486 



HYDRODYNAMICS IN SHIP DESIGN 



Sec. 66.22 



The position of the section of maximum area 

 is marked as 0.515L from the FP. The tentative 

 value oi fs = 0.06 is laid off at the FP and a 

 tangent to the section-area curve at the FP is 

 drawn by working backward the formula in 

 Sec. 24.12. Since fs is 0.06, the intercept @ is 

 1.00 - 0.06 = 0.94. Multiplying 0.94 by 0.9, 

 which is the tentative value of /^ , gives the 

 intercept © as 0.846. Adding 0.846 to 0.06 

 indicates that the tangent at the FP intersects 

 the midlength ordinate at a value of A/ Ax of 

 0.906. Although the corresponding values are 

 shghtly different for the final section-area curve. 

 Fig. 67.W illustrates the intercepts mentioned. 

 The value of /« is laid off as 0.02 but there are 

 insufficient data to indicate a good terminal 

 value of Ir . This preliminary yl-curve is omitted 

 for lack of space but the final curve is depicted 

 in Fig. 67.W. 



Integrating the preliminary curve numerically 

 gives an underwater hull volume of 572,050 ft' 

 and a Cp of 0.618. Both values are a little small 

 when compared to the previous figures of 574,000 

 ft' and 0.62, but before modifying the curve it is 

 well to see what the underwater form looks like 

 when other requirements are applied. The first 

 y4-curve appears sufficiently fair to permit sweUing 

 or shrinking it here and there, but it must first 

 be found where these volume changes are of most 

 benefit to the ship. A discontinuity in the ^-curve 

 is to be expected at the stern, where the single- 

 skeg area drops rather suddenly to zero. 



In this connection it is to be remembered that 

 ship sections, body plans, and waterUnes, are 

 customarily laid off to the molded dimensions 

 of a ship. For a metal vessel this is to the outside 

 of the framing and the inside of the plating. 

 Furthermore, the rudder, roll-resisting keels, 

 propeller, exposed shafting, and other appendages 

 displace considerable quantities of water and 

 thus help to support themselves. The volume 

 occupied by the plating of a steel vessel is assumed 

 equivalent to about 0.0075 times the molded 

 volume if in-and-out strakes are employed. It is 

 about 0.005 times that volume if the plating is 

 flush, as in a welded vessel [Robb, A. M., TNA, 

 1952, p. 77]. The volumes occupied by the append- 

 ages are readily computed when they are roughed 

 out. 



For the ABC ship it may be assumed at this 

 stage that the shell is to be rather fully welded 

 and nearly all flush. Taking a value of 0.0055^, 

 the corresponding volume is (0.0055) (574,000) = 



3,157 ft' and the weight is 3,157/35 = 90.2 t; 

 say 90 t. This leaves a molded displacement of 

 16,400 t or 574,000 ft' as the end point in working 

 up the final ^-curve and the underwater hull form. 

 66.22 Longitudinal Position of the Center of 

 Buoyancy. As an indication of the fore-and-aft 

 position where the CG must He, an integration 

 of the preUmin ary s ection-area curve shows that 

 the value of LCB is about 0.506 or 0.507L, 

 reckoned abaft the FP. This position is slightly 

 abaft the midwidth of the lane in Fig. 66. N. 



5a 51 50 49 48 47 46 



LCB in Percentage of Ship Lenqih L from FP 



Fig. 66.N Usual Longitudinal Position of 

 Center of Buoyancy LCB 



Incidentally, this diagram differs slightly from 

 that of Fig. 24. H in its extension to higher values 

 of Cp . In view of the uncertainty in the position 

 of the limits, the lanes in both figures are bounded 

 by broken lines. 



On most of the plots in this chapter, beginning 

 with Fig. 66.A and ending with Fig. 66.N, there 

 are spots formed by a pair of concentric circles 

 with the lower half of the intervening space 

 blacked in. These indicate the values of the several 

 coefficients and parameters corresponding to the 

 completed preliminary design of the ABC ship. 

 They are the same as those listed for the fifth 

 approximation in Table 66. e of Sec. 66.11. 



66.23 Preparation of Small-Scale Profiles and 

 Sections. The time has now come to see what 

 the proposed ship is to look like. It is possible to 



