Yim 



Fig. 1. Stem Waveform by a Sink Line Transform Stem 



the appropriateness of this flow model in the vicinity of the transom 

 stern. The integral term is the local disturbance which dies down 

 rapidly with |x| , and the expression of t] in x < can be inter- 

 preted as the body streamline of the half body which is formed by a 

 sink on the free surface with a totcil flux equal to uti.ajS upo/(pg) = ZttM. 

 This kind of two-dimensional half body was treated by Af remov [ 6] In 

 investigating the flow near a transom stern, thus obtaining pressure 

 distribution of the two-dimensional half body. 



y = - "Hoe 



in 







(8) 



with the parameter a ^ 0. He obtained a sharp rise of pressure near 

 the edge of the transom stern where the pressure is zero, the value of 

 atmospheric pressure. This sudden rise of pressure at the stern can 

 also be observed from experiments of planning ships [ 7] . 



However, the application of the two-dimensional analyses is 

 generally valid only near the transom stern. In addition, in designing 

 the afterbody near the transom stern, the investigation of hydrodyna- 

 mlc Interactions between other parts of ship hull and transom stern 

 Is innportant, especially the superposition of ship wave systems from 

 bow, stern, and any discontinuities of the hull; this will be discussed 

 later. 



III. SHIPS WITH TRANSOM STERNS AND BOW BULBS 



It seems reasonable to say that the general representation of a 

 ship with a transom stern and a bow bulb may be achieved by comi- 

 blnlng singularity distributions: a source distribution along a given 

 base surface with either point or line doublets or sources for the bow 

 bulb, and a line sink distribution for the transom stern along a line 



576 



