3.2 Change of the hydrodynamic force on the difference of acceleration
In undergoing lateral berthing maneuver, the ship makes lateral moving with the support of a tugboat, but acceleration movement is made with the hull from rest to uniform movement. Thus change of the flow field influenced by the difference of the acceleration movement depending on the number of the tugboat and the power of the tugboat is hereby examined. Even if the lateral moving velocity is the same, it is considered that the hydrodynamic force acting on the ship hull according to the difference of the acceleration is greatly different. To examine the change of the hydrodynamic force effected by the difference of the acceleration, computation was made from rest to uniform movement T = 5.0 using the CFD method in case that H/d = 7.0 where the water depth is deep enough and H/d = 1.5 where the water depth is relatively shallow taking up the 3 types of different nondimensional acceleration (i.e., NDA 0.5,1.0, and 2.0). Computation result of hydrodynamic forces according the acceleration is shown together with the experiment result in Fig. 6 (H/d=7.0) and 7 (H/d= 1.5), respectively. It is confirmed that the CFD result is in coincidence with the experiment with good accuracy. Thus it might be possible to compare and examine the hydrodynamic force by the use of the result of the CFD.
Let the hydrodynamic force under the lateral moving of the ship hull can be classified into inertia force and lateral force. Then first of all, the inertia force in case that NDA is 2.0 was twice as large as the force in case that NDA is 1.0 taken as a criterion. The inertia force in case that NDA is 0.5 was half of the one referred to above. In case that NDA is 1.0, the inertia force in a deep water H/d = 7.0 was 4.8, whereas the value was 7.2 in a shallow H/d = 1.5. Thus it is ensured that among the hydrodynamic forces subjected to the difference of the acceleration, the inertia force became larger by being dependent exclusively on the acceleration.
At the next stage, the time for the lateral force to reach uniform velocity became shorter and the lateral moving velocity was expedited. Thus a tendency was noted that the higher the nondimensional acceleration is, the larger the lateral force is.
Fig. 6 
Comparison of hydrodynamic forces according to the acceleration (H/d 7.0). 
Fig. 7 
Comparison of hydrodynamic forces according to the acceleration (H/d 1.5). 
The lateral force component obtained by deducting the inertia force from the computation result of the CFD method is shown in Fig. 8 and 9. By comparing Fig. 8 with Fig. 9, the lateral force becomes approximately 3 times larger with H/d = 1.5 than with H/d = 7.0 and is greatly susceptible to the influence of the shallow water. Meanwhile as long as the water depth was the same, almost none of the difference was noticed with the maximum value (just after acceleration) brought about by the difference of the acceleration. However the tendency of transitional lateral force is was slightly different. In case that the water depth is shallow (H/d = 1.5), the lateral force was increased for a while just after starting the uniform movement. Such features remarkably appeared when the acceleration is very high.
Fig. 8 Comparison of lateral drag force(H/d 7.0).
Fig. 9 Comparison of lateral drag force(H/d 1.5).
3. ATTEMPT OF MODELING FOR LATERAL DRAG FORCE
The lateral force ranging from a resting state to uniform movement are aligned according to the lateral moving distance of the hull based on a report released by Sadakane et al^{9),10)}. Details of the above are shown with respect to each depth of water in Fig. 10 (H/d=7.0) and 11 (H/d=1.5). The Xaxis of both the figures correspond to the lateral moving distance S, whereas the Yaxis comply with the transitional lateral force coefficient Cwy (Cwy = F /0.5 p LdU0^{2} ).
Fig. 10 
Lateral drag coefficient according to the moving distance(H/d 7.0). 
Fig.11 
Lateral drag coefficient according to the moving distance(H/d 7.0). 
