necessary to evaluate the manoeuvrability of a ship in different load conditions at the initial design stage.