Yim 



proportional to the stern draft. Now, we would like to use the In- 

 direct approach to the transom stern theory. Noting that a sink line 

 on the free surface is tantamount to the constant pressure distribution 

 ahead of the line and that it produces a negative cosine regular wave 

 and a depression in the free surface immediately behind the sink line, 

 we expect to get streamlines similar to the transom-stern ship from 

 a combination of a normal ship- singularity distribution and the tran- 

 som s ink. 



First the free-surface streamline due to a two-dimensional 

 sink line is plotted to establish the validity of this model, which will 

 be used later for plotting the streamline near the transom. Then, 

 several simple original ship singularities are considered so that 

 basic ship models can be modified to those having transom sterns. 

 Since the transom sink is supposed to behave like a stern bulb [ 1] 

 to cancel stern waves, a bow bulb [3,4] made of a source is also 

 considered together with the stern sink to cancel bow waves as well 

 as to supply source strength which helps form a closed body. Thus, 

 optimum strengths for the bow bulb source together with the transom 

 stern sink are calculated to minimize the total wave resistance. 



The wave resistances with and without the bow bulb and the 

 transomi stern are calculated. The Sretensky formula for wave 

 resistance is used since It Is much simpler to program In the high- 

 speed computing nnachlne than the Havelock formula. Finally, 

 approxlnnate wavefornas near the stern are investigated, which will 

 help in designing a good afterbody near the transom stern. 



This is part of a project in which the ultimate goal Is to under- 

 stand more the physical meaning of a transom stern in the wavemaklng 

 resistance of a ship; to obtain better design criteria for ships with 

 transom sterns; to find out the possibility of an Improved ship design 

 with the gained knowledge, and, hopefully, to design a good ship with 

 a transom stern, making full use of high-speed computers as well as 

 testing the model In a towing tank. 



Although this Is a small part of ship- designing problems, It 

 Is not easy to complete In a short time. At this stage, it is merely 

 hoped that this paper will achieve several objectives: (1) to validate 

 the mathemiatlcal model of a ship having a transom stern as a stepping 

 stone to analytical investigation of transom sterns, (2) to determine 

 the practical ranges of parameters within which the application of 

 bulbous bows and transom sterns would be beneficial, and (3) to 

 Initiate a computational procedure which would be used for an overall 

 design program using a high-speed digital computer. 



574 



