Analysis of Ship-Side Wave Profiles 



computation of the wave resistance. Nevertheless, this idea is develop 

 ed by the authors in a very original manner and they have done a con- 

 siderable amount of theoretical and experimental work. 



To obtain a ship form and a singularity distribution adapted 

 to each other, one can start 



- either from the ship hull and attempt to determine the sin- 

 gularity distribution to be associated with it, 



- or from a given singularity distribution and determine the 

 ship hull generated by that distribution. 



The first path was first followed by Havelock. The sources 

 are distributed in the longitudinal plane of symmetry and calculated 

 by means of an approximate formula which implies the assumption 

 that the length/beam ratio is considerably large and that the free sur- 

 face behaves as a mirror. This first approach gives a solution which 

 can be termed as Zero Froude number approximation for thin ship. 

 At this stage, the theory is interesting from a scientific point of view 

 only. The agreement between the measured wave resistance and the 

 "residuary" resistance is too poor to be acceptable by naval archi- 

 tects. The Zero Froude number approximation transforms the real 

 problem into a Neumann exterior problem. For solving that problem, 

 in a rigorous manner, one can use a source distribution on the hull 

 surface itself. Methods have been proposed by several authors - Hess 

 and Smith [lj , Landweber and Macagno [2] et al - in order to deter- 

 mine the source distribution. To my knowledge, it does not seem that 

 the discrepancy between the measured resistance and the residuary 

 resistance sensibly decreases ; it may even increase in some cases. 

 It appears therefore that the Zero Froude condition may be one among 

 the most important causes for discrepancy between theory and exper- 

 iment. 



The second path is that of Professor Inui and his School. The 

 given source distribution is located in the plane of symmetry and com- 

 pleted by its image with respect to the plane of the free surface at 

 rest. The ship form is obtained by integrating the system of differ- 

 ential equations for the streamlines of the relative motion. For the 

 ship form so obtained the given source distribution can be considered 

 as the rigorous solution of the Neumann problem related to the double 

 model derived from that form. But this method does not permit to 

 get over the drawback of the Zero -Froude number condition. 



In their paper, the authors present a "wave -analyzed source 

 distribution" such that the ship-side wave profile derived from this 



747 



