### 1. Introduction

### 2. Test facility and test conditions

### 2.1 Test facility

### 2.2 Model ship and test conditions

### 3. Experiment

### 3.1 Equation of motion

*X*,

*Y*and

*N*are denoted for hydrodynamic forces acting on the KASSs hull as surge force, sway force and yaw moment, respectively.

*m*,

*I*and

_{zz}*x*are the mass of KASS, moment of inertia in yaw motion and the longitudinal center of gravity of the ship, respectively.

_{G}*u*and

*v*is the velocity in x-axis and y-axis, respectively.

*ṙ*is the acceleration of angular.

*Y*

_{v}_{|}

_{v}_{|},

*Y*

_{r}_{|}

_{r}_{|},

*N*

_{v}_{|}

_{v}_{| }and

*N*

_{r}_{|}

_{r}_{|}. The mathematical model of the hull forces is described in Eqs. (2)- (4). The prime represents for non-dimensional value. where

*X′*,

_{vv}*X′*and

_{rr}*X′*are the surge derivatives.

_{vr}*Y′*,

_{v}*Y′*

_{v}_{|}

_{v}_{|},

*Y′*,

_{r}*Y′*

_{r}_{|}

_{r}_{|},

*Y′*and

_{vvr}*Y′*are the sway derivatives.

_{vrr}*N′*,

_{v}*N′*

_{v}_{|}

_{v}_{|},

*N′*,

_{r}*N′*

_{r}_{|}

_{r}_{|},

*N′*and

_{vvr}*N′*are the yaw derivatives.

_{vrr}*v′*and

*r′*are non-dimensional sway velocity and angular velocity, respectively.

### 3.2 Ballasting test and inertia test

*I*. Fig. 6 shows the inertia test in full loading condition. The results of the inertia test are listed in Table 4. The differences of measured

_{zz}*I*and target

_{zz}*I*are smaller than 5%. This error value can be accepted in captive model test.

_{zz}### 3.3 Experimental setup

### 3.4 Data analysis

*X*,

*Y*and

*N*are the hydrodynamic forces acting on the KASSs hull as surge force, sway force and yaw moment, respectively.

*X′*,

*Y′*and

*N′*, are the non-dimensional of hydrodynamic forces acting on the KASSs hull as surge force, sway force and yaw moment, respectively. The definition of the non-dimensional hydrodynamic forces is shown in Eqs. (5) - (7).

### 4. Result

### 4.1 Validation result

### 4.2 Experimental results

^{2}and 0.0651 m

^{3}. The wetted area and wetted volume of case 4 are 0.993 m

^{2}and 0.0509 m

^{3}. The wetted area and wetted volume decrease due to the decreasing of loading condition. In addition, the hydrodynamic forces acting on the ship hull is the water pressure acting on the wetted area of ship. Therefore, the hydrodynamic forces decrease in lower loading condition.

### 4.3 Hydrodynamic coefficients

^{nd }order polynomial function.

*X′*,

_{vv}*Y′*,

_{v}*Y ′*

_{v}_{|}

_{v}_{|},

*N ′*and

_{v}*N ′*

_{v}_{|}

_{v}_{| }coefficients are determined based on the OTT results.

*X ′*,

_{rr}*Y ′*,

_{r}*Y ′*

_{r}_{|}

_{r}_{|},

*N ′*and

_{r}*N ′*

_{r}_{|}

_{r}_{| }coefficients are determined based on the CMT results.

*Y ′*,

_{vvr}*Y ′*,

_{vrr}*N ′*and

_{vvr}*N′*coefficients are determined based on the CMTD results and the hydrodynamic coefficients which are estimated from OTT and CMT. The hydrodynamic coefficients are obtained by Least Square Method. Fig. 12 shows the fitting value and measured value to obtain the

_{vrr}*X*,

_{vv}*Y*,

_{v}*Y*

_{v}_{|}

_{v}_{|},

*N*and

_{v}*N*

_{v}_{|}

_{v}_{| }coefficients in various loading conditions. In the case of OTT, the effect of drift angle on hydrodynamic forces are investigated. Fig. 13 shows the fitting value and measured value used to obtain the

*X*,

_{rr}*Y*,

_{r}*Y*

_{r}_{|}

_{r}_{|},

*N*and

_{r}*N*

_{r}_{|}

_{r}_{| }coefficients in various loading conditions. Fig. 14 shows the fitting value and measured value to obtain the

*Y*,

_{vvr}*Y*,

_{vrr}*N*and

_{vvr}*N*coefficients in various loading conditions. To confirm the accuracy of the expression, the fitting curves expressed as the solid line and symbol are the measured value are plotted in Figs. 12,-14. The fitting curves accuracy is a good agreement with the measured value. The hydrodynamic coefficients depend on the loading condition obtained from the Least Square Method are listed in Table 5. The hydrodynamic coefficients change dramatically due to the effect of the loading condition.

_{vrr}*Y*and

_{v}*N*coefficient slightly decreases when the loading condition reduces. However,

_{v}*Y*and

_{r}*N*coefficient changes dramatically in various loading conditions. In addition, the linear coefficients as

_{r}