Sec. 66.15 



STEPS IN PRELIMINARY DESIGN 



479 



The height KB of the center of buoyancy CB 

 above the basehne is determined at this stage by 

 the Normand formula, often known as the Morrish 

 formula [Normand, J. -A., "Formules Approxima- 

 tives de Construction Navale (Approximate 

 Formulas for Naval Architecture)," Paris, Arthus 

 Bertrand, 1870; Pollard, J., and Dudebout, A., 

 "Th^orie du Navire," 1890, Vol. I, p. 113; 

 SNAME, 1893, p. 29] 



KB = H 



-(- + —) 



(66.iii) 



For the ABC design at this stage H is 26 ft, V is 

 574,000 ft', andA^ = 510(73)0.713 = 26,545 ft', 

 whence ¥/A^ = 574,000/26,545 = 21.62. 



Then KB = 26 - 1/3(13 + 21.62) = 14.46 ft, 



KM = KB + BM = 14.46 + 16.16 = 30.62 ft, 



KG = KM - GM = 30.62 - 4.38 = 26.24 ft. 



This means that, with the assumptions made, 

 the CG of the fully loaded vessel lies very nearly 

 in the designed waterline. It should easily be 

 possible to keep the CG below this limit, even 

 with a fairly large abovewater hull and with the 

 sizable upper works required for passenger 

 quarters. On the other hand, the CG is not so 

 high as to produce undesirable rolling features 

 [Vedeler, G., INA, 1925, p. 166]. It is, in fact, 

 somewhat lower in proportion than is customary 

 for ocean hners [de Vito, E., INA, 1952, Table 

 VIII; partial abstract in SBSR, 13 Nov 1952, pp. 

 642-643]. 



The expression KB^ /H i s available as a rough 

 check on the value of BM, where k varies from 

 0.08 to 0.10 [Attwood, E. L., and Pengelly, H. S., 

 pp. Ill, 476]. For a rectangular box hull, BM = 

 0.08357^- For the ABC design, where B is at 

 present 73 ft and H is 26 ft, BM = (say)0.08(73) V 

 26 = 16.40 ft, compared to the value of 16.16 ft 

 determined previously. 



A complete preUminary design requires, at this 

 or at a slightly later stage, an estimate of the 

 vertical and horizontal CG position as determined 

 by the weights [PNA, 1939, Vol. I, pp. 102-103], 

 including if possible a check from the known 

 values for a somewhat similar ship. It requires 

 also an estimate of the transverse metacentric 

 stability for the light as well as the loaded 

 condition; possibly also for one or more inter- 

 mediate loading conditions. As these are not 



directly a part of the hydrodynamic design they 

 are omitted here. 



The range of stability and the heeling or righting 

 energy pertaining to dynamic metacentric sta- 

 bility are approximated, according to Sec. 68.6, 

 when the abovewater hull has been roughed out. 



66.15 First Sketch of Designed Waterline 

 Shape. The next step in determining the shape 

 of the vessel is to lay out the designed waterline. 

 The diagrams of Fig. 24. G illustrate some historic 

 yet highly instructive waterhne shapes. Fig. 51.C 

 depicts the actual designed-waterline shapes for 

 six typical vessels in several speed-length groups. 

 The B/Bx values for many other waterline shapes 

 are to be found on the SNAME Resistance Data 

 sheets. 



Because of the effect of the waterline slopes 

 forward upon surface wavemaking and of the 

 waterline slopes aft upon separation, the shape 

 of the waterplane depends upon the speed-length 

 quotient T^ or F„ at which the vessel is to run. 

 Since the relative speed of the ABC ship is rather 

 high, with a T, of 0.908 and an F, of 0.270, a 

 small waterline slope at the stem and an easy 

 waterline in the entrance are indicated, to keep 

 down the pressure resistance Rp due to wave- 

 making. With the small length-beam ratio of 

 6.986, and the Ukelihood of using a bulb bow, a 

 considerable degree of hoUowness in the entrance 

 waterlines is a certainty. Taking into account 

 the speed ratios listed and the Cp of 0.62, S. A. 

 Vincent's data of 1930 [MESA, Mar 1930, Fig. 5, 

 p. 139; revised unofficially to 1952] indicate 

 something between a very hollow and a moderately 

 hollow entrance waterline. 



A study of nominal WL entrance slopes is for 

 easily driven hulls, plus available reference data 

 on the subject, produced the graphs of Fig. 66.1. 



Fig. 66.1 Graph op Design Values for Waterline 

 Slope is at Entrance 



