Ship Form of Minimum Wave Resistance 



Figure 12 



SOME CASES OF SMALL WAVE RESISTANCE 



As shown by Krein and Bessho, there is no definite solution of the problem 

 to minimize Michell's integral for a given volume. This fact suggests that the 

 theory of minimum wave resistance discussed so far is not the only way to ob- 

 tain a ship form of small wave resistance. Inui [15] has shown that the wave 

 resistance can be reduced to a great extent by addition of a bulb at the bow which 

 enables the cancellation of the wave generated by the main hull. This method 

 was refined by Yim [16]. He considered a combination of a source distribution 

 representing the ship's hull and a distribution of dipoles along a vertical line of 

 infinite length at the bow. According to him, the wave resistance can be elimi- 

 nated when a suitable choice is made in the combination of sources and dipoles. 

 The vertical dipole distribution of Yim's model shows a vertical cylinder of in- 

 finite length at the bow. Instead of it, one may consider a source distribution on 

 the vertical line. In fact, it is possible to make the wave resistance vanish by a 

 suitable choice of source distribution along a horizontal line and those along 

 vertical lines at both ends of the horizontal distribution. As the simplest exam- 

 ple, let us consider a source distribution along a horizontal line of length L = 2-i 

 on the free surface. Choose the density of sources given by the following 

 equation: 



o-j(x) 



<-r) 



-I < 



(68) 



If a distribution of sources along an infinite vertical line at x = ^ and that of 

 sinks along a vertical line at x - -I have density distribution given by 



cr^Cz) = m^ exp ( -\ , < z < 00 



\ -vf, ' 



221-249 O - 66 - 67 



(69) 



1041 



