Shown in Fig.11-(b) is the results of the numerical simulation applied to the proposed timing. Compared with Fig.11-(a), the steering result of the numerical simulation expresses the human steering characteristics more rationally. As a result, the heading and trajectory by numerical simulation accord with the mariner's.

　

4.2.3 Method by the distance to new course

　

 In this study, the distance to new course was also tried to apply to the timing. In this case, when the loop width is smaller than 10 degrees, the good result is shown like the proposed method described in section 4.2.2. However, when the loop width is 25 degrees, the result is worse than the proposed method. In generally, when the distance to new course is estimated, the 15-degree rudder angle for altering course and 7-degree rudder angle for checking turn are applied. In case of a ship with 25-degree loop width, the distance to new course may be unable to be estimated by the method. Using the larger rudder angle for checking turn, we can obtain the distance; however, that is not a regular method but a method as the case may be.

　

 It is verified that it is better to use the distribution of δcal to estimate the steering point to alter course.

 The relation between the peak of the δcal - distribution and the length of a ship is shown in Fig.13. The horizontal axis indicates the length of a ship and the vertical axis indicates the rudder angle utilized as the timing for altering course. The peak value of δcal is proportional to the length of a ship, however, it is independent of the loop width. In a normal fairway, a ship's course is steadied at the eve of a steering point so the third member concerning ψpresent can be neglected in Formula (5). K1 and K2 depend on the length of a ship, not on the loop width. Therefore, the steering point for altering course can be expressed with the function of the length of a ship.

　

 The steering point to alter course can be estimated by Fig.13 and Formula (5).

　

4.3 The comparison of human control with numerical simulation on lateral deviation and rudder angle

　

 The comparison of the human control with the numerical simulation are shown in Fig.14 〜 Fig.17, each of which shows the maximum lateral deviation, mean lateral deviation, rudder angle for checking turn and proportion of the rudder angle for checking turn respectively. The horizontal axis in each figure indicates the result by the numerical simulation and the vertical axis indicates the result by the human control. These figures include the data of all the ship utilized for this experiment. The solid line in each figure indicates the regression line. The reason why each of the lines concerning the rudder angle does not pass the origin is that human rudder control is discrete control like a step.

　

 Each of the correlations coefficients is more than 0.85. The data indicate that there is high correlation between the human control and the numerical simulation. The control law enables us to estimate handling results on unstable ships.