Abstract: This paper is mainly concerned with the safe navigation between vessels moving each other in restricted waterways under the effect of wind. The manoeuvring simulation was carried out parametrically for different ship types, ship-velocity ratios, separation and stagger between ships, and wind velocity and direction. As for the calculation parameters, the ratios of velocity difference (hereafter, U2/U1) between two ships were considered as 0.6, 1.2, 1.5. From the inspection of this investigation, it indicates the following result. Considering the interaction force only as parameter, the lateral distance between ships is necessarily required for the ship-velocity ratio of 1.2, compared to the cases of 0.6 and 1.5 regardless of the ship types. Furthermore, regardless of the ship-velocity ratio, an overtaking and overtaken vessel can be manoeuvred safely without deviating from the original course under the following conditions; the lateral distance between two vessels is approximately kept at 0.5 times of ship 1 and 5 through 10 degrees of range in maximum rudder angle. Also, for the case of wind, an overtaken PCC vessel navigating at low speed should be cautioned with high alert, and it is considered that speeding up an engine is required if necessary. However, for the case of VLCC, if the wind was the only factor to be considered, the course of an overtaken vessel did not deviate from its intended path with range of 10 degrees in maximum rudder angle, even though the wind velocity is about 15m/s.

　

 In confined waters, potential hazards of collision and grounding are maximum, and control errors could result in costly damages to both the ship and environment. So, the control of ships in confined waters, particularly in narrow waterways, has been receiving a great deal of attention in recent years because of the ever-increasing size of ships such as tankers and bulk carriers. Also, the problem of ship controllability in confined waters due to the effect by restricted waterways, such as shallow water effect or inherently restricted nature of waterways is the concern not only of naval architects and ship operators but also of engineers who will design future waterways. In the meantime, the main reasons related with ship accident are composed of three factors. One of the increasingly important factors in marine risk analysis concerns human factors and the potential impact of operator error, another is the factor due to the ship manoeuvring characteristics, and a third is the one due to the external disturbances, such as strong wind effect, confined manoeuvring boundaries, shallow water effect, and considerable hydrodynamic interaction forces between vessels moving closer each other. So, the ship manoeuvring and ship-ship interaction in confined water have been important problems in channel design and ship operation in harbours, and the problems are complicated because of the shallow water effects as well as ships are operating near other ships. Therefore, the manoeuvring motion due to the hydrodynamic interaction forces between vessels moving each other in close proximity in restricted waterways, such as in a harbour, or in a narrow channel, has been of considerable interest, because the safe operation and effective control of the vessel require a good understanding of the hydrodynamic interaction forces that encounter. In particular, the situation for the specific case of overtaking between ship and ship in restricted waterways under the effect of wind is made more complex by wind, restricted manoeuvring boundaries, and the interaction effects of ships on each other. So, it is extremely important that the ship operator should be able to maintain full control of the ship during operations. For this to be possible, the hydrodynamic interaction between ships in restricted waterways should be properly understood, and the works on this part have been reported for the past years. Yeung [1] studied on the interactions of slender ships in shallow water by applying slender-body theory. The approach used in this paper is based on the theory of matched asymptotics, and at the outset, the free surface is assumed to be rigid, which implies that the effects of waves are neglected. Also, Yeung et al. [2] analyzed hydrodynamic interactions of a slow-moving vessel with a coastline or an obstacle in shallow water using slender-body theory. In this paper, the assumptions of the theory are that the fluid is inviscid and the flow irrotational except for a thin vortex sheet behind the vessel. Similar works were also reported by Davis[3]. Kijima et al[4] studied on the interaction effects between two ships in the proximity of bank wall. Kijima et al.[5] studied on manoeuvring motion of a ship in the proximity of bank wall. Yasukawa[6] studied on the bank effect on ship manoeuvrability in a channel with varying width. Also, Beck[7] studied on forces and moments on a ship moving in a shallow channel. Also, Cohen et al. [8] analyzed experimental and theoretical hydrodynamic forces on a mathematical model in confined waters. In the mean time, Landweber et al. [9] studied the interaction between two bodies translating in an inviscid fluid. Also, Korsmeyer et al.[1] analyzed the theory and computation for the interaction forces among multiple ships or bodies which are operating near to each other. However, in many of the above-mentioned papers, the transient sway force and yaw moment experienced by a ship in transit near other ships was investigated. Thus, the detailed knowledge on manoeuvring characteristic for the safe navigation while avoiding terrible collision in fixed structures or between ships is still being required to prevent marine disasters.

　

 The coordinate systems fixed on each ship and on the earth are shown by oi - xiyi(i =1,2) and o - xy, respectively in Fig.2.1. Consider two vessels designated as ship 1 and ship 2 moving at speed Ui(i = 1,2) in an inviscid fluid of depth h. In this case, each ship is assumed to move each other in a straight line through calm water of uniform depth h. Sp12 and ST12 are lateral and longitudinal distances between ship 1 and ship 2 in Fig.2.1. Vw, v mean the wind velocity and wind direction. Both calculation methods and theoretical backgrounds related in this were reported in the previous research work[4], but non-dimensional expression for the lateral force, CFi , and yawing moment, CMi, affecting upon two vessels is given by

　

　

 where Li is the ship length of ship i and di the draft of ship i. p is the water density.

　

　

3.1 Conditions of calculation

　

 In this section, the hydrodynamic interaction forces acting on two ships while overtaking in shallow waters have been examined. A parametric study on the numerical calculations has been conducted on four different ship types as shown in Table 1 and Table 2. As shown in Table 2, for the case of 1.0 in L2/L1 and for the cases of 0.6, 1.2 and 1.5 in U2/U1 as the parameters, the hydrodynamic interaction force s between two ships in open sea have been computed. In this case, provided that of a ship 1 (denoted as U1) is maintained at 10kt, the velocities of overtaking or overtaken ship 2 (denoted as U2) were varied, such as 6kt, l2kt and l5kt, respectively.

　

　

　

3.2 Hydrodynamic interaction forces between ships in case of overtaking situation

　

 Fig.3.1 displays the computed lateral force and yawing moment coefficients between two ships with various different ship types in h/d1 = 1.2. The separation between two ships was chosen to be 0.2 L1 under the condition of U2/U1 = 1.2. The solid lines show the result of interaction forces and yawing moment for the case of general cargo ship. The dashed lines mean the result of interaction force s and yawing moment for the case of tanker, and the dotted lines show the result for the case of PCC. The dash dot lines mean the result for the case of container. From this figure, regardless of the ship types, the effect of hydrodynamic interaction forces acting on the overtaken vessel is bigger than the one of the overtaking vessel.