430 



HYDRODYNAMICS IN SHIP DESIGN 



Sec. 62.3 



ship form, Wendel has this to say [TMB Transl. 

 260, pp. 13-14]: 



"It is true that this kind of approximation must be 

 considered as somewhat rough since it takes into account 

 neither the specific shape of the displacement body nor the 

 width-depth ratio; nevertheless a better approximation 

 which, no doubt, would also be more complicated, seems 

 to be unnecessary so long as we confine ourselves to 

 slender bodies." 



Plate 4 of Lewis' 1929 SNAME paper gives 

 values of the following reduction factors for an 

 elUpsoid of revolution, covering a range of 

 L/Bx or L/D ratio of from 3 to 18: 



Ri for heaving motion or pure translation in a 

 vertical plane. This is the same set of values 

 as given by C. W. Prohaska, in his graph 

 marked "Lamb" [ATMA, 1947, Fig. 25, p. 

 197], where the small diagram indicates this 

 type of motion. 



i?2 for rotational motion in a vertical plane, pre- 



sumably about a transverse axis at midlength 



and middepth 

 R^ for 2-noded flexure, with deformation occurring 



by shear deflection only; this latter feature is 



important to remember 

 724 for 3-noded flexure, with deformation occurring 



by shear deflection only; this again is important 



to remember. 



Fig. 62.1 is a graph giving numerical values of 

 these four factors. 



For the 2-noded flexure by pure shear, repre- 

 sented by diagrams 2 and 3 in Fig. 62.E and by 

 diagram 6 in Fig. 62. G, the added weight of 

 entrained liquid for each transverse segment is 

 multipHed by the Lewis reduction factor R^ . 

 The weights for all the segments are then super- 

 posed upon the weights of the masses composing 

 the structure, machinery, cargo, and other parts 

 of the ship, applying the weight ordinates at the 

 proper points or stations along the diagram which 



Fig. 62.1 Graphs of Reduction Factors R of F. M. Lewis and J. L. Taylor for Thkee-Dimensional Flow 



