Pien 



than Model S- 101 at F = 0.30. At first, as in the case of Model S-101, only one 

 singularity distribution element Ej over the same distribution area as in Model 

 S-101 is used. Only the restraint of a certain displacement volume requirement 



is imposed on the optimization of Ej 

 below: 



at F = 0.30, The E, so obtained is shown 



Ej(^,0 = 3.5127^- 5.4415^ + 13.3125^ - 24.4694^ + 13.6865^- 



(10) 



Figure 3 gives the plot of the corresponding density distribution. 



-1.0 -0.8 -0.6 -0.4 -0.2 0.2 0,4 0.6 0.8 1.0 



Fig. 3 - Surface source density distribution of Model A 



The body plan of the model generated by Ej is shown in Fig. 4. It is denoted 

 as Model A. It has a L/B ratio of 6.06 which is less than half that of Model S-101. 



Figure 5 shows the comparison of C^ curves of Models A and S-101. Up to 

 a Froude number of 0.31, Model A actually has less wavemaking resistance than 

 Model S-101. This result proves the point that a thick ship can have less wave- 

 making resistance than a much thinner ship. 



If a singularity distribution is uniform in the draft direction, the free waves 

 produced by layers of singularities at various depths are all in phase even though 

 the magnitude is reduced as the depth is increased. There is no cancelling ef- 

 fect between them. To obtain favorable interference, the density distribution 

 should vary with depth. To demonstrate this idea, a new singularity distribution 

 element, say E, , is added to the singularity distribution of Model A. Let us 



1120 



