Figure 13 shows the computed motions of SWATH 6D. The heave amplitudes pre- 

 dicted by the slender-body theory are much larger than those predicted by the strip 

 theory. Compared with experiment, the results of the mixed method are best except 

 for high A/L values. 



The pitch amplitudes computed by the unified slender-body theory and by the 

 mixed method are too large and do not show good comparison with the results of strip 

 theory or the experiment. In contrast to the results for SWATH 6A, the mixed method 

 does not compute the pitch amplitude properly. This indicates that the added mass 

 and damping coefficients in Figure 8 by the slender-body method may be in significant 

 error. This error might be caused by solving the strip theory with the Frank close- 

 fit method and by replacing O with O as mentioned in the discussion of the added 

 mass and damping coefficients. 



SUMMARY AND CONCLUSIONS 



3 

 In this report the unified slender-body theory developed by Newman is applied 



to predict the motion of SWATH ships in following seas. Only for a limited range of 



X/L values is there an improvement for heave motion. For pitch motion, except small 



encounter frequencies, the results are worse than those of strip theory. When the 



encounter frequency is large, the pitch motion becomes extremely large. The reason 



for this discrepancy seems to lie in the fact that the strip theory is solved by the 



Frank close-fit method, and not by the multipole expansion. From the present study, 



the following conclusions may be drawn: 



1. In the unified slender-body approach, the largest contribution to the 

 hydrodynamic coefficients results from the solution of the strip theory itself. 

 Correct computation of the source strength at the origin is necessary to compute the 

 three-dimensional source strength exactly. Therefore, for the outer approximation 

 of strip theory, the multipole expansion method should be applied instead of the 

 Frank close-fit method. 



2. A more careful analysis should be made in computing the excitation forces 

 by the strip theory. Application of the Helmholtz equation is mathematically more 

 correct. However, there is a singularity in this solution when the heading angle 

 of the incoming waves is zero or 180 degrees. The two-dimensional Laplace equation 

 computes the heave excitation force correctly, but the pitch excitation moment is 

 computed incorrectly. 



45 



