0.6 



0.4 



S 2 (0co) 

 -X1 



0.2 



0.0 



0.0 



NO BULB 



WITH BULB 



Figure 10 - S, 



of a Wigley Hull (b 

 Bulb (r, = 0.0285h, z 



the phase difference of each elementary wave 

 does not change bow wave resistance from the 

 linear theory. 



The stern wave amplitude is exactly the 

 same as the linear value 



0.2, h = 0.0625) with and without 

 = 0.7h) 



considered to be totally missing in the wave 

 resistance, j in the Srettensky formula for bo 

 waves would start not from zero but from a 

 certain number minimum J = Jj such that 



A (8) = P + iQ 

 s s s 



but the phase difference S2 S (6) should be com- 

 puted by the ray theory together with the ray 

 path which is shown in Figure 11. Then it is 

 also obvious that the stern wave resistance is 

 the same as the linear stern wave resistance. 

 The total wave resistance may be obtained simi- 

 larly by considering that the total wave ampli- 

 tude is 



where 6„i is the value of 8t« 

 waves start to reflect. If 



from which bow 



and e 



= 2 for J 

 for J i J 



The result is shown in Figure 12 where 

 considerable shift of the phase of hump and 

 hollow of the wave resistance due to bow 

 stern wave interaction is noticeable. 



iks (8) 

 (P + iQ, ) e - D + (P + iQ ) 



ik (s, (8) - sec9) 



(44) 



Here, the bow and stern wave interaction ap- 

 pears in the wave resistance. That is, only 

 the interaction term changes due to the phase 

 change caused by the nonuniform flow. This 

 fact is exactly the same as in two-dimensional 

 theory. 



The actual computation of wave resistance 

 is performed by the Srettensky formula using 

 the relation 



(d. - 1) 



(45) 



and the corresponding values of S2 are obtained 

 by interpolation. When a portion of elementary 

 waves near 8c» = is reflected from the ship 

 hull, the larger part of the energy in this 

 portion of elementary waves will be dissipated 

 by breaking waves, and the wave resistance will 

 decrease, but the momentum loss due to breaking 

 waves will increase. If such energy was con- 



y 0.2 



1.0 1-2 1.4 1.6 1.8 2.0 2.2 



Figure 11 - Ray Paths of Stern Waves of 

 a Wigley Hull (b = 0.2, h = 0.0625) 



12 



