On the other hand, the hydrodynamic forces on catamaran due to viscosity can be approximately expressed in the similar form as monohull vessel.

　

The longitudinal hydrodynamic force is expressed as:

　

　

where: X(u) denotes the resistance during approaching, Xvr is the non-linear hydrodynamic derivative.

　

The lateral hydrodynamic force is expressed as:

　

YH = Yv + Yrr + Yvv|v|v + Yvr|v|r

NH = NvV + Nrr + Nvvrv²r + Nvrrvr² + Nrr|r|r　(8)

　

 where: Yv, Yr, Nv, Nr are the linear hydrodynamic derivatives, and Yvv, Yrr, Yvr, Nvrr, Nrr non-linear hydrodynamic derivatives.

 In this case hydrodynamic derivatives have large dependence on the speed of the vessel. These hydrodynamic derivatives are estimated in term of the MMG model and adjusted at different speed.

　

 The approaching resistance of catamaran, X(u), is different from that of monohull ship because of the interaction between two demihulls. On basis of extensive investigation into this subject, the following expressions are adopted:

　

　

and

　

　

 where: S is the wetted area of the catamaran, L denotes the length of the hull, Cb is the block coefficient of the demihull. Ct, Cf, △Cf are the coefficients of total resistance, friction resistance and allowance for friction resistance. Cr0 Kr denote the coefficient of residual resistance on the demihull and the interaction factor.

　

 The curve of the total resistance is shown in Fig.4.

　

　

3.4 Other External Forces and Effects

　

3.4.1 Wind force

　

 Reference [11] shows that the wind force acting on the manoeuvring high speed craft is in the same manner as for conventional ships. Therefore, the wind effect is represented as aerodynamic forces in the model and expressed as follows:

　

　

 where: ρa denotes the density of air, UR αR and are the relative speed and angle of wind, Af and As, denote the transverse and the lateral projected area above ship's waterline; LQ4 denotes the overall length of ship; Cwx (αR ) and Cwy (αR ) denote the wind coefficients which are obtained from regressive formula.

　

3.4.2 Wave force

　

 Many research works indicate that the main factor affecting on ship manoeuvring motion is the wave drift force. In order to estimate the wave drift force, the following formula is used [16]:

　

　

 where: ζD denotes the amplitude of wave, λ the length of wave, χ the angle of wave encounter. The coefficients CXD, CYD, CND take the following forms:

　

　

3.4.3 Current effect

　

 Current effect includes the effects of uniform and non-uniform current. The former is treated in the traditional way, while the latter is referred to the work done by Yang [16].

　

3.4.4 Shallow water effects

　

 In practice, shallow water has some effects on the waterjet propelled catamaran. In order to describe the small alteration of the ship's behavior with decreasing water depth, the following formulation expressing the dependency of the coefficients on water depth is adopted [8]:

　

　

 where: D stands for coefficients related to hydrodynamic forces in shallow water and D0 is the base value in deep water. h denotes the ratio of draft to water depth, f(h) is the correcting factor.

　

 The authors once coded a manoeuvring program for the ship with twin propellers and rudders, which is expressed in C++ language with the guidance of OOP (Object-Oriented Programming). In the program, the breakdown of forces is exploited in the structure of class, including hull class, propeller class, rudder class, and external effect class, which characterizes the program more efficient. In present case the waterjet class is inherited from the propeller class. Furthermore, the interface for the 3D simulation and simulator application are reserved in the program.