The calculations carried out by [13] indicate that when the frequency 

 2 

 parameter -x — is greater than 4.5, the wave damping becomes negligible and 



the use of infinite frequency approach is justified. The difference between 



the Lewis transformation and Tasai close-fit methods is due to the number of 



terms used in the conformal mapping of the flow around the ship section onto 



the flow around a circle. Otherwise they both use a series of multipoles. 



The Frank close-fit method uses a surface source distribution method 

 and replaces the section of a vessel with segmental singularities. 



Application of various methods for the sectional heaving added mass and 

 damping distribution of a destroyer model with a bulbous bow (Davidson A 

 Destroyer Model) is shown in Figs. 1 and 2. [22] 



Atlhough it has often been suggested that the accurate representation 

 of the sectional shape is not very important, it is not quite true because 

 the determination of the shearing forces and bending and torsional moments 

 require accurate description for all sections, whereas in motion calculations 

 integration over the length iron out the small errors. Ref. [22] suggests 

 that it is not advisable to use the Lewis transformation method, (that is the 

 two or three parameter family) when transforming the sections near the fore 

 and aft end of the ship except for heaving and pitching predictions of con- 

 ventional ship forms. 



An important consideration for the use of the Frank close'-fit method is 

 the condition that the section contour should satisfy the so-called "Lyapunov" 

 regularity conditions [2 2], Non-compliance with these conditions throws doubt 

 on the validity of the Frank approach; for example, forward sections of a ship 

 with a bulbous bow do not fulfill these requirements. In fact, for such shapes 

 Frank [1967] has shown that there exist radiationless frequencies. Therefore, 

 Ref. [22] recommends that for these types of geometry a multipole method such 

 as the Tasai close-fit method, shtuld be adopted. 



57 



