• Korean Journal of Mathematics
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• v.8 no.1
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• pp.27-32
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• 2000

In this paper, we show that for any continuous map $f$ of the circle $S^1$ to itself, (1) $x{\in}{\Omega}(f){\backslash}\overline{R(f)}$, then $x$ is not a turning point of $f$ and (2) if $P(f)$ is non-empty, then $R(f)$ is closed if and only if $AP(f)$ is closed.

• Journal of Navigation and Port Research
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• v.45 no.6
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• pp.298-305
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• 2021

Identifying the effect of turning characteristics on collision avoidance for Maritime Autonomous Surface Ships (MASS) can provide a key to avoid the collision of MASS. The purpose of this study was to derive a method to identify the effect of turning characteristics, which can be changed by various rudder angles and the ship's speed, on collision avoidance. The turning circle was observed using a mathematical model of a 161-meter-long ship, and it was analyzed that the turning circle had an effect on collision avoidance through numerical simulations of collision avoidance for four collision situations of two ships. The evaluation results using the two variables, the minimum relative distance between two ships and the minimum time at the minimum relative distance, demonstrated that the rudder angle has a major influence on the change of the minimum relative distance, and the ship's speed has a major influence on the change of the minimum time. The evaluation method proposed in this study was expected to be applicable to collision avoidance as a measures in remote control of MASS.

• Journal of Fisheries and Marine Sciences Education
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• v.21 no.1
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• pp.59-67
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• 2009

It is necessary for navigator to understand sufficiently maneuverabilities based on experiences and the data which were gotten from several tests of the ship when he maneuver his vessel. By the way most navigators used to rely on his experiences or feelings only maneuvering ship. But when he encounters situations he did not experience before he may be in difficulties. So navigator must get both experiences and data based on experimental results. In this paper author performs several tests such as turning test, Zig-zag test and spiral test to provide informations of maneuverabilities for navigators. The obtained results are as follows: There occurs almost no difference in size of the turning circle by the changes of ship's speeds. The scale of the turning circle was decreased exponentially when the rudder angle was increased. The maneuverabilities is better turning to starboard side than to port side. Maneuverabilities are more effective when the rudder is used to small angle than to large angle. As a result of spiral test course stability was comparatively seemed to be good.

• Journal of Ocean Engineering and Technology
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• v.31 no.5
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• pp.335-339
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• 2017

This study investigated the sea trial performance of a wave piercing high speed planing hull (WPH). The bow shape of the boat is sharp, and it has no chine or spray strip like a normal planing boat. The skeg is attached to the bottom of the boat in the longitudinal direction from the bow to the stern. The speed performance was analyzed as the speed dropped in a wave, and the seakeeping performance was compared with that of a planing boat with a similar velocity coefficient by measuring the vertical acceleration of the bow in the wave. The turning circle was compared with Lewandowski's estimation for a planing boat. As a result of this study, it was confirmed that the velocity drop of the developed WPH was not large in a wave, and the vertical acceleration was greatly reduced compared with that of a normal planing boat. The turning circle was somewhat larger than the estimated results for a planing boat, but the overall tendency was the same.

• Journal of the Korean Society of Fisheries and Ocean Technology
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• v.46 no.1
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• pp.56-69
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• 2010

This study was intended to determine the maneuverability of the vessel CHARMBADA. When the rudder angle was at $10^{\circ}$, $20^{\circ}$ and $30^{\circ}$, the maximum advance by slow, half and full ahead were varied in the range of 523.6-131.3m, 528.8-177.2m and 530.6-219.7m, respectively. The maximum transfer was 799.9-181.3m, 792.1-232.8m and 807.7-316.9m, respectively. The turning circle ability was better during starboard turning. When the rudder angle was $10^{\circ}$, $20^{\circ}$ and $30^{\circ}$, variation in the maximum advances was 392.0m, 245.0m and 153.0m. The maximum transfer was 528.0m, 339.0m and 218.0m, respectively based on the regression equations. As the rudder angle became bigger, the maximum advance or maximum transfer became smaller by the exponential function. The advance inertia took 127sec, 145sec, 181sec each until the vessel speed was 7.0konts, 12.0konts, 17.0konts. The static inertia took 245sec, 269sec, 300sec each until the vessel speed was under 2.0konts and the advance distance was 114.4m, 181.2m, 197.0m each. Accordingly, the static inertia was inclined to increase to scale according to the increase in vessel speed. For the CHARMBADA, the smaller the rudder angle was, the much bigger the turning circle became due to adhesion to the skeg, thereby lowering the vessel's turning ability.

• Journal of the Korean Society of Fisheries and Ocean Technology
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• v.22 no.2
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• pp.22-30
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• 1986

It is very important for a navigator on bridge to know the maneuverability of his ship sufficiently at sea. Generally, the data of a turning circle test have long been used to study and evaluate the maneuverability of a ship. But referring only the data of the turning circle test method, he can not evaluate his ship's maneuvering characteristics sufficiently. So nowaday the test method added Z test to turning circle test for more detail references is considered to be desirable. In this paper, the authors performed PAL test and Z test together in order to study the maneuverability of M. S.Pusan 403, training ship of the National Fisheries University of Pusan. According to the results of PAL test, the rudder effect in port rudder angle of the M. S. Pusan 403 was found to be more effective than that in starboard one, because her changing amounts of angular velocity, turning radius and tangent speed in port rudder angles were found to be larger than those of them in starboard rudder one in unsymmetry. The relation between her drift angle(.8) and rudder angle (0) was found to be changing with .8=0.640 in direct proportion. As it appeared that her calculated K'-values were smaller than the standard K'-values of different kinds of ships in accordance with her Z test, her turning ability was found to be lower. The running distance of a turn in her 10$^{\circ}$ Z test was about 8.3 times her own length and was found not to be exceeded the standard maneuvering distance, therefore she was considered to have good maneuverabilities synthetically.

• Journal of Navigation and Port Research
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• v.33 no.9
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• pp.603-608
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• 2009

In this paper, a 3m-class free running model ship will be introduced with its manoeuvring performance experiments. The results of turning circle test and zig-zag test will be explained. The developed system are equipped with GPS, main control computer, wireless LAN, IMU (Inertial Measurement Unit), self-propulsion propeller and driving rudder. Its motion can be controlled by RC (Radio Control) and wireless LAN from land based center. Automatic navigation is also available by pre-programmed algorithm. The trajectory of navigation can be acquired by GPS and it provides us with important data for ship's motion control experiments. The results of manoeuvring performance experiment have shown that the developed free running model ship can be used to verify the test of turning circle and zig-zag. For next step, other experimental researches such as ship collision avoidance system and automatic berthing can be considered in the future.

• Journal of Institute of Control, Robotics and Systems
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• v.11 no.4
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• pp.363-368
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• 2005

This paper proposes an LOS(line-of-sight) guidance system of a ship for path following. From the viewpoint of a control configuration, guidance is a special type of compensation algorithm that is placed in front of the controller to accomplish navigational objects. A guidance system generates a reference trajectory for trajectory tracking or path control and decides the desired velocity, position and heading angle. A control system executes commands based on a reliable guidance law during navigation. An LOS vector from the vessel to a point on the path between two way-points in straight-line navigation or a point among turning circle in turning navigation is selected, and then a heading angle is calculated to converge the desired path based on the LOS vector. The LOS guidance law is defined for the straight-line and the turning circle, respectively. The effectiveness of the suggested LOS guidance system is assured through computer simulation.

• Journal of the Korean Society of Fisheries and Ocean Technology
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• v.37 no.4
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• pp.275-284
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• 2001

The for this study, turning circle tests and maneuvering indices were conducted to study and evaluate the maneuverabilities of the fishery training ship M.S. A-RA(G/T : 990tons). The results obtained were summarized as follows : 1. The advances of the starboard and port of the turning circle were measured based on the dumb card test method were 198m, 192m, the size of tactical diameters of them were 194m, 188m, respectively. 2. The advances at the starboard and port of the turning circles were measured according to the DGPS positioning obtained 196m, 194m, the size of tactical diameters of them were 194m, 190m, respectively. 3. The results were compared which came from the sizes of turning circle measured up with the dumb card test method during the trial test and from the size of turning circle measured according to the DGPS positioning. The advance of the turning circle measured at the time of the starboard turning according to the DGPS positioning was 1m longer than that of the trial test. And it was 21m shorter at the time of the port turning. 4. The rudder was steered at $35^{\circ}$ of rudder angle each starboard and port while the ship M.S. A-RA was advancing at full speed of 13 k't. The velocity of the ship was reduced to 7.8 k't at $180^{\circ}$ of turning angle and 6.0 k't at $360^{\circ}$ of turning angle and mean values of turning angular velocity of the port and starboard were $2.4^{\circ}$/sec and $2.3^{\circ}$/sec, respectively. 5. The Z test at each $10^{\circ}$, $20^{\circ}$, and $30^{\circ}$ of rudder angle was carried out to have the maneuvering indices K and T measured. K for the each rudder angle were 1.24, 1.45, and 1.65 while T for the each rudder angle were 0.33, 0.20, and 0.14. That is, K at the Z test at $30^{\circ}$ was greater than at the Z test of $10^{\circ}$ and $20^{\circ}$ while T at the $30^{\circ}$ Z test was less than at the Z test of $10^{\circ}$ and 20.

• Journal of the Korean Society of Fisheries and Ocean Technology
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• v.51 no.2
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• pp.245-256
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• 2015

This study is intended to provide navigator with specific information necessary to assist the avoidance of collision and the operation of ships to evaluate the maneuverability of dead weight tonnage 8,000 tons Oil/Chemical tanker. The actual maneuvering characteristics of ship can be adequately judged from the results of typical ship trials. Author carried out sea trials based full scale for turning test in ballast condition and full load condition, semi balanced rudder and flap rudder. The turning circle maneuvering were performed on the starboard and port sides with $35^{\circ}$ rudder angle at the normal continuous rating. The results from tests could be compared directly with the standards of maneuverability of IMO and consequently the maneuvering qualities of the ship is full satisfied with its.