468 



HYDRODYNAMICS IN SHIP DF.Sir.N 



Sec. 66.7 



length, show that the minimum value of Rg/A 

 occurs at a Cp of about 0.52 for a B/H of 2.25, 

 and at a Cp of 0.54 for a B/H of 3.75. These 

 values are considerably less than the average Cp 

 value of 0.62 given by the lower design lane of 

 Fig. 66.A. This is because the longer and more 

 pointed forms, with the lower Cp values of 0.52 

 to 0.54, have too much wetted area and friction 

 resistance for the specified displacement volume. 



Similarly, the design lane of Fig. 66. A, in the 

 higher ranges of 7", , gives values of Cp which are 

 lower than those indicated by the regions of lowest 

 residuary resistance per ton ratio, Rr/A, in the 

 TSS contours. This is because the lane is positioned 

 to suit high-speed vessels like destroyers which 

 have to drive easily at cruising speeds that are 

 much lower than the designed speeds. For a vessel 

 designed to run always at high speeds, or for a 

 vessel with sufficient nuclear fuel to elimhiate the 

 cruising-radius problem, at least so far as fuel 

 only is concerned, the optimum Cp for a T, of 

 2.00 would be in the range of 0.65 to 0.70 or 

 more, depending upon the fatness ratio, as 

 indicated by the TSS contours. 



Restrictions on length and other factors often 

 require a Cp somewhat higher than the best 

 figures. 



The middle of the lower lane gives values of 

 Cp from about 0.614 for the short 500-ft ship to 

 about 0.624 for the long 525-ft ship. A good value 

 of Cp , at least at this stage, appears to be about 

 0.62. 



A number of formulas, most of them for 

 straight lines, have been developed to approximate 

 the steep part of the "roller coaster" Cp lane of 

 Fig. 66. A in the restricted region of T, between 

 0.50 and 0.90. These ignore the need for design 

 information appl3dng to vessels in other speed- 

 length ranges. 



Beyond the left end of the lower lane, with T, 

 and Fn approaching zero and with wavemaking 

 practically nonexistent, the Cp may approach a 

 very high value as an asymptote, probably of 

 the order of 0.90 to 0.95 or more. This means 

 that craft which are not required to travel fast 

 can approach a rectangular box shape, as illus- 

 trated in Fig. 66. C and as explained under barge 

 design in Part 5 of Volume III. 



It is again emphasized that the fatness ratio 

 or prismatic coefficient for every ship need by 

 no means lie within the lanes of Fig. 66. A, or 

 that other parameters need conform to correspond- 

 ing graphs to follow in tliis chapter. Special cases 



Fig. 66.C A Speed-Length Quotient of Nearly 



Zero and a Prismatic Coefficient Approaching 1.00 



A horse-propelled cargo carrier on the Erie Canal in 



1916. Photograph by the author. 



and requirements call for special designs. The 

 lanes are simply to give the designer an idea of 

 the range of values for a vessel of normal form 

 that drives easily. 



66.7 The Maximum-Section Coefficient; The 

 Draft and Beam. There is little in the way of 

 reliable information, empirical or otherwise, from 

 which to select a tentative maximum-section 

 coefficient Cx for any point in the complete range 

 to T^ or F„ . This is equally true, for that matter, 

 in a range of any other parameter [Taylor, D. W., 

 S and P, 1943, Fig. 70, pp. 63-64]. This may be, 

 for the reason stated in Sec. 24.10, that variations 

 of Cx in themselves have little effect upon hull 

 resistance. However, the branched design lane 

 of Fig. 66.D gives an indication of the general 

 region in which a good Cx is to be found, for 

 approximately the same ranges of T, and F^ 

 as in Fig. 66. A. 



The limiting optimum value of Cx is 1.00 at a 

 T„ of 0.0, as for a square- or rectangular-section 

 hull which rarely has to move. When it does 

 move, hull drag is usually no problem. The 

 ratio Cx may well be made greater than I.O, in 

 fact up to 1.1 or more, if there are practical 

 reasons for doing so, such as adding blisters for 

 underwater-explosion protection. As V/'vL in- 

 creases, the design lane widens until at a T, of 

 1.05, F„ of about 0.31, the value of Cx for good 

 design lies between 1.00 and 0.90. At still higher 

 T, and F„ values, two classes of vessels are 

 distinguished: 



(1) Those intended for high speeds, where beam 

 is sacrificed to keep down the longitudinal water- 

 line curvature and to reduce resistance due to 

 wavemaking but remains adequate for the service; 



