Shallow Water Problems in Ship Hydrodynamics 



C/l 



-1.0 -0.8 



(BOW) 



-0.6 -0.4 -0.2 0.2 0.4 



NORMALIZED STATION CO-ORDINATE x 



0.6 



0.8 1.0 



(STERN) 



Fig. 3 Blockage coefficient C(x) for Series 60, block 0.80 ship 



VII. THE SIDE FORCE DUE TO BEAM SEAS 



Once we have obtained the blockage coefficient C(x) or its 

 inverse the porosity P(x) for any given ship-water bottom geometry, 

 we have all the information about the ship that is necessary to solve 

 the outer acoustic -like problem to determine the wave force on the 

 ship. Numerical techniques for solving the problem formulated in 

 Section 5 are described by Tuck [ 1970] and by Taylor [ 1971] and will 

 not be discussed in detail here. 



It is sufficient to observe that the outer problem can be re- 

 duced to solution of an integral equation, using methods analogous 

 to those described by Honl, Maue and Westphal [ 1961] , in which 

 P(x) appears as an input quantity. This integral equation can be 

 solved by direct numerical quadrature, followed by matrix inversion, 

 leading to numerical values for the basic unknown potential 

 (|>(x,0^,-h). 



This potential is proportional to the pressure difference 

 across the ship, and hence we may obtain the net force F on the 



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