Wave Analysis Techniques to Achieve Bow-Wave Reduction 



sphere of unit radius r = l and submergence f = 1 was located at x = -3t7, y ^ o 

 and the total wave system obtained by superposing the data listed in Table 1 or 

 2 on itsel f with a phase shift of 30 steps. This corresponds to a Froude number 

 F^ = Vl/L of about 0.326, since the nondimensional separation L of the two 

 spheres is here 3tt taken center to center. 



The result of this analysis is depicted in Fig. 2 where, in order to avoid 

 overcrowding, only two sets of points are indicated in addition to the continuous 

 theoretical curve, namely, the solid dots from slope analysis and the open dots 

 from height analysis (with truncation correction), each cut running through 240 

 steps from x = 477 to -20t. The corresponding figures for wave resistance are 

 2.018 (theory), 1.994 (slope analysis), and 1.892 (height analysis). 



Finally, in order to test the method on a typical ship-wave pattern gener- 

 ated by a continuous distribution of sources and sinks the theoretical wave sys- 

 tem of the Inuid S-201 was selected. This model has been described frequently 

 in previous work (see Ref. 6b for instance); therefore details will be omitted. 



Fig. 2 - Amplitude spectrum of a pair 

 of submerged spheres F^^ = 0.326 



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