Application of Wavemaking Resistance Theory 



NUMERICAL COMPUTATIONS 



Theoretical Representation of a Hull Form — Singularity 

 Distribution 



For theoretical analysis of the wavemaking resistance of a given hull form, 

 the latter is theoretically represented by a singularity distribution. Since our 

 aim is to obtain a hull form with low wavemaking resistance rather than to pre- 

 dict the wavemaking resistance of a given hull form, the singularity distribution 

 has been chosen as the starting point. After a suitable distribution has been 

 found, the hull form is then generated from it. 



A distribution of singularities in space is defined by their location as well 

 as their density. Our ultimate objective is to find an optimum singularity dis- 

 tribution which will generate a hull form with low resistance and practical pro- 

 portions, and at the same time is convenient for theoretical analysis. 



It is obvious that a central plane distribution cannot yield practical hull 

 proportions, and it must be discarded. On the other hand, if we choose the hull 

 surface as the location (as has been done in Ref. 3), the density is automatically 

 fixed. In such cases, even though we can always choose a satisfactory hull ge- 

 ometry to start with, we have no room left for improvement of the wavemaking 

 resistance. A logical choice of the location is somewhere between the central 

 plane and the hull surface. 



The gross overall ship dimensions can be effectively controlled by the loca- 

 tion of the singularity distribution. Our procedure is to select this location first 

 and then to determine the density distribution on the chosen location such that 

 the wavemaking resistance will be kept low. Let ^ , v, and ^ be the nondimen- 

 sional coordinates normalized by one-half of the ship length. The origin is lo- 

 cated at the midship section on the undisturbed free surface. The positive di- 

 rections of ^, Tj, and i are in the forward, port, and upward directions 

 respectively. 



Equation (1) defines an T7-surface on which our singularity distribution is 

 placed. 



rj = ±B(^) [1-(1- a - b) x^" - ax^" - bx"] (1) 



with 



^ 



Ph(0 



For < <f < P,(0 



and 



X = "^ For -P (O < d" < 



where B(0, Pb^^)' and P^CO define the midship section, bow profile and stern 

 profile of the 77 -surface, respectively. Parameters a, b, and n are needed to 



1115 



