### 1. Introduction

### 2. Simplified Model for Loading and Off-loading Scenarios and Evaluation of Heading Angle Control Performance

### 2.1 Off-loading Scenario

### 2.2 Environmental Conditions

### 2.3 Simplified Model for Evaluation of Heading Angle Control Performance

*M*,

_{total}*M*,

_{FLBT}*M*

_{170}

*,*

_{K}*M*

_{30}

*and*

_{K}*M*

_{5}

*indicate the substituted mass, and the masses of the FLBT, 170K LNG carrier, 30K LNG-BS, and 5K LNG-BS, respectively.*

_{K}*I*,

_{zz,total}*I*,

_{zz,FLBT}*I*

_{zz,}_{170}

*,*

_{K}*I*

_{zz,}_{30}

*and*

_{K}*I*

_{zz,}_{5}

*indicate the substituted yawing moment of inertia, and the yawing moments of inertia of the FLBT, 170K LNG carrier, 30K LNG-BS, and 5K LNG-BS calculated at each center of gravity, respectively.*

_{K}*r*,

_{FLBT}*r*

_{170}

*,*

_{K}*r*

_{30}

*, and*

_{K}*r*

_{5}

*indicate the distances from the single center of gravity of all the four floating bodies to the center of gravity of the corresponding floating body.*

_{K}*G*(

*x⃗*,

*ξ⃗*),, which is represented by Eq. (3), and the boundary integral in Eq. (4). where where

*x⃗*and

*ξ⃗*are the field and source points, respectively, and the density function,

*σ*(

*ξ⃗*), is an unknown value determined only by the boundary conditions. The density function,

*σ*, can be determined through a system of equations derived from the boundary conditions of an object. The surface potential of the object,

*ϕ*, can be calculated using the determined density function,

*σ*, and Eq. (4). The calculated mass,

*a*, can be obtained by substituting the calculated potential,

_{ij}*ϕ*, into Eq. (5). where

*ρ*is the seawater density and

*n*(

_{j}*j*= 1,2,6) represents the normal vectors of the body surface. The panel mesh applied to the calculation is shown in Fig. 6 and the displacement error was within 0.065% in the modeling. The calculated added mass is summarized in Table 4.

*.*(2017) was used. The wind tunnel test was conducted in Force Technology in Denmark, as shown in Fig. 7. The model ship was made of high-density polyurethane foam and was used for the test by separating the top part of the ship under test from the repair surface and below.

*.*(2018). To calculate the wave drift load, a high-order boundary element method based on the free-surface green function (Choi and Hong 2002) was used, and a gap flow damping term was applied to reduce the non-physical resonance of the gap of the floating body. Detailed calculations can be found in the study by Kim et al

*.*(2018).

*F⃗*,

_{total}*F⃗*,

_{FLBT}*F⃗*

_{170}

*,*

_{K}*F⃗*

_{30}

*are*

_{K}*F⃗*

_{5}

*the substituted horizontal load, and the horizontal loads of the FLBT, 170K LNG carrier, 30K LNG-BS, and 5K LNG-BS, respectively.*

_{K}*M*,

_{z}*,*

_{total}*M*,

_{z}*,*

_{FLBT}*M*

_{z}_{,170}

*,*

_{K}*M*

_{z}_{,30}

*and*

_{K}*M*

_{z}_{,5}

*are the substituted yawing load moment, and the yawing load moments of the FLBT, 170K LNG carrier, 30K LNG-BS, and 5K LNG-BS, respectively.*

_{K}*r⃗*,

_{FLBT}*r⃗*

_{170}

*,*

_{K}*r⃗*

_{30}

*, and*

_{K}*r⃗*

_{5}

*are the distance vectors from the center of gravity of all the four floating bodies to the center of gravity of the corresponding floating body. The substituted wind and current loads are shown in Figs. 9 and 10. For the wave drift load, the load response amplitude operator (RAO) was regenerated by the wave height of the incident wave and shown in Fig. 11.*

_{K}*M*and I

*represent the mass and moment of mass inertia of the floating body, respectively.*

_{ii}*a*,

_{ij}*ẍ*and

_{i}*ẋ*represent the added mass, acceleration, and velocity in each direction of motion, respectively, where the values of 1, 2, and 6 for

_{i}*i*and

*j*represent the surging, swaying, and yawing directions, respectively. Moreover,

### 3. FLBT Heading Angle Simulation with Multiple Moored Vessels

### 3.1 Simplified Model Verification through Model Test

*.*(2018). The environmental conditions of the model test are shown in Table 5 and Fig. 13, with a total of five cases including the cases where the heading angle was not controlled and where the heading angle was maintained and controlled at 10°, −10°, −20°, and −30°. The model test results were used for verification.

### 3.2 Heading Angle Characteristics of FLBT with Moored Loading and Off-loading Vessels

### 3.3 Control Performance of Heading Angle of FLBT with Moored Loading and Off-loading Vessels

### 4. Conclusion

The validity of the simplified model was confirmed through a comparison with a model test result. Although this model is only applicable to the same operating conditions under low maritime conditions, this study will be useful to determine the operational range.

Through the heading angle characteristic under the operating conditions defined in this study, it was confirmed that the current load, which is the largest component, has the most significant effect on the static heading angle and this suppresses the long period slewing motion that occurs when the wind and wave drift loads act individually. Long period slewing motion against the wind and wave drift loads is due to the yawing instability, and it was observed from the numerical analysis that the stability could be improved by increasing the surging resistance.

The static heading angle due to the operating conditions was the angle at which 5K and 30K LNG-BSs were exposed to environmental loads, and it was confirmed that the ocean wave shielding effect of the FLBT and LNG carriers cannot be obtained, which indicates that the loading and off-loading performances are degraded. This heading angle characteristic suggests that heading angle control using a stern thruster is necessary to improve the loading and off-loading work performances.

A numerical analysis was performed under the collinear environmental load conditions to verify the general heading angle control performance. Through the results of numerical analysis, it was confirmed that heading angle control is possible for the environmental loads ranging from 90° to 270°.

To estimate the environmental conditions under which the loading and off-loading work performances can be improved, the direction of the wave drift load that can have a shielding effect was fixed, and the heading angle control performance was examined while changing the remaining environmental disturbances. Consequently, it was possible to control the wind and current loads in all the directions. This indicates that it is possible to have the shielding effect against the ocean wave for the operating conditions defined in this study with the capacity of the currently designed stern thruster.