478 



HYDRODYNAMICS IN SHIP DESIGN 



Sec. 66.14 



66.14 First Estimate Relating to Metacentric 

 Stability. Before the preliminary design proceeds 

 too far it is well to know the general situation 

 relating to transverse metacentric stability. While 

 this can not be determined accurately until the 

 waterline shape is fixed, the waterplane coefficient 

 Cw and other characteristics of the waterline 

 generally are determined, in turn, by the meta- 

 centric-stability requirements. 



In years gone by the value of Cw was approxi- 

 mated by the use of a ratio between (1) the 

 prismatic coefficient Cp and (2) the waterplane 

 coefHcient Cw , known as the relation coefficient, 

 symbolized by Cy ■ This ratio was found to be 

 more nearly constant than other ratios among 

 the various form coefficients and was used for 

 estimating Cw before the lines were drawn 

 [Barnaby, K. C, BNA, 1948, p. 24]. 



Based upon the satisfactory service performance 

 of a large number of merchant vessels, from small 

 cargo ships to large liners, with data kindly 

 furnished by the U. S. Maritime Administration, 

 the diagrams of Fig. 66. H have been prepared. 

 They give acceptable relationships between (1) the 

 prismatic coefficient Cp and the waterplane 

 coefficient Cw , corresponding to the relation 



coefficient just described, and between (2) Cw and 

 the transverse inertia coefficient Cit ■ 



To use the diagram, start with the value of Cp , 

 say 0.62 for the ABC ship, then cross horizontally 

 to the lower diagonal line. The abscissa of this 

 first intersection gives a good average value of 

 Cw , in this case 0.713. Then go up this ordinate 

 to the upper diagonal line, whereupon the ordinate 

 of the second intersection gives the value of C, j- , 

 approximately 0.561 for the ABC design. Because 

 of certain differences in normal-form ships with 

 different numbers of propellers there is one 

 diagram for single-screw vessels and another for 

 twin- and multiple-screw vessels. Using the 

 values picked for the single-screw ABC design, 

 the square moment of area of the waterplane 

 works out as/ = [BUL)C,t]/12 = [73' (510)0.561] 

 /12 = 9,275,150 it\ The metacentric radius BM, 

 equal to I/V, is 9,275,150/574,000 or 16.16 ft. 



Long experience demonstrates that a reasonable 

 value of transverse metacentric height to satisfy 

 both comfort and safety requirements is about 

 O.OGBx [Niedermair, J. C, SNAME, 1936, pp. 

 419-420; INA, 1951, p. 144]. For the 73-ft beam 

 of the ABC ship this gives GM = (0.06)73 or 

 4.38 ft. 



0,60 0.65 0.70 0.75 080 085 0.90 



Woterplone Coefficient Cw 



060 065 070 0.75 080 005 0.90 



Woterplone Coefficient C-^v 



Fig. 66.H Data for Selecting Waterplane Coefficient and Transverse Moment-of-Arba Coefficient 

 FOR Given Prismatic Coefficients 



