8.1 Effect to Loop Width by Stern Profile Indices s3 Combined with Rudder Area Ratio

　

 In order to compensate the disadvantage in course stability when SB is adopted, rudder area and/or skeg profile area should be increased with taking care of propulsive performance. It is noticed by the mean line of loop width of SB group in Fig. 10 that if AR/Ld of 1.5% is increased to 2.0%, loop width decreases by about 4°. On the other hand, it is estimated by the mean line in Fig. 11, that the change of loop width by 4° corresponds to the change of s3 by about 0.20. This means, as a result, that s3 decrease by 0.20 corresponds to the decrease of AR/Ld (%) by 0.50 (Example: 2.00-1.50). This is in other word that a certain increase of skeg area defined by the indices s3 is approximately effective as two times of the increase of the rudder area. The relationship between loop width and rudder-skeg area ratio, is shown in Fig. 14 by the index (AR + 2s3)/Lxd which is almost linear. Although the reason of linearity should be further investigated, two dimensional projected skeg area seems to affect much for the course stability [31]. The idea to use the total of the rudder area and skeg profile area was originally given by Dr. Nomoto during the written discussion for the author's study [31].

　

　

　

Additional plots to compare with tendency in Fig. 10 and Fig.11

◎: (○+0.7)...(SB base)

○: STANDARD AR/Ld (INV G base)

　

8.2 Estimation of Loop width by parameters combined with two and three dimensional parameters

　

 The loop width estimation chart by rudder-skeg area ratio given in Fig. 14 could be one of the convenient tool in the initial design stage, however, it had two points to be further investigated [2]. The one is that the parameter used is two dimensional and it does not reflect three dimensional hull form factors such as U or V frame lines or the difference of fullness of the aft part.

　

 Sasaki considered that the loop width is affected by the form factor K which represents the frame lines whether they are U shaped or V shaped. It is said that the ships with U shaped stern frame line are more course stable than those with V shaped frame line. In addition to the K value, Sasaki selected another parameter γA which represents the aft part fullness of the ship. γA is given as

　

　

 where L is the length and B is the breadth of the ship. CPA is the prismatic coefficient of the aft part hull.

 Fig. 15 shows Sasaki's line for the loop width with the parameter K (Form factor) and the ship's aft part fullness γA defined as above [29][32]. Sasaki's lines were given on the basis of the shipyard's databases (triangular plots) where the design of the stern profile and the rudder area ratio which desides the rudder-skeg area ratio in Fig. 14 is considered to be done by the shipyard's uniformed procedure.

　

　

　

 Another point to be investigated in Fig.14 is that most of the data of the loop width are not those of the recently built ships, which might not represent the modern hull form and rudder design. Considering such circumstances, the author tried to collect additional data of the loop width obtained in sea trials together with the indices and parameters; rudder-skeg area ratio, form factor K, aft fullness γA, and analized them as mentioned below. This activity was done in the work for the symposium on manoeuvrability held by Western Society of Naval Architects of Japan [33] with the cooperations by Dr. Sasaki and various members in shipyard's of the said society.

　

 The plots (round shaped) of the loop width in Fig. 15 are the data newly given by many shipyards in addition to Sasaki's plots. These ships are mainly large full ships and the loop widths are those in fully loaded conditions. These plots seem to scatter from Sasaki's line, but the author found that the histogram of the deviation of newly collected plots shows normal distribution, which means that Sasaki's line is reasonable.

　

 Taking this opportunity, the author further investigated these indices and parameters related to the loop width and proposed two charts which will be usefull in estimating the loop width. Fig. 16 is the relationships between the loop width and the rudder-skeg area ratio defined in Fig. 14. The plots are divided into two groups; the group with the fullness γA > 0.65 and the one with γA ≧ 0.65. The suffix to each plot is the figure of the form factor K (Schenherr based). The author's straight line originally proposed in Fig. 14 is shifted to Fig. 16, but the plots in Fig. 14 and those in Fig. 16 are different ones. Although there are scatters of the plots, provably due to sea trial results, Fig.16 shows the tendency that

　

　

(1) the more the rudder-skeg area ratio, the less the loop width.

(2) the more the fullness γA , the more the loop width.

(3) the form factor K affects loop width; the bigger the K value, the smaller the loop width.

(4) the plots are in wide range, but almost all of them are below the author's line defined in Fig. 14 which was given in the former different study [2].

　

 Fig.17 is another indication of the loop width with reference to fullness γA Plots are divided into two groups; the group with the rudder-skeg area ratio > 2.8%, the other with the ratio ≧ 2.8%. The suffix is the figure of rudder-skeg area ratio. The tendency of Fig. 17 shows that

　

(1) the bigger the fullness γA, the bigger the loop width.

(2) the bigger the rudder-skeg area ratio, the smaller the loop width.

　

 The author expects that the series of model tests supplement the sea trial results and clarify the relationships between the loop width and the parameters indicated above.

　

 Fig. 16 and Fig. 17 will be practically utilized in estimating the loop width in accordance with the advance of the initial design stage where the principal dimensions, the stern profile and the rudder, Cpa, the frame line selection of U or V shaped are decided with the trade-off each other under the restrictions by the performances and the specifications other than manoeuvrability.