### 1. Introduction

*C*) of a system and the distance between

_{G}*C*and the center of the turret (

_{G}*C*). The maximum yaw angle in regular waves was analyzed, and it was found that when the turret is closer to

_{T}*C*, the yaw motion is larger (Yadav et al., 2007). Sanchez-Mondragon et al. (2018) compared the results of a similar study with different configurations and wave steepness. The configuration and the environmental conditions were varied, and the turret position and the mooring stiffness influenced the specific wave period between 15.0 and 19.0 s.

_{G}### 2. Model Description

*L*) × 14 m (

*B*) with an available depth of 1.5 m. With a scale ratio of 133.33, the total volume of the model achieves a 1.00% difference between the measured and target displaced volume (measured: 163,554 m

^{3}) for full load conditions. The main parameters of the original FPSO designed by Samsung Heavy Industries and the scale model are summarized in Table 1.

### 2.1 Coordinate System

*K*) is regarded as

_{G}*C*, and that of the locally fixed reference frame (

_{T}*K*) is regarded as the center of the midship section. When the FPSO rotates with respect to

_{L}*C*, the surge and sway forces and yaw moment are applied to

_{T}*C*. Thus, the movement of

_{G}*C*(

_{G}*X⃗*) is described with respect to

*K*and the turret position (

_{G}*X⃗*), as shown in Fig. 1.

_{T}*X⃗*can be described using Eqs. (1)–(3) (Ragazzo and Tannuri, 2003; Sanchez-Mondragon et al., 2018). where

_{T}*a*is the distance between

*C*and

_{G}*C*,

_{T}*ψ*is the yaw angle, and (

*T*(

*ψ*)) is the attitude matrix of the vessel.

### 2.2 Turret Mooring Arrangement

### 2.3 Test Conditions

### 3. Experiment of Heading Stability

### 3.1 Experimental Setup

### 3.2 Experimental Results

*H*) of 5.33 m was considered. The results of the yaw angle for each period in Table 3 are shown in Fig. 5. The heading angles converged depending on the varying wave periods, and the vessel heading rotated closer to the incoming direction of regular waves, which have relatively short periods in both sea states. Moreover, the equilibrium headings are identical for both oblique sea and the beam sea conditions at the same wave period except for the three longest wave periods.

### 4. Numerical Analysis

### 4.1 Hydrodynamic Computation

### 4.2 Heading Stability Analysis with the Vessel’s Hydrodynamic Characteristics

### 4.3 Relative Motion of the Turret and Vessel

_{11}), sway (B

_{22}), and yaw (B

_{66}) directions was calculated based on the recommendations of BV NR-493 (Bureau Veritas, 2015). To minimize the effect of roll on the yaw motion (Lugni et al., 2015), the linear roll damping coefficient (B

_{44}) was considered based on the result of a free decay test, which was obtained using the relative decrement method. The rotational stiffness (

*k*) and rotational damping (

*τ*) were alternately applied in the range of 0 to 1.00E07.

*M*) becomes greater than the moment due to friction (

_{ext}*M*) on the contact surface between the vessel and turret. As the external load increases, the turret is released from the vessel and then both rotate independently. The vessel rotates toward the predominant environmental load, while the turret rotates until the difference between moments caused by the external force and the moment generated by the distortion of mooring line (Caille et al., 2014).

_{friction}### 5. Estimation of Turret Parameters

### 5.1 Rotational Stiffness

*k*) caused by the turret. The model ship was placed on a cradle and a disc to wrap it with a wire that is attached to the bottom of the turret. One end of the wire was secured to the disc, and the other was connected to the weight through a pulley, as shown in Fig. 12(a). The traveling time and distance were measured when the turret rotates with differing weights (Fig. 12(b)). Constant velocity sections were considered to obtain the rotational velocity of the turret.

*k*) was approximately 1.93 kN for the scale prototype. where the frictional moment of the roll bearing is obtained by Eq. (5) (Koyo, 2007) where

*P*is an equivalent weight load on the bearing,

*μ*is the friction coefficient and equal to 0.0015 (Koyo, 2007), and is the diameter between the ball centers (Fig. 13(b)).

### 5.2 Rotational Damping using Rotational Velocity (RDV Method)

*M*=

_{total}*M*) on the vessel in the yaw direction due to environmental load is the same as the sum of load RAO and wave drift force. So the difference between the rotational velocity with (

_{wave}*ψ̇*=

_{with}*ψ̇*

_{exp}) and without (

*ψ̇*) additional parameter acting on turret deemed as a turret rotational damping which should be considered for the turret-moored FPSO in Orcaflex. As a result, the rotational damping (

_{without}*τ*) using the difference between the rotational velocity of the model test, and the simulation without consideration of additional parameters on turret can be defined as Eq. (6).

*M*=

_{total}*M*) on the vessel in the yaw direction due to environmental load is the same as the sum of response amplitude operator (RAO) load and wave drift force. The turret’s rotational damping is considered as the difference between the rotational velocity with additional parameters (

_{wave}*ψ̇*=

_{with}*ψ̇*

_{exp}) and without them (

*ψ̇*) acting on turret deemed. As a result, Eq. (6) defines the rotational damping (

_{without}*τ*) obtained using the difference between the rotational velocity of the model test and the simulation without additional turret parameters.

### 5.3 Rotational Damping using Equilibrium State (RDE Method)

*m*: mass of the vessel*m*: added mass or added moment of inertia of the vessel with respect to the_{ij}*K*(_{L}*i*=1,2,6,*j*=1,2,6)*x*: the_{g}*C*position with respect to the_{G}*K*_{L}*I*_{66}: moment of the inertia of the vessel with respect to the*K*_{L}*a*: distance between*C*and_{G}*C*_{T}*F*: restoring force from the mooring system on_{my}*C*in sway, and can be obtained by Eq. (8)_{G}

*F*and

_{x}*F*are the mooring restoring forces on

_{y}*C*in the surge and sway directions, respectively.

_{T}*f*: environmental force on the vessel in sway direction, which is defined in Eq. (9)

_{y}*M*: moment in yaw direction generated by external force, and is defined in Eq. (10) (Sanchez-Mondragon et al., 2018).

_{ext}*M*

_{CG}: yaw moment at

*C*due to the environmental forces

_{G}*M*

_{CT}: rotational moment at

*C*induced by the interaction between the turret and vessel

_{T}*M*

_{CT}=

*τ*(

*r*−

_{turret}*r*), where

_{vessel}*r*and

_{vessel}*r*are the rotational velocity of the vessel and turret, respectively, and

_{turret}*τ*is the rotational damping.

*τ*can be obtained by solving Eqs. (7) and (10). It is assumed that the restoring force in the sway direction is equal to the restoring force in the surge direction, so the results of the static pull-out test in the surge direction were used for the sway direction.

*k*) and the rotational damping (

*τ*) on turret surface obtained by the RDV method and RDE methods. The red, blue, and magenta lines represent the experimental results, the simulated results with turret parameters obtained in the RDV method, and the simulated results with turret parameters obtained in the RDE method, respectively. The RDV results and RDE results showed a tendency of a large fish-tailing phenomenon appearing before approximately 1,000 s. However, compared with Figs. 7,–9, the overall heading angles tend to agree well with the experimental results. As with the results of the model tests, the amount of fish-tailing was decreased, and there was no rotation toward the wave direction at wave periods longer than 10.38 s.

*τ*results are reasonable.