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3. EVALUATION OF NAVIGATIONAL DIFFICULTY BY AUTO-TRACKING SIMULATION
The second question is "How can we evaluate the safety of navigation of a ship?" Although, there can be many answers to this question, we tried to find an answer from the viewpoint of manoeuvrability of a ship. It is clear from this viewpoint that a ship which is easier to navigate is safer than others. So, we modified the question as "How can we evaluate the difficulty of navigation?" The difficulty of navigation has been usually evaluated in two ways. One is the evaluation by the pilots [8] [9], the other is the evaluation by the physical indices such as the rudder index and swept-path index [10] [11]. In many cases, both indices are used simultaneously to complement each other, and it has been found that a ship, which is well reputed by the pilots, gives less usage of rudder and smaller swept path for a given mission. [8] [11] Therefore, we used the rudder index and the swept-path index calculated from the auto-tracking simulation for the evaluation of the navigational difficulty.
3.1 Auto-Tracking Simulation
Auto-tracking simulations in two kinds of artificial seaway were executed for the rating of navigational difficulty. Fig. 11 shows the two artificial seaways; 10° bent seaway and 30° bent zigzag seaway. The manoeuvring motion of a ship is modeled by the first order Nomoto's equation with PD controller [12];
where,
Ψ: Heading angle [rad]
Ψd: Desired heading angle [rad]
K : Rudder gain
T : Time constant
KP: Proportional gains ( = Tωn / K)
KD: Differential gains ( = (2Tζωn -1) / K)
For simplicity, propeller revolution is assumed to be constant and no environmental disturbances are considered. Controller gains are selected to achieve ζ as 0.8 and ωn as 2π・(U/L).
Fig. 11 Two artificial seaways for auto-tracking simulation.
Fig. 12 |
Characteristics of designed auto-tracking controller during the initial 10°heading changes |
Characteristics of this controller can be illustrated by Fig. 12, which shows the initial 10°heading angle changes for different L/U ratios. Our controller makes a ship with the smaller L/U response the more rapidly and this is well matched to the experience of navigation that, if the hull form and speed are the same, the shorter ship has the better turning ability [12].
3.2 Rudder Index and Swept Path Index
For the evaluation of navigational difficulty, we used two physical indices; rudder index and swept path index. Rudder index, RI is defined as
where,
T: Overall controller operating time [sec]
δ(t): Rudder angle during T [rad]
This index reveals the averaged usage of rudder during the given mission, and it is well known that a ship devaluated by pilots usually needs more operation of rudder to achieve the same mission [8]. Second index is the swept-path index, SI which is defined as
where,
β(t): Drift angle [rad]
This index gives the averaged drift angle during the given mission. It has been reported that pilots feel difficulty when the drift angle is larger than 10 degree [11].
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