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 Fig.4.14 and Fig.4.15 show the results for deviated maximum lateral distance from the original course with function of SP12/L1 for the case of overtaken and overtaking VLCC under the condition of (U2/U1 = 1.5. From these figures, it indicated that the results for two ships represent almost qualitatively same tendency, compared to the case of U2/U1 = 1.2. Meanwhile, regardless of wind velocity and direction, an overtaken and overtaking vessel can be manoeuvred safely without deviating from the original paths under the two conditions; the lateral separation between two vessels is approximately kept at 0.5 times of ship 1 and the maximum rudder angle should be smaller than 10 degrees.
 
Fig.4.17 
Deviated maximum lateral distance from the original course with function of wind velocity and direction for VLCC
 
 
 In the meantime, the results for deviated maximum lateral distance from the original course with function of SP12/L1 for the case of overtaken and overtaking VLCC under the condition of U2/U1 = 0.6 are shown in Fig.4.16 and Fig.4.17. From these figures, regardless of wind velocity and direction, an overtaken and overtaking vessel can be manoeuvred safely without deviating from the original paths under the two conditions; the lateral separation between two vessels is approximately kept at 0.5 times of ship 1 and the maximum rudder angle should be smaller than 10 degrees.
 
5. CONCLUSIONS
 From the simulation of ship manoeuvring motions on the safe navigation between ships while overtaking in shallow waters, the following conclusions can be drawn.
 
 For the case of VLCC, if the wind was the only factor to be considered, the course of a ship did not deviate from its intended path with ranges of less than 10° in maximum rudder angle regardless of the wind velocity, even though the wind velocity is about 15m/s. On the other hand, in case of PCC with large area of wind pressure acting on the structure above the water surface, the course of a ship did not deviate from its intended path with ranges of less than 15° in maximum rudder angle under the condition of 1.2 and 1.5 in U2 / U1 . However, for the case of U2/U1 = 0.6, an overtaken vessel with ranges of 15 degrees in maximum rudder angle is uncontrollable regardless of SP12/L1 under the condition of V = 90° and VW 15 m/s, while it is guided securely with intended direction for the overtaking vessel. Also, in case of v = 45° under the condition of VW 15 m/s, an overtaken vessel with ranges of 15 degrees in maximum rudder angle regardless of SP12/L1 is pretty much deviated from the original course. This fact seems to be due to the reason that in case where the wind velocity is very large in comparison with the advance speed of the PCC, she is uncontrollable because the area of wind pressure acting to the structure above the water surface is far larger than other ship types, such as VLCC or general cargo ship. Accordingly, an overtaken PCC vessel navigating at low speed should be cautioned with high alert for the case of wind, and it is considered that speeding up an engine is required if necessary.
 
REFERENCES
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[3] Davis, A.M.J.: Hydrodynamic Effects of Fixed Obstacles on Ships in Shallow Water, Journal of Ship Research, Vol.30, 1986.
[4] Kijima, K., Furukawa, Y. and Qing, H.: The Interaction Effects Between Two Ships in the Proximity of Bank Wall, Trans. of the West-Japan Society of Naval Architects, Vol.81, 1991.
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[6] Yasukawa, H.: Bank Effect on Ship Maneuverability in a Channel with Varying Width, Trans. of the West-Japan Society of Naval Architects, Vol.81, 1991.
[7] Beck, R.F.: Forces and Moments on a Ship Moving in a Shallow Channel, Journal of Ship Research, Vol.21, 1977.
[8] Cohen, S.B. and Beck, R.F.: Experimental and Theoretical Hydrodynamic Forces on a Mathematical Model in Confined Waters, Journal of Ship Research, Vol. 27, 1983.
[9] Landweber, L., Chwang, A.T. and Guo, Z.: Interaction Between Two Bodies Translating in an Inviscid Fluid, Journal of Ship Research, Vol.35, 1991.
[10] Korsmeyer, F. T., Lee, C.-H. and Newman, J. N. : Computation of Ship Interaction Forces in Restricted Waters, Journal of Ship Research, Vol.37, 1993.
[11] Kijima, K., Nakiri, Y., Tsutsui, Y. and Matsunaga, M.: Prediction Method of Ship Maneuverability in Deep and Shallow Waters, Proceedings of MARSIM and ICSM 90, 1990.
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