400 HYDRODYNAMICS IN SHIP DESIGN Sec. 61.8 



TABLE 61.b — Derivation op Values op Vnly/gh From Selected Values op Critical-Speed Ratio V„/y/gh 



speed loss determined by inspection is about 20.3 per cent. 

 This discrepancy, although not a major one, is due un- 

 doubtedly to Schlichting's use of data for unlimited 

 shallow water which were observed in a model basin of 

 rather Umited width. 



As a matter of interest, the total resistance in deep 

 water at 10.58 kt, represented by the point K2 , is about 

 25,750 lb. That at the same speed in the 24-ft depth, 

 represented by the point H2 , is about 42,800 lb, some 166 

 per cent of the deep-water resistance. 



Only a short segment of the shallow-water {Rth — V) 

 curve is required for this problem. However, it is well to 

 plot a considerable portion of it, so that other shallow- 

 water problems which arise in the design stage of a ship, 

 or in an analysis of its trials, may readily be solved. 



61.8 Case lb: To Find the Shallow-Water 

 ResistancefromtheDeep-Water Resistance-Speed 

 Data. Determining the shallow-water resistance 

 Rrh for any speed, assuming a given depth of 

 water h, and a knowledge of the deep-water 

 (ft Too — F„) data, is equivalent to drawing a set 

 of {Rt — V) curves for both conditions and 

 comparing the total-resistance values at any 

 selected ship speed V. This is exactly what was 

 done in Case la of Sec. 61.7, when a curve of 

 total resistance Rt on a, base of critical-speed 

 ratio y„/V^ was calculated for deep water, 

 and a curve of total resistance in water of depth 

 h was constructed from it. The segment C2J2 of 

 Fig. 61. H represents the increase in total resist- 

 ance at a critical-speed ratio corresponding to 

 the horizontal position of those points. The 

 segment H2K2 is the ARt for a critical-speed 

 ratio corresponding to the abscissa of both H2 

 and K2 , as calculated at the end of the preceding 

 section. 



When the depth h is fixed or known, the actual 

 ship speeds may be determined by multiplying 

 each of the critical-speed ratios by the factor 

 y/ gh and then converting the ft-per-sec values 

 thug obtained (if English units are used) to kt. 



Alternatively, a scale of kt may be calculated 

 and added along the lower edge of Fig. 61. H. 



61.9 Case Ic: To Find the Deep- Water 

 Speed and Resistance When the Shallow-Water 

 Speed and Resistance are Measured. Assume 

 that a ship is, by force of circumstances, required 

 to run trials in shallow water of a known depth h. 

 Assume further that it is possible, by a means 

 not stated, to measure the total ship resistance 

 Rrh at the depth h, as well as the speed F* , for 

 the range of speeds covered by the trials. It is 

 desired to know the corresponding deep-water 

 total resistances Kr„ and speeds V^ ; or, in effect, 

 to construct an (ftr= — F„) curve from the known 

 {Rrk - Vh) curve. 



The procedure described here is roughly the 

 reverse of that for Ca,se la in Sec. 61.7. Referring 

 again to Fig. 61. B, the method involves starting 

 from a known shallow-water curve containing 

 points such as Ci and Hi and constructing a 

 deep-water curve having a series of points such 

 as Ai . 



Smce the depth h is specified, it is best to 

 construct a graph similar to that in Fig. 61.1 on 

 a base of V/ "s/gh. 



The ratio y/Ax/h and the value of F^/Vff^ 

 (for any given spot such as C3) are first deter- 

 mined by calculation. The ratio Vu/Vi is then 

 picked from the experiment curves of Fig. 61. G. 

 Dividing this ratio into VJ V^ gives Vi/ vgh. 

 The ordinate passing through the point B3 of 

 Fig. 61.1 is then erected at this value and the 

 horizontal line C3B3 is drawn. The intermediate 

 speed is Vj , equal to F* divided by the F^/Fj 

 ratio. 



The friction resistance Rpi for the intermediate 

 speed Vi is next calculated or determined; this is 

 represented on the base of V/y/gh by the ordi- 

 nate to the point F3 . In order to find the slope 



