Developments in Theory of Bulbous Ships 



kj = rL/V2 



L = Length of ship 



m = Nondimensional source strength 



R = Nondimensional wave resistance 



V = Uniform velocity at x = -«> 



x,y,z = Right handed rectangular coordinate system with z positive up- 

 ward, X in the direction of the uniform velocity v, and the origin 

 on the mean free surface 



Y^ = Bessel function of the second kind 



a - Half entrance angle 



Cj = First order wave height 



Ci£ = Second order wave height 



<f , 7], C = Coordinate system equivalent to - x,y, z 



-y. - Nondimensional doublet strength 



K = Nondimensional quadrupole strength 



f^(5^) — {^ ~ tf) cos + y sin iK 



REFERENCES 



1. Bessho, M., "On the Wave Resistance Theory of a Submerged Body," 60th 

 Anniversary Series, Vol. 2, SNAJ, 1957. 



2. Bessho, M., "On the Minimum Wave-Resistance of Ships with Infinite 

 Drafts," Proceedings of International Seminar on Theoretical Wave- 

 Resistance, University of Michigan, 1962. 



3. Dillon, E. S. and Lewis, E. V., "Ships with Bulbous Bows in Smooth Water 

 and in Waves," Trans. SNAME, Vol. 63, 1955. 



4. Havelock, T. H., "The Wave Pattern of a Doublet in a Stream," Proc. Roy. 

 Soc, A 121, pp. 515-23, 1928. 



5. Havelock, T. H., "Ship Waves: the Calculation of Wave Profiles," Proc. 

 Roy. Soc, A 135, pp. 1-13, 1932. 



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