Yim 



^ 



Fig. 9 - Optimum distance between source and doublet, 

 optimum radius of bulb (a,b, r are non-dimensionalized 

 with respect to the depth f) 



HIGHER ORDER EFFECT ON THE ELEMENTARY WAVES 



In the case of a sine ship (26a) which has theoretically only positive sine 

 waves starting from the bow and the stern, Inui and his colleagues observed in 

 their experiment with Inui's model of the sine ship a forward shifting of the 

 wave phase. Therefore, they had to stick their bulb quite a bit forward of the 

 bow instead of locating the bulb center at the stern. They seem to have had a 

 serious concern about this discrepancy between the theory and the experiment. 

 It has been speculated in Japan that the explanation may be in the orbital wave 

 motion on the ship boundary (Takahei, 1960), or in the non-zero Froude number 

 effect (Inui, 1962), since Inui's model is exactly right for his source distribution 

 only in the case of zero Froude number. Inui used two correction factors which 

 are determined by experiments to correct this observed effect together with the 

 influence of viscosity. We will now discuss an explanation for Inui's observa- 

 tions which are based on higher order wave theory. 



For a long time since Havelock's representation of a ship by a singularity 

 distribution, people have been very curious about the exact ship form generated 

 by these singularities which satisfy all the conditions including the linearized 

 free surface condition for a non-zero Froude number. Havelock (1936) and 

 Bescho (1957) considered submerged simple bodies including the free surface 

 effect on body representation, and indicated this effect could be large. Sisov 

 (1961) formulated a higher order theory of wave resistance on surface ships. 



1086 



