Motion and Resistance of a Low-Waterplane Catamaran 



The strip approximations employed in our analysis of mo- 

 tions and hydrodynamic loadings are based on a two-dimensional 

 approximation of the fluid motion at each transverse cross section. 

 A solution for the velocity potential associated with heaving, swaying, 

 or rolling twin cylindrical bodies of arbitrary but uniform cross 

 sectional forms has been developed by the method of source distri- 

 bution. Lee, Jones, and Bedel (1971) show good agreement between 

 theoretical and experimental values of heave added mass and damp- 

 ing of four different types of twin cylinders. Figure 3 compares 

 heave added mass and damping in nondimensional forms a 33 /(P-y-) 

 and b-^/fpv-w) where V- is the immersed volume at the mean posi- 

 tion versus the frequency number — 5— for twin rectangular cylinders. 

 The dotted lines in Figures 3a and b are the theoretical results for 

 one cylinder only. If the separation distance between the two cylin- 

 ders is large, one would expect that the added mass and damping coef- 

 ficients for the twin cylinders approach those for the single cylinder. 

 Thus the difference between the solid and dotted curves in these two 

 figures can be regarded as the measure of a hydrodynamic interac- 

 tion between the two hulls. The added mass reflects the local beha- 

 vior of the fluid motion near the body, whereas the damping is sensi- 

 tive only to the farfield behavior of the fluid motion. Here in figures 

 3a and b we can observe that both local and far-field behavior of 

 fluid motions generated by a single cylinder is quite different from 

 the behavior of twin cylinders. 



Two types of singular solutions may occur at certain frequen- 

 cies in the problem of oscillating twin cylinders. One is associated 

 with a mutual blockage effect between two cylinders, and the other 

 is associated with the method of singularity distributions; see John 

 (1950). The former is of both mathematical and physical origin; the 

 latter is strictly of mathematical origin and applies to both single 

 and twin cylinders. The former type of singular behavior is shown in 

 figure 3c at the frequency number of about unity. The experimen- 

 tal results seem to confirm the singular behavior. The frequencies 

 at which such singular behavior occurs can be determined by 



2 



= 1Z7 TT for n = 1 > Z > ■ ■ ■ 54 ) 



g (b/a - 1) 



where the definition of a and b is as shown in figure 3a. 



The second type of singular behavior is shown in figure 3d 

 by the solid curve. This type of singular behavior results from the 

 break down of the solution of the Fredholm-type integral equation at 



489 



