3.4 The relation between the length of a ship and rudder angles for checking turn

　

 The relation between the length of a ship and the maximum rudder angle for checking turn is shown in Fig.8 and the relation between the length of a ship and the proportion of the rudder angle for checking turn is shown in Fig.9. The horizontal axis in each figure indicates the length of a ship. The vertical axis in upper figure indicates the maximum rudder angle and one in the lower figure indicates the proportional rudder angle for checking turn respectively. The symbol "×" indicates the mean values concerning the loop width which is 10 degrees.

　

　

　

 The maximum rudder angle for checking turn and the proportion of the rudder angle for checking turn tend to increase as the length of a ship becomes large.

　

3.5 Summary of the tendency

　

 In summary, the results of the experiment are as follows.

　

 The tendencies of the lateral deviation and of the rudder angle for checking turn corresponding to the spiral loop width and to the length of a ship are shown in the previous chapter. In order to evaluate the maneuverability for position control concerning unstable ships, we should analyze standard human characteristics on unstable ships and discuss a human rudder control law for the position control.

 Moreover, the estimated standard human characteristics can be available to design a fairway.

　

 In this chapter, the rudder control law and the standard human characteristics are evaluated to estimate human position control results on unstable ships.

　

4.1 Formularization of human characteristics on ruder control

　

 It is widely recognized that the control law described in the Formula (4) enables to estimate the standard rudder control when a human maneuvers a stable ship in a restricted water area [1].

　

　

 In order to estimate the human constants, parallel shift maneuver shown in Fig.10 has been conducted by the mariners. Ships utilized for the maneuver are the same in the previous chapter. The parallel shift maneuver is adequate to estimate the human constants, because the motion of a ship is larger than the motion in an ordinary fairway and rudder angle to lateral deviation can be also measured directly. The reason why the distances of the parallel shift are set as L/2, L/4 and L respectively that we would like to obtain rudder angles to various lateral deviation.

　

 The constants can be estimated by the method of least squares applied to the handling results which are δ, xε, ψε, ψε and V.

　

 The constants concerning lateral deviation (K1) and heading deviation (K2) are shown in Table 3. The constant concerning a rate of turn (K3) is shown in Table 4. The constants K1 and K2 are fixed values for every length of a ship. On the other hand, the constant K3 varies with both the length of a ship and the loop width.

　

　

　

　

4.2 Estimation of a steering point

　

 In a restricted water area, a steering point to alter course is decided by turning ability of a ship, because her trajectory is affected by the point. The point to alter course is also related with rudder angle for altering course and affects the subsequent rate of turn, lateral deviation and ruder angle for checking turn. Therefore, when a numerical simulation is conducted, the difference of the point affects a trajectory of a ship. In this section, the estimation method of a steering point for altering course is discussed.

　

4.2.1 Method by comparison of lateral deviation with heading deviation.

　

 According to the previous report on stable ships by Senda et al. [1], a steering point for next fairway in the numerical simulation is defined as -(K1 × xnext) becomes equal to (K2 × ψnext) , where ψnext is heading deviation to next fairway and xnext is lateral deviation to the next fairway. Applying the steering point and Formula (4), we have conducted a numerical simulation. A fairway utilized for the numerical simulation is the same one shown in Fig.1. An example of the results is shown in Fig.11-(a). The length of a ship is 150m and the loop width is 25 degrees. Each of the figures shows rudder angle, heading and trajectory sequentially from the top. In each of the figure, a thick line indicates a result by the numerical simulation and a thin line indicates the mariners'. As in the top of the figure, the timing of steering on the numerical simulation is earlier than the humans'. Once given to unstable ships, a rate of turn accelerates grater than stable ships even if a rudder angle is small. Therefore the heading and the trajectory on the numerical simulation do not trace the human's.

　

 In case of stable ships, the method shows good agreement with humans', however, the method is not suitable for unstable ships because of changing human characteristics on steering.

　

4.2.2 Method by the frequency of a calculative rudder angle at a steering point

　

 It is believed that there is close relation between a steering point and a rudder angle for altering course, because mariners decide them in consideration of turning ability, lateral deviation to the next fairway, the altering course angle, the present turning velocity and the present speed. Assuming this concept, one can express the steering point as the rudder angle shown in Formula (5).

　

　

Where,

　

 In order to estimate the steering point, xnext, ψnext, ψpresent and Vpresent at which the mariner has begun to alter course in the fairway shown in Fig.1 are substituted for the Formula (5) for every length of a ship and a distribution of δcal is estimated.

　

 The data shown in Fig.12 are the distribution of δcal on the 150-meter ships. As Figure 12 shows, δcal has a peak between 20° and 22°. The highest frequency of δcal is applied to the timing of the steering point to alter course in the numerical simulation. As δcal reaches the peak, the ships begin to steer the rudder angle for altering course in the numerical simulation.