Pien 



assume that the only restriction put on E3 is that the displacement volume of 

 Model A should be increased by one-third. The optimum E3 so obtained is 

 shown below. 



;i5.977cf - 137.8429f + 441.3259,f - 575.0504^ + 259.4315^5]^' 



(11) 



This is derived in such a manner that the wavemaking resistance due to the 

 combined singularity distributions of Ej and E3 is an optimum at F = 0.3. Let 

 us denote the model, generated by Ej and E3 , as Model B. Figure 6 shows the 

 comparison between the C^ curves of Models A and B. Despite the fact that 

 Model B has one-third more displacement volume than Model A, it has less 

 wavemaking resistance at F = 0.3. 



To illustrate the importance of section shape upon the wavemaking resist- 

 ance, let us consider a third case, Model C, which has the following singularity 

 distribution: 



M(^,0 = 3EiC^ + E3/3^^ 



(12) 



where E^ and E3 are defined in Eqs. (10) and (11), respectively. 



It is obvious that to the first order of approximation Models B and C have 

 the same sectional area curve. Figure 7 shows the comparison of the C^ curves 

 of Models B and C. The differences between these curves are quite large. This 



Fig. 6 - Comparison of C^ curves of Models A and B 



1122 



