7.1 Relationships between Stern Profile Indices and Reversed Spiral Loop Width.

　

 In order to feature the stern profile, the portions of the projected area of stern form surrounded by the rectangular composed of the base line, A.P and SS 1/2, and either of the designed draft, the rudder top horizontal line or the shaft center line are defined as s1, s2 and s3 respectively as shown in Fig. 11. Among the indices s1, s2, and s3, indices s3 are found to show clearly the difference of the stern profiles with each other; Inverted-G, Mariner and SB. The relative yaw damping effect by the skeg-like stern profile is estimated to be remarkable in the area below shaft center where wake is small.

　

 Fig. 11 clearly shows that the smaller the figure s3, the larger the loop width, which agrees with the tendency in Fig. 10 where loop widths increase along with the change of stern profiles from Inverted-G to Mariner, then Mariner to SB. It seems that loop widths increase gradually in the range of s3 more than 0.40, however, if it is below 0.35 they could increase rapidly. The arrow marks in Fig. 11 mean the correction of actually fitted AR/Ld to the Standard AR/Ld proposed by the author.

　

7.2 Stern Profile Indices s3 of Ships Delivered and their Features

　

 Typical stern profiles of Inverted-G, Mariner and SB are as shown in Fig. 11, however, their details have features in every ship and shipbuilder with yearly changes for about 10 years. Fig. 12 shows such features in case of SB. In Fig. 11 the histogram of the indices s3 are shown, calculated for vessels built in Japanese shipyards for recent 10 years which are mainly VLCC class and other large full ships including the ships in Fig. 11 [28][29]. It is noticed in Fig. 11 that s3 figures of Mariner and SB are in the wide range of 0.20〜0.60, but s3 of SB seems to have concentrated to the range of 0.25〜0.40, among which the peak is especially between 0.30〜0.35 provably because of energy saving competitions to improve the propulsive performance.

　

7.3 Features of Stern Bulb in View of Reversed Spiral Loop Width

　

 The data of the reversed spiral loop width of SB in sea trials in Fig. 10 are limited in number, however loop widths of recently built VLCC and similar vessels are estimated to show considerably large figures, if we recognize the peak of s3 as 0.30〜0.35 with same scales in Fig. 11.

　

　

 Similar situation seems to be recognized by Raestad. Raestad stresses from the classification society's standpoint that full shape modern hull form and SB ships with small deadwood are much more course unstable than the traditional hull form like Series 60 [30]. He also notes that the ships with ∇^1/3/L larger than 0.2 shows extraordinary course unstable features and needs very large rudder area ratio, much more than that by DNV guide line in order to satisfy the overshoot angles by IMO A751 (18) and indicates the curve for such necessary AR/Ld in Fig. 13.

　

　

 By the author's study SB ships are estimated to have sufficient course stability, if they are fitted with the rudder of (Standard AR/Ld + 0.7)%, considering the difference between the mean lines of Inv-G and SB in Fig. 10. The AR/Ld on this basis for several ships with SB, plotted in Fig. 13, are recognized to be very close to the AR/Ld curves given by Raestad. This shows the author's study results in Fig. 10 and Fig. 11 agree with Raestad's view.