Application of Wavemaking Resistance Theory 



to forego the usual way of specifying a number of hull proportions and hull co- 

 efficients intended for good resistance characteristics based on past experience. 

 Basically, the chief objective of a design is to produce a ship which is safe to 

 operate and economical to build and run, to carry a specified displacement at a 

 specified operating speed. The conditions imposed in any design problem should 

 not include any hull form coefficients related to the resistance. They are not to 

 be spelled out as design conditions, but rather are to be determined in the proc- 

 ess of design. 



In our design problem, the objective is not to obtain the optimum hull form 

 among the family covered by our theoretical representation scheme, but rather 

 to find one hull form in this family which satisfies the design requirements and 

 has an acceptable low level of wavemaking resistance. From a practical point 

 of view, further reduction in wavemaking resistance has no great significance 

 after such a level has been reached. 



Our theoretical representation of hull forms is rather general, and the de- 

 sign conditions to be specified vary from one problem to another. In order to 

 have a computing program that will cover a large variety of design conditions 

 and perform the optimization, we split the surface source distribution in Eq. (2) 

 into four elements. Equation (2) can be viewed as a polynomial of L with coeffi- 

 cients as functions of ^. Each of the L terms is considered as a singularity 

 distribution element. These elements are denoted by Ej, E 2, E 3, and E^ re- 

 spectively, corresponding to the zero, first, second, and third power terms of i 

 in the case of surface source distribution. Similarly, E^ , E^^ E^, and Eg rep- 

 resent the four elements of surface doublet distribution. The line source dis- 

 tribution is denoted by Eg and the line doublet is denoted by Ej^. Altogether, 

 we have ten independent singularity distribution elements. 



Consider E^ as an example. It is expressed as follows: 



2 3 ,4 5 , . 



with Ej(-^') = -Ej(f) and define: 



Jo 



) X ? rfff 



(6) 



''0 



) d^ (7) 



Ti = E^(l). (8) 



Equations (6) to (8) define three possible restraints to be imposed on the ele- 

 ment Ej . They are grossly related to the displacement volume, the midship 

 area, and the entrance angle of the waterline. Similar restraints are defined 

 for the rest of the nine elements. In the case of the surface doublet distribution, 

 the first restraint is related to the ICB position of a half body and the second 

 one is related to the displacement volume. In the case of the line source or line 



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