428 



HYDRODYNAMICS IN SHIP DESIGN 



WL , StQiO WL 



Sec. 62.3 



Sta 15 in Diaqram 6 



Pure Bendinq Deformation, with All Transverse Sections Remommq Plane 

 and Normal to Neotrol Axis 



Fig. 62.G Second Stage in Transformation of Oscillating Cylindrical Bar to Ship Structure in 2-Noded 



Vertical Vibration 



and unit length. He used this quantity as a 

 reference because, in the process of setting up 

 the relationship, the deeply submerged 2-diml 

 circular-section segment of Fig. 62. A is brought 

 to the surface so as to float with a waterHne cor- 

 responding to its horizontal diameter. If the top 

 half of the circular-section segment is removed, 

 the lower half of semicircular section is still 

 buoyant, because its mass is 0.5irpa^ per unit 

 length and the mass of the displaced water is 

 exactly the same. 



Lewis' relationship is in the form of a "co- 

 efficient" C, defined as follows: 



Added-liquid mass for a ship-shaped 



segment of unit length, beam B, and 



section draft to bottom of section 



Cl„,u = ■ 



Half of the added-liquid mass for a 

 circular-section segment of unit 

 length, radius a or beam B = 2a 



This, incidentally, although called "the inertia 

 coefficient for that (ship) section" by Lewis, is 

 not a true inertia coefficient in accordance with 

 modern general usage. It might be distantly 

 related to such a coefficient but only because the 



ship-shaped section of Lewis is transformed from 

 a circle. 



Because C. W. Prohaska also has a relationship 

 of this kind, supported by different analytical 

 and experimental data, and also designated as C, 

 it appears wise to substitute for the symbols 

 CLewiB and Cprohaska & fc-symbol corresponding to 

 those listed in various places in Figs. 62. A and 

 62. B. A suitable symbol appears to be fcgeot 

 which, for 2-diml flow in a translational mode, is 

 exactly the same as Cl^wis above. For a rectangu- 

 lar ship section having a [(beam) /(section draft)] 

 ratio of 2.0, with square corners at the bilges, 

 /csect is 1.512 (given as 1.51 in the referenced 

 figures). The value of fcgect for rectangles of other 

 proportions are given in a graph by F. M. Lewis 

 and K. Wendel [SNAME, 1929, PI. 4 at top; 

 TMB Transl. 260, Jul 1956, Fig. 21 on p. 3-4]. 

 For a ship section of semicircular shape having a 

 B/H ratio of 2.0, ksect is 1.00, since in this case 

 the added mass of the ship section corresponds 

 to the added mass of the semicircular section 

 used as the reference. 



It is now possible to determine the added- 

 liquid mass per unit length of a ship section cor- 

 responding to one of the shapes depicted by 



