為了提升海上拖帶作業系統的穩定性及安全性，本文利用一套結合耐海性與操縱性的非線性六度運動數學模式，建立出一套拖船－拖纜－被拖船整體非線性運動狀態動力學模組，並以四階Ｒｕｎｇｅ－Ｋｕｔｔａ之數值方法來模擬計算船隻在波浪中的時程領域運動反應。
由於在實際海況中，除了受到風、流的影響之外，波浪作用力所造成的影響更為巨大，在波力及波力矩的作用，船隻航行的航向穩定性與靜水中相去剩甚遠。因此，在文中先於靜水對繫纜位置、拖纜長度、拖帶速度等要素對拖帶系統航向穩定性及拖纜張力變化的影響進行分析，以了解拖纜系統的基本特性。之後，再加入風、洋流、波浪來模擬實際海況中的情況，探討在不同海況、不同外力方向下，拖船速度、拖纜張力的安全性及拖帶系統的穩定狀況，以找出最安全的航行方法。經由本研究的分析結果討論，可知本文所建立的數學模式，對於評估海上拖帶作業技術與安全有相當大之助益。

In order to promote the stability and safety for the ship towing operation system, the present paper develops a nonlinear mathematical model including the seakeeping and maneuvering characteristics to simulate the ship motion behaviors for the ship doing towing task in waves. The time history solutions of the six degrees of freedom of motions for each ship, i.e. towing ship and towed ship, are solved by 4th Runge-Kutta method
Because of the effect of the wind, the wave and the current at sea, the ship’s course and stability are quite different from those in calm water. The wave usually plays the main role of the external disturbances and always causes some serious difficulties to the ship steering, especially in executing the towing task at sea.
In the paper, the effects of mooring position, towing line length and towing speed on the course stability and towline tension are analyzed firstly for the ship towing system in calm water. Then the effect of the wind, the current and the wave are added in the numerical model to investigate the effect of each factor, especially for the wave with different sea states. From the results of the present study, the better operation technique for the ship towing system can be found. Therefore the nonlinear model developed here for simulating the ship towing system in waves can be regarded as an useful tool for promoting the ship towing technique and it safety at sea.

1. Bailey, P.A., Maneuvering of a ship in a seaway, PhD Thesis, University of Southampton, UK, 1999.
2. Crossland, P. and Johnson, M.C., “A time domain simulation of deck wetness in head seas,” Proceeding of RINA International Conference on Ship Motions and Manoeuverability, London, UK, 1998.
3. Fang, M.C., Lee, M.L., and Lee, C.K., “The simulation of water shipping for a ship advancing in large longitudinal waves,” Journal of Ship Research, Vol. 37, pp. 26-137, 1993.
4. Funaji, S., Kijima, K., and Furukawa, Y., “Ship maneuvering performance under the influence of external disturbances (in Japanese),” Transaction of the West-Japan Society of Naval Architects, Vol. 106, pp. 47-56, 2003.
5. Hamamoto, M. and Kim, Y.S., “A new coordinate system and the equations describing maneuvering motion of a ship in waves (in Japanese),” Journal of the Society of Naval Architects of Japan, Vol. 173, pp. 209-220, 1993.
6. Hamamoto, M., Matsuda, A., and Ise, Y., “Ship motion and the dangerous zone of a ship in severe following seas (in Japanese),” Journal of the Society of Naval Architects of Japan, Vol. 175, pp. 69-78, 1994.
7. Hirano, M., “On the calculation method of ship maneuvering motion at initial design phase (in Japanese),” Journal of the Society of Naval Architects of Japan, Vol. 147, pp. 144-153, 1980.
8. Hirano, M. and Takashina J., “A calculation of ship turning motion taking coupling effect due to heel into consideration,” Transaction of the West-Japan Society of Naval Architects, Vol. 59, pp. 71-81, 1980.
9. Hirano, M. and Takashina J., “Ship Turning Trajectory in Regular Waves,” Transaction of the West-Japan Society of Naval Architects, Vol. 60, pp. 17-31, 1980.
10. Inoue, K., etc., “The Course Stability of Towed Boats,” Transaction of the West-Japan Society of Naval Architects, Vol. 42, pp. 11-25, 1971.
11. Inoue, S., Hirano, M. and Kijima, K., “Hydrodynamic derivatives on ship manoeuvring,” International Shipbuilding Progress, Vol. 28, pp. 112-125, 1981.
12. Inoue, S., Hirano, M., Kijima, K., and Takashina, J., “A practical calculation method of ship maneuvering motion,” International Shipbuilding Progress, Vol. 28, pp. 207-222, 1981.
13. Isherwood, R.M., “Wind Resistance of Merchant Ships,” Transactions of RINA, Vol. 115, pp. 327-338, 1973.
14. Kijima, K. and Wada, Y., “Course Stability of Towed Vessel with Wind Effect,” Journal of the Society of Naval Architects of Japan, Vol.153, pp. 117-126, 1983.
15. Kijima, K., etc, “On the Towing System for Disabled Ships,” Journal of the Society of Naval Architects of Japan, Vol.188, pp. 191-199, 2000.
16. Kijima, K. and Nakiri, Y., “On the practical prediction method for ship manoeuvring characteristics (in Japanese),” Transaction of the West-Japan Society of Naval Architects, Vol. 105, pp. 21-31, 2003
17. Kishimoto, T. and Kijima, K., “On the Towing System for Disabled Ships(2nd Report),” Journal of the Society of Naval Architects of Japan, Vol.191, pp. 77-85, 2002.
18. Munif, A. and Umeda, N., “Modeling extreme roll motions and capsizing of a moderate-speed ship in astern waves,” Journal of the Society of Naval Architects of Japan, Vol. 187, pp. 51-58, 2000.
19. Tanaka, M., “Experimental Study on the Course Stability of a Towed Boats,” Transaction of the West-Japan Society of Naval Architects, Vol. 56, pp. 1-9, 1978
20. Umeda, N. and Hashimoto, H., “Qualitative aspects of nonlinear ship motions in following and quartering seas with high forward velocity,” Journal of Marine Science and Technology, Vol. 6, pp. 111-121, 2002.
21. Yoshimura, Y. and Nomoto, K., “Modeling of manoeuvring behavior of ships with a propeller idling, boosting and reversing (in Japanese),” Journal of the Society of Naval Architects of Japan, Vol. 144, pp. 57-69, 1978.
22. Yukawa, K., etc., “On The Towing of Wrecked Tanker’s Fore Part at Rough Sea,” Journal of the Society of Naval Architects of Japan, Vol. 191, pp. 87-96, 2002
23. 關西造船協會，造船設計便覽(日文)，海文堂出版株式會社，東京，1983。
24. 高品純志，港灣域船操縱運動計算法關研究(日文)，博士論文，東京大學，日本，1992。
25. 朱軍、程虹等，波浪作用下纜船拖帶系統非線性運動數值模擬，海洋工程第２４卷第３期，２００６年。
26. 林緯作，環境外力下船舶拖帶模擬計算系統之研發與應用，國立台灣大學工程科學及海洋工程學研究所，民國九十四年。
27. 徐玉樹，順浪中船舶之穩度安全性，國立成功大學造船暨船舶機械工程研究所碩士論文，民國八十六年。
28. 羅志宏，船舶在波浪中之非線性運動操控模式之探討，國立成功大學造船暨船舶機械工程研究所博士論文，民國九十五年。