3. On the Turning of Tug-Towed Ships Systems
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概要
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We have discussed the course stability of a tug-towed ships system in the Journal of the Society of Naval Architects of West Japan No. 42, 43, 44 and 46, In this paper, the author theoretically and experimentally deals with the turning motion of the tug-towed ships system in still water by the parameters-a ship's course stability criterion, towing points, length of towing ropes, number of towed ships, rudder angle and rudder area of the tugboat, radius of gyration of each ship and size of towed ships. The results are as follows: (1) During the region of short towing rope's length, the last towed ship has a larger radius than the tugboat, then by the increase of the towing rope's length, the last towed ship gradually tends to turn with the smaller circle and eventually when the towed rope length is over the critical rope's length q_<cun>, the system falls into irregular motion, ,and this is identified and qualitatively agrees with the experimental results. (2) The effect of the fore-towing point, towing rope's length and the towed ships to the values of A_<d0>, T_<r0>, T_<ad0> and R_<e0> are small and it can be neglected, and those values are given in the eq. (18). (3) The steady turning of the tug-towed ships system by the steering of the rudder of the tugboat is only possible when the towing rope's length is under the critical towing rope's length q_<cun>L and which is given in eq. (9). (4) The larger the rudder angle and the rudder area ratio of the tugboat are the smaller the radius of steady turning of the towed ships system and. the values of A_d, T_r and T_<ad> of each ship of the system are. (5) As the rudder angle and rudder area ratio of the tugboat are constant, a. the radius of steady turning and the values of A_d, T_r and T_<ad> decrease, when the number of towed ships increases, b. the radius of steady turning becomes larger, when the towing rope's length increases, and the fore-towing points are apart from the center of gravity of the towed ship except of the last towed ship. And because of the increase of the radius of steady turning, the values of A_d, T_r and T_<ad> become larger, when the towing points are placed apart from the center of gravity of the towed ships, c. the effect of the derivatives of towed ships are included in the factor μ as given in eq. (11), d. the effect of radius of gyration of tugboat itself is large, when the value of the radius of gyration of tugboat increases, the values of A_d, T_r and T_<ad> grow large, and the effect of radius of gyration of towed ship is small and negligible.