Sec. 61.7 



PREDICTED BEHAVIOR IN CONFINED WATERS 



397 



(2) When the depth of shallow water is to be 



determined: 



Case 2a. On the condition that the shallow-water 

 resistance shall not exceed a given frac- 

 tion of the deep-water resistance, say 

 1.02, for a given speed 



Case 2b. On the condition that the shallow-water 

 speed shall not fall below a given frac- 

 tion of the deep-water speed, say 0.99, 

 for a given resistance. 



Cases 2a. and 2b. are discussed in Sec. 61.11. 



A Umiting case in the first class involves a 

 determination of the reduction in speed for a 

 specified depth when this reduction does not 

 exceed 1 or 2 per cent at the most. A similar case 

 in the second class involves a determination of the 

 minimum depth at which the effects on speed and 

 resistance shah be minor, say plus and minus 1 

 and 2 per cent, respectively. 



Some problems encountered in practice start 

 with the deep-water ship performance as a basis. 

 Others require that the deep-water performance 

 be predicted from the shallow-water behavior. 

 In either case, the relationship between total and 

 friction resistance with speed in deep water must 

 still be known. These may be found: 



(a) From the usual effective- and friction-power 

 curves derived from tests of ship models 



(b) By calculation from i^„ and full-scale Cg , 

 Cf , and Ct values on the SNAME RD Summary 

 Sheets for vessels that are identical or nearly so 



(c) By calculation from tests on standard series 

 models or models of similar ships. 



To draw curves of full-scale deep-water friction 

 resistance and of total resistance, based on ship 

 speed, such as those through Ei — H and through 

 Ai — Ji of Fig. 61. B, respectively, requires at 

 least three spots on each, and preferably five. To 

 obtain these, it is necessary to work from the 

 F„ and Cr values on the SNAME Expanded 

 Resistance Data sheets rather than from the 

 SNAME Summary Sheets. The tables which 

 follow illustrate the principal steps in these 

 calculations, as well as the derived values for each 

 step. In all tables the ATTC 1947 or Schoenherr 

 meanline has been used for calculating the friction 

 resistance Rp , at a, standard temperature of 59 

 deg F, 15 deg C, for standard salt water. The 

 value of ACf is taken as 0.4(10"') in all cases. 



There follow four practical examples illustrat- 

 ing a suitable procedure for problems falling 



under the several cases of the first class. The 

 vessels selected are those for which SNAME 

 Resistance Data sheets are available. The results 

 would be about the same for other vessels having 

 nearly identical resistance-speed curves. 



61.7 Case la: To Find the Shallow-Water 

 Speed from the Deep-Water Resistance-Speed 

 Data. The first example, numbered 61.1 for 

 convenience, covers Case la of the preceding 

 section. There, working from predicted deep- 

 water data as to the speed and resistance of a 

 ship, it is desired to determine the shallow-water 

 speed, in a depth h, for the same total resistance 

 i^r as in deep water. The region for which shallow- 

 water data are desired is at and just below the 

 designed speed of the vessel. 



Example 61.1. The ship selected is the ore carrier 

 covered by SNAME RD sheet 9, represented by TMB 

 model 3818. The ship is 370 ft long by 64 ft beam by 

 17.5 ft draft, with a displacement of 8,850 long tons. 

 The designed speed is 12.5 kt, for which T, = 0.65, 

 Fn = 0.194. The ship runs from deep water into a shallow 

 estuary 24 ft deep. If the actual deep-water speed is 13 

 kt, slightly greater than the designed speed, what is the 

 speed in the estuary with the same total resistance? 



Briefly stated, the procedure is to construct a resistance- 

 speed curve for the given depth of shallow water, and then 

 to determine, from this curvej the ship speed at which 

 Rth is the same as for deep water. Referring to Fig. 61.B 

 in Sec. 61.3, this requires: 



(a) The construction of (Rto, — V„) and (Rpa, — V„) 

 curves for deep water, such as those through Ai — Ji and 

 El - H 



(b) The determination of the positions of the points Bi 

 and Ci for a series of selected points Ai 



(c) Drawing an (Rti, — Vh) curve through the Ci spots 



(d) Picking off the ship speed at Hi for which Rn equals 

 Rt^ . In detail, the Vi and V^ values are to be found for a 

 series of Va, values. At each point Ai a line AiBi is to be 

 drawn parallel to EiFi , giving the ordinates of Bi and Ci . 



The basic conditions for the ship and the water are 

 first set up, and the numerical values derived from which 

 the desired data are obtained. From the RD sheet men- 

 tioned, the maximum-section coefficient Cx of the ship is 

 0.9922 and the wetted surface S of the model is 87.82 ft'. 

 The scale ratio X(lambda) of the model is 370/20.274 = 

 18.25, so that X' is 333.06. The ship wetted surface is thus 

 (87.82) (333.06) or 29,249 ft^. This latter value may also 

 be taken directly from the SNAME RD Summary Sheet 

 listing this vessel. It is assumed that the deep-water and 

 estuary surfaces are at sea level, where g = 32.174 ft per 

 sec', and that both bodies are salt water at 59 deg F, 

 where the mass density p(rho) = 1.9905 lb-sec' per ft*, 

 and the kinematic viscosity v{n\i) = 1.2817(10"') ft' per 

 sec. 



The area of the maximum section is 64(17.5)0.9922 = 

 1,111.3 ft'. This is very close to the Ax of the model 

 times X', or 3.342(333.06) = 1,113.0 ft'. The value of the 



