PREDICTION OF TEE SLEW MOTION FOR A SHIP MOORED IN IRREGULAR WAVES
Seung Keon Lee (Pusan National University, KOREA)
Hyo Jae Jo (Korea Maritime University, KOREA)
Dong Hoon Kang (Pusan National University, KOREA)
Abstract: A time domain analysis of the motion of a single point moored ship in regular and irregular waves is presented. Linear and nonlinear wave forces are calculated by the convolution integrals of the impulse response functions and wave elevations. 3-D panel method is applied to get the linear and quadratic frequency transfer functions of wave forces on the vessel. It is shown that the consideration of first and second order wave forces is important in the calculation of the slew motion(of a moored ship) in irregular waves.
It is important to predict and control the excessive lateral motion of a moored ship in wind, waves or currents, to prevent the dredging of anchor or collision with other ships. Many researchers like Fujino , Obokata , Kijima  proposed the prediction and reduction methods of such motion. McWilliam et al  considered the first and second order wave forces on a single point moored ship. Jiang et al  calculated the motion of a single point moored tanker subjected to current, wind and waves. In this paper, the authors tried to calculate the effect of irregular waves, in the slew motion of a moored ship. At first, linear and quadratic frequency transfer functions of wave forces are calculated by 3-D panel method. These transfer functions are Fourier transformed to get the impulse response functions. Irregular waves are reproduced with use of ISSC spectrum, and the convolution integrals of irregular wave and impulse response function are carried out to get the wave forces in time domain. M.M.G maneuvering equations are used to simulate the motion of a ship. Inoue  formulas are applied to predict the hull forces, and the tension of mooring line is calculated under catenary assumption.
2. EQUATION OF MOTION
Surge, sway and yaw motion of a ship in regular or irregular waves are expressed by equation (1). Figure 1 shows the coordinate system and definition of each parameters.
Fig.1. Coordinate system
Here, the subscript H, WV, T means hull forces, wave forces and tension of mooing line. Hull force XH , YH, NH are predicted by the Inoue formulas, and the added masses and moments are gotten from the Motora chart .
3. CALCULATION OF WAVE FORCES
In this paper, KRISO 300K VLCC  is used for the calculation. On the Table 1, the principal particulars of the model are listed. 3-D panel method is applied to get the frequency transfer function of the linear and nonlinear wave forces on the model. Figure 2 shows the mesh distribution for the model ship. Total 620 panels are distributed on the hull, and the boundary value problem to get the strengths of each sources on the panels is solved. Figure 3 is showing the frequency transfer functions of first order wave forces. Second order wave forces are calculated. considering relative wave elevation ζa, 1st order velocity potential φ(1), and the rotation angle of the ship α.
Table 1. Principal particulars of model ship
|KRISO 300K VLCC
Mesh distribution for the wave force calculation
Fig. 3. Linear frequency transfer function of 1st order wave forces