Ship Waves and Wave Resistance 



waves passing through the plane 77= y between c= -X and - - X, Roughly speak- 

 ing, the diagram shows that at least a record of five times the ship's length 

 within the Kelvin pattern is necessary to attain 80 percent of the resistance. 

 Our calculation showed that omission of the local wave components did not sig- 

 nificantly change the result even for Y less than 1, 



In Fig. 3, we have plotted the ratio of resistance derived from transverse 

 cut analysis to exact second-order resistance as function of distance X from 

 midship section. The diagram essentially reflects the decay of the local waves 

 in relation to the residual free wave system. The data for this calculation were 

 selected in correspondence with investigations of Kobus in Ref. 13; the influence 

 of a tankwidth equal to 5/3 the ship's length is included. 



Fig. 3 - Ratio of the calculated resistance R^'^-*(x) from the 

 transverse cut analysis (6) (wave elevation and x slope) to 

 the asymptotic value R^^^ (tank width equal to 5/6 the ship 

 length, >'q = 3.86, and infinite strut) 



SUMMARY 



With the above analytical considerations, an attempt was made to coordinate 

 the intuitive approach of Sisov with the rigorous procedure of Wehausen. Allow- 

 ing some simplifications, we found that even the latter leads to a representation 

 of the second-order wave potential by sources only, located on the undisturbed 

 free surface and on the longitudinal centerplane of the ship; in particular, all 

 line integrals can be eliminated. Additional resistance can be expressed in 

 terms of first-order flow components which determine these singularities. Only 

 a region of the free surface close to the ship need be considered. 



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