4.1 Simulation of ship manoeuvring motions under the influence of the hydrodynamic interaction forces

　

 In this section, the ship manoeuvring motions are simulated numerically using the predicted hydrodynamic interaction forces and the ship manoeuvring model of Kijima et al.[11], and the external force and moment acting on two ships in confined water can be expressed as follows:

　

= X'Hi + X'pi + X'Ri + X'Wi (2)

　

= Y'Hi + Y'pi + Y'li + X'Wi (3)

　

= N'Hi + N'pi + N'li + N'Wi (4)

　

 where, m'i represents non-dimensionalized mass of ship i, and m'xi, m'yi represent x,y axis components of non-dimensionalized added mass of ship i, βi means drift angle of ship i , respectively. The subscript H, P, R, I and W mean ship hull, propeller, rudder, component of the hydrodynamic interaction forces between two ships and wind respectively. The wind force and moment acting on ship were estimated by Fujiwara et al. [12]. A rudder angle is controlled to keep course as follows:

　

δi = δ0i - Ki(Ψi + Ψ0i) - K2ri - K3(Spi - S'poi)　(5)

　

 where, δi, Ψi, r'i represent rudder angle, heading, non-dimensional angular velocity of ship i, and S'pi is non-dimensionalized predicted course . Subscript '0' indicates initial values.