Yim 



(3) Unless the lines are extremely hollow the best position of the bulb is 

 with its center at the bow, that is, with its nose projecting forward of the hull. 



(4) The bulb should extend as low as possible consonant with fairness in the 

 lines of the hull. 



(5) The bulb should be as short longitudinally and as wide laterally as pos- 

 sible, again having regard to the fairness of the lines. 



(6) The top of the bulb should not approach too nearly to the water surface; 

 as a working rule it is suggested that the immersion of the highest part of the 

 bulb should not be less than its own total thickness." 



G. Weinblum (1935) dealt with this same problem by expressing the form of 

 a ship with a bulbous bow in terms of a polynomial according to Michell's thin 

 ship approximation. His theory was also supplemented by model experiments. 

 He expressed a different view from Wigley's, concerning the best vertical posi- 

 tion of a bulb (Wigley's rule [4] and [6] ). According to Weinblum 's result for an 

 extremely hollow form of ship, a uniformly distributed bulb along the stem line 

 was superior (taking into account the wave resistance only without considering 

 other effects like spray) to the bulb located near the keel, both having the same 

 sectional area. However neither Weinblum or Wigley suggested any optimum 

 variation of bulb size with the speed. 



Since then, some experimental investigations on bulbous bows were per- 

 formed by Lindblad (1944) in calm water and by Dillon and Lewis (1955) in 

 smooth water and in waves. However, after Wigley (1936) and Weinblum (1935), 

 no significant theoretical development on bulbous ships seems to have been 

 made, until Takao Inui and his colleagues made a great contribution on this sub- 

 ject. This will be discussed in a later section in some detail. 



In this report, first the necessity of a bulb for minimizing wave resistance 

 will be discussed, followed by a brief review on Inui's explanation of the bulb 

 effect. Inui, using the concept of Havelock's elementary surface waves brought 

 us a clear understanding of the mechanism of bulbs and an easy approach to 

 their design. 



Yim (1963) found the ideal bulb or the doublet distribution on a semi-infinite 

 vertical stem line which completely cancels the sine regular waves starting 

 from the stem of a given ship. For the cosine waves from the ship bow, a 

 source line or a quadrupole line are considered. The separation of waves and 

 the wave resistance into the components as in the diagram of Fig. 1, simplified 

 the analysis of the bulb effect at the bow or the stern of a ship. The size and 

 the form of the bulb, which are functions of ship shapes and Froude numbers, 

 are supplied extensively. The location of the bulb is of course related to the 

 ship shape and the type of bulb. However, the higher order effect is found to be 

 non-negligible. These are discussed in the next sections. 



Throughout this report, inviscid, homogeneous, incompressible, and poten- 

 tial flow around a fixed ship is considered. The origin of the right handed Car- 

 tesian coordinate system is located on the bow of the ship and on the mean free 



1066 



