Sec. 61.9 



PREDICTED BEHAVIOR IN CONFINED WATERS 



401 



of the friction-resistance curve in the region 

 between Vi/'\/gh and V^/wgh it is necessary 

 to calculate Rp for a speed somewhat higher than 

 Vi so that the point E3 may be plotted. It is 

 well, in fact, to calculate Rp for a series of ship 

 speeds, say the ones corresponding to the F„ 

 values in the speed range under consideration on 

 SNAME ERD sheet 2. This is done in Table 61.c 

 for the example set up subsequently in this sec- 

 tion, and the results are plotted in the long-dash 

 hues of Fig. 61.1. 



The problem is now to find the speed V„ for 

 which the intermediate speed V i is the correct 

 one for the specified depth. It is known, first, 

 that Foo is definitely greater but probably not 

 too much larger than Vj ; also that the value 

 V^/'Vgh is greater than Vi/y/gh by exactly 

 the same ratio. Entering the theoretical curve 

 of Fig. 61. E with the known ratio Vj/'Vgh, a 

 value of F„ and a ratio of V i/V„ are selected for 

 trial at a value of 'V„/'\/~gh somewhat larger 

 numerically than the given F^/V^. If the 



wave-speed ratio Vi/V„ , applied to the tentative 

 deep-water speed F„ , gives a ship speed V , 

 equal numerically to the intermediate speed 

 previously determined from the potential-flow 

 ratio, then the tentative speed F„ , and the 

 critical-speed ratio V^/y/gh, are the correct 

 ones. Otherwise, the process is repeated until the 

 intermediate speeds and the speed ratios are 

 numerically the same. 



Having found the proper value of V^/'s/gh 

 and the speed F„ , erect this ordinate on Fig. 

 61.1; it is the one on which A3 is located. Then 

 through B3 draw a line parallel to F3E3 , meeting 

 the V„/\/gh ordinate at A3 . This is one point 

 on the desired {Rt=, — F„) curve. The remaining 

 points are located in the same way. 



With the (i^Too — F„) curve as derived in this 

 manner there may be plotted for comparison and 

 reference the deep-water resistance-speed curve 

 as predicted from model tests or as calculated 

 from standard series or other data. An example 

 of this case follows. 



0.55 0.56 0.57 0.58 0.59 060 0.61 0.62 0.63 0.64 0.65 0.6 6 



I 



STEPS 



1. From Observed Data 

 Plot (Rjh-Vh) Curve 



2. For Q Selected Value 

 ofVh, Calculate Vh/V^ 



3. With Vf^/Vj Ratio picl<- 

 ed from Fig. 61. G, Det- 

 ermine Vj/-yQh 



4. From Point C3 Draw 

 Horizontol Line to B3 



5. For Voo/y^ Value 

 Slightly Greoter thon 

 at Bj, Determine 

 ^l/X» Ratio and Tent- 

 ative Vooyfj^ from Fio 



). Frorn Tentative Volue 

 ""f M»/v^ '^i"'^ Corr- 

 esponding Volue of 

 Vj/Vjo ond Check for 

 Aoreement with 

 Vi/Ygh Ratio at B3 



: When Correct Vo<,/VqTi 

 is Known, Draw B3A3 

 Parallel to F3E3. Det- 

 ermine Aji.etc. in Some 

 Manner and Draw (Rtoq-Voo)' 



Scale for Ship Speed Vh in Depth h Mo'y Be Added Here 



FiG.'^ei.I CoNSTBUCTioN OF A Deep-Wateb Resistance-Speed Cubve Fbom a Known Shallow-Watbb Cubve 



