Wavemaking Resistanoe of Ships with Transom Stern 



The wave height near the stern due to a point source at the 

 bow can be approximated also by the method of stationary phase: 



Cb = 4k^exp (kz,) y^ cos (kx, + I ) (54) 



The wave height near the stern due to the transom stern sink, 

 approximated by the two-dimensional one, was given earlier, say ^ , 



As a result, the total sum of t,^, ^-, t,^, and ^g would repre- 

 sent an approximate wave height in the wake of the ship near the 

 transom stern. The streamlines on the body near the stern can be 

 obtained by considering the pressure which is given by the singularity 

 representation as was done in Eqs, (6) and (7). The streamlines near 

 the bow may be obtained by a double model approximation. The inte- 

 grated scheme to produce approximate body streamlines will be pro- 

 grammed for a high-speed computer in the near future. 



VIII. NUMERICAL RESULTS AND DISCUSSIONS 



The optimal strength of singularities for the transom stern 

 and for the bow bulb are shown in Figs, 2,4, and 6. The former is 

 shown in terms of the deadrise angle a of the afterbody near the 

 stern. The latter is shown in terms of the radius of the correspond- 

 ing half body produced by the point source located in the infinite 

 medium* These are all functions of Froude numbers for the given 

 hull shapes. The wave resistance at each Froude number is computed 

 for the given hull with the transom stern and the bow bulb optimal at 

 a given Froude number j see Figs. 3, 5, 7, and 8, 



587 



