6.1 Indices Utilized for Stern/Rudder Design

　

 The course stability and the course-of-change ability with response to steering are more important than simple turning performances for large full ships like VLCC. Therefore, the author is to propose a method to evaluate indices for relative yaw damping by comparing the standard rudder area ratio with actually fitted ones and to show their relationships with reversed spiral loop width. During the initial design stage, it is important to select not so many parameters which are available and reasonably represent the performance. Such parameters of ship forms and rudders are limited to Length L, Cb / (L/B), B/d and AR / Ld, except the newly proposed stern profile ratio which defines the non-dimensional projected area. This ratio is adopted by the author's view that cut-up of stern profiles in SB might spoil their course stability.

　

　

6.2 Standard Rudder Area Ratio Required by Course Stability

　

 When the author proposed the procedure to decide the Standard rudder area ratio AR/Ld with suitable relative yaw damping (AR/Ld・K' ), assuming the course stability depends on the ship's principal particulars; Cb / (L/B) and B/d, most of the ships for the analysis were with Inverted-G type sterns and conventional rudders [24]. In this proposal, the Standard AR / Ld and the allowable AR / Ld are defined and design charts for these are given by investigating the relationships between relative yaw damping (AR / Ld・K' ) and AR / Ld. These were obtained by the 10°Z test analysis of which method was originally given by Nomoto [25].

　

 Four typical ships A, B, N and C with different relative yaw damping (AR / Ld・K') were investigated, by which the standard and the allowable AR / Ld were defined as shown in Fig. 8. The inclination of the tangent of r' 〜δ curves and comments on manoeuverbility by ship's operators are also taken into consideration in the study. (Refer to Table 3). The standard AR / Ld chart is shown in Fig. 9. The couse stability of a certain ship can be judged relatively by comparing the actually fitted AR / Ld with the standard AR / Ld and above mentioned bases on ship A, B, N and C. The rankings for course stability are defined by this comparison. In case of Cb/ (L/B) and/or B/d figures of the ships newly designed are larger than those of the AR / Ld charts, figures by linear extrapolation give good approximations which was confirmed during the study of DW400,000T ULCC with L/B=5.0 [10].

　

6.3 Relationships between Stern Profile/ Rudder Area Ratio and Loop Width

　

 As most of the stern profile of large full ships, mainly VLCC, were almost Inverted-G type untill first half of 1970's, the author's study mentioned in 6.2 was based on that [24] . After that Mariner stern increased due to larger propellers with lower revolutions and these days SB has been the main stream in view of the resistance and propulsion. As reversed spiral tests are common for full shaped vessels like VLCC in addition to 10°Z steering tests, the author indicated the loop widths obtained in sea trials in Fig. 10 with reference to the course stability based on the analysis of 10°Z [26].

　

　

　

 The mark "Standard AR / Ld" at 0 position means that a certain ship has the standard AR / Ld (%) based on the author's method in view of course stability. It is recognized by Fig. 10 that the loop width decreases if the actually fitted rudders have larger AR / Ld than the Standard AR / Ld, and if they are smaller than the standard, the width increases. Generally, it shows that the loop width of Inv.-G group is the smallest, then Mariner which is larger than Inv.-G and the SB the largest, even if their movable rudder areas are same.

　

 If we look at the position of the Standard AR / Ld, loop widths distribute in the range of about 0°〜4° in case of Inv.-G, 4°〜8°for Mariner and 8°〜9°for SB which is the largest. Fig. 10 is utilized to estimate the change of loop width by increase or decrease of AR / Ld compared to the standard AR / Ld in view of course stability. This was originally proposed during the study for DW400,000T ULCC [10] and introduced in a Ship Design Manual [27].