Sec. 61.14 



PREDICIED BEH/WIOR IN CONFINED WATERS 



409 



water and deep-water total resistances at points 

 such as C, and A, on Fig. 61. B could be neglected. 



For estimates of the change in total resistance 

 at the same speed, when moving from deep to 

 shallow water, the problem is considerably more 

 difficult, since the answer depends upon the slopes 

 of the graphs of Rr on V in the region being 

 investigated. 



Because of the lack of reliable methods for 

 transforming increased total resistance in shallow 

 water to terms of increased power, discussed in 

 Sec. 61.16 following, there is some merit in a 

 prediction method by inspection which endeavors 

 to predict the increased power directly. Even 

 though a ship is rarely pushed in shallow water 

 to speeds which would be considered normal if the 

 water were deep, it is helpful to know approxi- 

 mately how much power would be required under 

 these circumstances. 



A graph suitable for such a purpose is the partial 

 diagram at the top of Fig. 61.L, having contours 

 of the ratio (shallow-water power) /(deep-water 

 power) plotted on appropriate arguments. Follow- 

 ing the procedure developed by 0. Schlichting, 

 these are y/Ax/h and V/y/gh, where F is a 

 given speed, in either deep or shallow water, and 

 "Vgh is the solitary-wave speed in water of 

 depth h. 



The contours in Fig. 61.L are indicated as 

 tentative, since they are derived from isolated 

 data observed on one series of ship trials, that of 

 the German torpedoboat S119', see reference (4) 

 of Sec. 61.22. These data are recorded graphically 

 in Fig. 61. A. They are reduced, in the lower 

 diagram of Fig. 61. L, to graphs indicating the 

 ratios of indicated power Pj in shallow water to 

 Pj in deep water, for four depths of shallow water, 

 on a basis of the ratio V/'S/gh, the same as for 

 the upper diagram in that figure. It is assumed 

 for this reduction that a depth of water h equal 

 to 0.951L, indicated in Fig. 61. A, represents 

 deep water. It is further assumed that the pris- 

 matic coefficient Cp of this vessel is 0.64, f rom 

 which Ax is calculated to be 45.5 ft^ and vAx 

 is 6.75 ft. The four graphs of the lower diagram 

 of Fig. 61. L therefore represent indicated-power 

 ratios at Va^/K values of 0.110, 0.137, 0.206, 

 and 0.294. 



Reduction of full-scale ship data in similar 

 fashion, from the references of Sec. 61.22, gives 

 contours which are extremely difficult, if not 

 impossible to reconcile with those of Fig. 61. L, so 

 much so that they are not included here. In most 



1. 



Closed Duct 

 b 



-- / ■"-, 



'^ — 



Hydraulic Rodius 

 R bh 



Open Channel 





Shollow Water of Unlimited Extent 



="^ Rh'H 



^\^^^^\W\^^\"^\\^\\\" 



Sh|p 



W n\\\\\\\1o:\\\\\\\V 



bh-Ax 

 H b+2h+G 



4- 



Channel with 5emi -Circular Cross 5ection 



y^ <^^?x. • " 0.5rrR(? 



Rh = — ^=0.5Rr 



Fig. 61. M Definition Sketches for Hydraulic 

 Radius 



of these cases the value oi Ax has to be estimated, 

 as was done for the SI 19. Available data from 

 model tests are, by the method of analysis 

 described, out of line with the ship data and with 

 each other. It seems clear at this stage (1956) 

 that all the pertinent variables in the confined- 

 water situation have not been taken into account. 

 61.14 Calculating and Using the Hydraulic 

 Radius of Channels. As is explained presently, 

 predictions of the effect of the sides and the bed 

 of channels upon ship resistance make use of the 

 characteristic channel dimension known as the 

 hydraulic radius, rather than the water depth h 

 used for shallow-water predictions. For a closed 

 duct with no solid body inside it this is the ratio, 

 described in Sec. 18.11, of the transverse duct 

 or flow area to the wetted perimeter of the duct. 

 This situation is depicted at 1 in Fig. 61. M, where 

 h, h, and Rn are aU drawn to the same scale, and 

 Rh has the dimensions of a length. An open 

 channel with no ship in it, as in diagram 2, has 

 wetted perimeter on only the bottom and the 



