Wavemaking Resistance of Ships with Transom Stern 



For a slender body model, Eqs, (11) and (35) are used for 

 the bare-hull source distribution, which is called a cusped cosine 

 ship here. For a Michell thin ship model, computations are per- 

 formed for Eq. (il) for cusped cosine and parabolic ships. For the 

 combined bare-hull source distribution, the influence of the location 

 of transom stern Xg is shown in Figs, 6 through 8. It can be under- 

 stood that there is an optimal location for the minimum wave resis- 

 tance as in the case of a bulbous bow; however, it is not computed 

 here. 



It is interesting and reasonable to see that the optimum size 

 of the bulb becomes the smaller for the large Froude numbers over 

 0,4, and eventually the strength becomes negative at Fp > 0.5. In 

 other words , for a large Froude number, a ship behaves like a single 

 point doublet far behind the ship so that the only way to reduce the 

 wave height is to reduce the ship volume. 



Indeed it is possible to take advantage of the transom stern 

 as well as the bulbous bow to reduce wave resistance In the Froude 

 number range Fp < 0. 5 by a proper combination of the ship hull 

 shape and the transom stern and the bow bulb. For the case of a 

 high-speed ship such as a planing boat, there is no alternative to 

 evade the detrimental cavitation without having the full separation 

 occur at the transom stern, whether it is beneficial to the wave 

 resistance or not. 



The numerical results of streamlines are not given in the 

 present paper because of their coniplexity. The approximate 

 method of computation of the streamlines near the stern is shown in 

 the previous section. When the ship draft is fairly large, compared 

 with the wavelength, the ship shape fronn the singularities can be 

 approximately computed from the double model. However, for a 

 transom stern, the free surface follows immediately behind the 

 usually shallow drafted afterbody. Thus, the modified slender body 

 theory used in the previous sections , combined with a double model 

 approach to the forward part of ship hull seems to be promising. 

 Some imaginative approximate configurations from the concerned 

 source distributions are shown In Fig. 9. 



Last, but not least, the importance of experiments on the 

 design of ships with transom sterns should be emphasized. There 

 are very few experimental results available [ 15] . However, this 

 has to be done in close coordination with the theory so as not to grope 

 in the dark. The theory is now on a solid foundation. More time and 

 effort are needed to achieve experimentally usable and complete 

 results on ships with transom stern. In the future, the author hopes 

 to finish a systematic computer program for designing ships with 

 bulbous bow and transom stern that includes information about the 

 wave resistance, the bulb size, the transom-stern draft, and the 

 main hull shape. 



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