forward speed is high. To overcome this convergence problem, it is instructive to 

 compare Equations (27) and (48). Equation (27) can be solved by the matrix in- 

 version or Gauss- Jordan method as long as the singularity problem in f (x) is solved. 

 By defining a new function, 



h(x-£) = f(x-£) K i x (49) 



and 



h(x-p = f(x-S) + [ F (e)-F(-e)l g = x 



the integral equation 



(Q h(x-C) d£ = o. + o. (j=3,5) (50) 



has the same solution as Equation (48). The advantage of solving Equation (50) is 

 that the matrix inversion method can be applied to it and has been found to yield 

 solutions for all speed ranges. In the low-speed range, the iteration method works 

 satisfactorily and, in this case, the solution of Equation (50) compares well with 

 that of Equation (48). 



RESULTS AND DISCUSSION 



In order to validate the numerical results of the present unified slender-body 

 theory, three hull forms have been selected: a twin ellipsoid hull, the SWATH 6A 

 hull, and the SWATH 6D hull form. The principal parameter values for these three 

 hull forms are given in Table 1. The twin ellipsoid is a mathematically exact hull, 

 and its performance at zero speed may be compared with the predictions of the strip 

 theory and the three-dimensional theory. The computations for SWATH 6A and SWATH 6D 

 have been carried out for speeds of 28 knots in head seas and 20 knots in following 

 seas. These results are compared with those of strip theory and experiments. 



Numerical computations for the twin ellipsoid have been carried out at zero 

 speed in head seas and are shown in Figures 3-6. In this case the three-dimensional 



14 



