Wave Analysis Techniques to Achieve Bow-Wave Reduction 



Table 2 

 List of Computed i (xlO"*) Values for a Submerged Sphere 

 (Parameters: r=i, f=i^y = 77; Variable, x=4: stepped 

 -Tj/lO until -207t) 



Similarly, the height data of Table 2 were analyzed according to Eqs. (13) 

 and (24) truncating in either case at -x = 207^. The results are indicated by the 

 two sets of discrete points in Fig. 1, the open dots being without truncation cor- 

 rection, Eq. (13), and the solid dots being with truncation correction, Eq. (24). 



The wave resistance was computed from each of the five amplitude functions 

 shown in Fig. 1 by the approximate formula (compare with Eq. (11)) 



60 



^w 8 Z—j 



A 2(2 - 1/s 2) 



(28) 



assuming a sufficiently large hypothetical tank width b= 30--. The following re- 

 sults were obtained. The exact theoretical value from curve 1 was 1.528. The 

 slope analysis, curves 2 and 3, yielded 1.400 and 1.493 respectively, while the 

 height analysis resulted in 1.511 and 1.407 with and with truncation correction. 



As a next step the wave pattern generated by a pair of submerged spheres 

 was examined to investigate interference effects. For this purpose a second 



741 



