TRANSVERSE SECTIONS UPON RESISTANCE. 305 



Another reason why there appears to be no particular necessity for having a system 

 which will apply to all lengths of ships from the model up is that in practice the ratio of 

 length to beam and beam to draught will vary considerably in passing from a small to a 

 large vessel, and therefore the results of any set of experiments must necessarily have a 

 somewhat limited application. 



The ratio of horse-power to displacement is also one of the factors entering into the 

 economy of vessels and hence in preliminary design work may have to be taken into account. 



A discussion of the proposed method is given in the appendix. 



In order to exaggerate certain features in the present paper so that the diagrams will 

 show more clearly the effect of the varying the shape of section of the vessel and to bring 

 them into the limited dimensions of the volumes of our Transactions, some of the figures 

 have been modified by a factor representing the cube of the speed-length ratio. 



RESULTS OF EXPERIMENTS. 



As a general comparison of U and V-shaped sections. Fig. 3, Plate 55, shows the 

 effect upon the resistance for a full and a fine vessel with (a) stem sections and (6) with 

 bow sections varied. With regard to the influence of bow sections it is apparent that, 

 within the range of speed suitable for the vessel concerned, the V-shaped sections are best 

 for the full form and the U-shaped sections for the fine form. 



When the stem sections only are varied, the influence upon resistance is not so marked, 

 but in general the U shape appears to give the better results. It should be remarked, how- 

 ever, that the so-called U sections aft are of the moderate type and not so pronounced as 

 the corresponding bow sections. 



The diagrams shown in Fig. 4, Plate 56, and Fig. 5, Plate 57, illustrate, for a selected 

 model, the variation of resistance in terms of speed due to modification of bow sections with 

 a constant medium type of stern, and modification of stem sections with constant medium 

 type of bow ; and also the influence of change of draught from the light to the deep load. 



Figs. 5, 6, 7, 8 and 9, Plates 57 to 61, show the percentage of parallel middle body 

 at which the resistance is minimum for any given speed, and the value of the effective horse- 

 power per ton at that speed. They have been obtained from curves similar to that shown 

 in Fig. 10, Plate 62, which illustrates the effect of the various changes for a selected speed- 

 length ratio of .581. Each of the above figures refers to a given draught or, for the models 

 concerned, a variation of breadth to draught of from 3.73 to 2.02. 



CONCLUSIONS 



A study of the diagrams will reveal certain facts which are of interest. In the first 

 place, it is evident that no hard and fast rule can be laid down as to the best type of bow and 

 stern sections for all ships at all speeds ; and, in the second, that the best type of section for 

 a given ship at the load draught is not necessarily the best for the same ship at lighter 

 draughts. The selection of the best type of section will depend upon : 



1. The speed-length ratio. 



2. The fullness of the vessel. 



3. The distribution of displacement longitudinally. 



4. The ratio of breadth to draught. 



Certain rather broad conclusions may, however, be drawn. In the finer types of vessels 



