THE ESTIMATION OF SHIP MANEUVERABILITY FOR CONTROLLING POSITION OF UNSTABLE SHIPS
NISHIMURA Tomohisa (Japan Coast Guard, Japan)
KOBAYASHI Hiroaki (Tokyo University of Mercantile Marine, Japan)
In consideration for position control, maneuverability on unstable ships is discussed. Several licensed mariners have maneuvered unstable ships along a fairway, using a ship handling simulator. A rudder control law based on the handling results is estimated. Although the constants, in the control law, which concern lateral and heading deviation are proportional to the length of a ship, they are same value to the loop width. On the other hand, the constants which concern late of turn are proportional to both the length of a ship and the loop width. Numerical simulations have been conducted on the fairway. The control law and the constants are utilized in the simulation. It has been confirmed that ship handling by a normal mariner can be estimated by the control law and the constants. Furthermore, the control law and the constants are applied to various unstable ships and the numerical simulations have been conducted. The control results concerning the lateral deviation and the rudder angle become worse as the length of a ship or the loop width becomes larger. It has been proved that ships may exceed the limitation on position control even if IMO standard is satisfied.
Maneuverability of unstable ships is evaluated by yaw checking and course keeping abilities. As to the abilities, IMO standard regulates that over shoot angle obtained by Zig-zag maneuver test must not overstep the prescribed value. In a restricted water area like a fairway however, we must discuss maneuverability to control a position of a ship as well as the yaw checking and course keeping abilities.
In this study, human characteristics on unstable ship handling in a fairway are estimated. The maneuverability which is necessary for safe navigation in a restricted water area is discussed on the basis of the estimated human characteristics.
A previous report on stable ships has clarified that results of position control obtained by human steering are influenced by the length of a ship . In this study, the length of a ship and the spiral loop width which is a typical index of the course instability are discussed to evaluate the maneuverability of unstable ships. Human characteristics concerning position control are estimated on the basis of handling results of unstable ships.
In this experiment, several licensed mariners maneuver various unstable ships in a fairway, using a ship handling simulator and rudder angles which is a factor in safe navigation in a fairway and lateral deviations from the center of the fairway are evaluated.
2.1 Experimental ships
Twelve types of ships are taken as an object in this study. Their principal dimensions and maneuverability constants are shown in Table 1 and Table 2 respectively.
The response equation of a rate of turn corresponding to a rudder angle is shown by Formula (1).
δ: Rudder angles,
ψ: Late of turn,
ψ: Turining acceleration,
L: Length of a ship,
T', K ', α': Maneuverability constants
Table 1 Principal dimensions
L: length, B: breadth, d: draft
Table 2 Maneuverability constants
|K' (non dimension)
|T' (non dimension)
2δc: spiral loop width
2.2 Experimental fairway
Shown in Fig.1 is a fairway utilized for the experiment. The fairway has two bending points and each of the angles is 30 degrees. The breadth of the fairway is set as the same length of the ships. Leading buoys are positioned on the extension of each the fairway in order to check the lateral deviation from the center.
The experiments have been conducted by five licensed mariners. They are required to maneuver the ships along the center of the fairway. In consideration of general velocity in fairways, the velocity of the ships is set as 12 knots. In order to estimate the basic human characteristics, no disturbance is set.
Fig.1 Schema of the fairway
3. RESSULT AND DISCUSSION
In our previous report, it has been developed that spiral loop width has a close relation to a rudder angle for checking turn  . In this study, the maximum rudder angle for checking turn and the maximum lateral deviation are measured and mean lateral deviation and proportion of rudder angles for checking turn are calculated. And then the relation between these values, the length of the ship and the loop width is shown.
The mean lateral deviation and the proportion (%) of rudder angles for checking turn are defined as Formula (2) and Formula (3) respectively:
where Σxε is the value summed up the distance from the center of the fairway, t is the time (sec.) spent in passing along the fairway, δMax is 35°rudder angle and Σδ is the value summed up rudder angles for checking turn every second
3.1 The relation between loop width and lateral deviation
Figure 2 shows the relation between the maximum lateral deviation and the loop width. Figure 3 shows the relation between the mean lateral deviation and the loop width. The horizontal axis in each figure indicates the loop width. The vertical axis in the upper figure indicates the maximum lateral deviation and one in the lower figure indicates the mean lateral deviation. The symbol "●" indicates the mean value concerning the 240-meter ships. The symbol "▲" indicates the mean values concerning the 150-meter ships.
The relation between maximum lateral deviation and loop width
The relation between mean lateral deviation and loop width
In case of the 240-meter ship, the maximum lateral deviation and the mean lateral deviation tend to slightly increase as the loop width becomes large, whereas, in case of the 150-meter ship, both of the lateral deviations show almost the same value regardless of the loop width.