Fieri and Lee 



certain eigen frequencies. 



Existence of such singular behavior in the solution of sec- 

 tional hydrodynamic coefficients can present troubles in applying 

 strip approximations to three-dimensional hydrodynamic coefficients. 

 Removal of the second type of singular behavior has been achieved 

 by imposing a rigid wall condition, i. e. , (J), = or a pressure relief 

 condition, i. e. , Q = 0, on the line z = inside cylinders. A mathe- 

 matical proof of legitimacy for employing this technique will be publi- 

 shed in the future. Figure 3 d shows heave added mass of a rectan- 

 gular cylinder obtained with and without the additional interior boun- 

 dary in the solution of the boundary-value problem. 



Removal of the other type of singularity may not be possible 

 unless a full threee -dimensional solution of the problem is achieved. 

 However, for catamarans having the inner hull separation distance 

 on the order of the beam of one hull, the lowest frequency at which 

 this singularity occur may lie out of the practical range of interest 

 in ship motions. For example, if we take b/a = 2 , the longest cri- 

 tical wave length X which can be encountered in head waves can be 

 obtained by 



2 



X =— / (55) 



c 



g ( 1 + ^1 +4U2 V^ r+2U >TA ) 



For a = 15' , we have 



U (knots) X (ft) 



c 



10 17.8 



20 77.2 



30 124. 1 



Comparison of theoretical results with experimental results 

 of three-dimensional added mass and damping for NSRDC Model 5061, 

 the description of which is given in Table 2 and figure 5 » is shown 

 in figure 4 for Froude numbers F n = and 0. 253 (10 knots). The 

 three-dimensional added mass and damping are obtained from the two- 

 dimensional added mass and damping by the strip approximation as 



5 Employment of this technique was first made by Paul Wood of the 

 University of California at Berkeley. 



490 



