Next, we carry out the computations of manenvering motions of 2 ships in overtaking condition by solving the motion equation eq.(29). Then, the added mass and the interaction forces appear in the motion equation are calculated by a 3D panel method. The calculation is done in the same time cycle at the moment when solving the motion equation.

  For simplicity, we assume no operation for avoidance of the ship collision and the zero surge force which means that the ship resistance and propeller thrust are always balanced. Therefore, the external forces FEk are zero. The viscous damping forces FVk are assumed to 1)e expressed as follows:

　

　

　

　

 where υ' = υ/U, γ' = γLpp/U and Y'υ', Y'γ', N'υ', N'γ'... are so-called the hydrodynamic derivatives for ship maneuvering. Here it should be noted that the discrimination for Ship 1 and 2 denoted by (1)/(2) is omitted. The hydrodynamic derivatives are predicted by Hirano's method[15] in conjunction with Kobayashi's method[14] for taking the shallow water effect into account. The predicted N'υ-term includes component of so-called Munk moment (m'11 - m'22). Since the component has been already included as a term in the motion equation for ship maneuvering, the component was reduced from the N'υ.

 We simulate the ships maneuvering motions induced when Ship 1 moves at starboard side of Ship 2 and overtakes Ship 2. For the simulations the ferries mentioned in previous section were used. The initial conditions for the calculations are as follows: Froude number of Ship 1 Fn1 = 0.2, Froude number of Ship 2 Fn1 = 0.1, so ratio of 2 ship speeds is U2/U1 = 0.5. Minimum lateral distance between ships is Sp = 0.25B. 2 water depths of deep (h/d = ∞) and shallow (h/d = 1.2) are assumed.

 Fig.5 shows the ship trajectories in deep and shallow water. In deep water, Ship 1 approaches to Ship 2 being at port side of Ship 1 due to the influence of the interaction forces, however no ship collision occurs. In h/d = 1.2 on the contrary ship collision is simulated because the magnitude of the interaction forces becomes considerably large in shallow water. The situation of the ship collision is as follows: when how part of overtaking ship (Ship 1) reaches to rear part of overtaken ship (Ship 2). Ship 1 gradually turns in the direction of Ship 2. Ship 1 moves to the port side and approaches to Ship 2, and finally reaches to the collision with Ship 2. This scenario is almost the same as mentioned in previous section.