Analyses of Multiple-Float-Supported Platforms in Waves 



The hydrodynamic moment arms, according to Eqs.(21), are 

 presented in Table 7. The subscript notation is analogous to that used 

 for Table 6, so that, for example, Zgg indicates the moment arm 

 for the hydrodynamic inertial sway force induced by sway motion. 



The roll moments may be expressed in terms of the heave and 

 sway forces and their respective levers as indicated in Table 8. 



The wave-exciting forces and moments may be expressed in 

 dimensionless form as shown in Table 9. 



The wave-induced moment can, of course, be represented in 

 terms of the sway and heave forces and corresponding moment arms 

 in accordance with Eq. (21), in a manner similar to the motion-induced 

 moments (Table 8). The separation of wave forces into odd and even 

 parts will be shown to be useful for the case of the catamaran-type ship. 



Rigidly Connected Twin Cylinders 



All of the above formulas may be applied for bodies a, b and 

 a + b, regardless of whether the bodies are similar (some care and 

 consistency must be used in choosing and using relevant dimensions, 

 draft and beam, for use in the dimensionless coefficients if the bodies 

 are not twins). Based on a limited number of numerical calculation of 

 twin cylinders, it is observed that the hydrodynamic forces, moment 

 and moment arms due to oscillatory motions are entirely identical in 

 magnitude for bodies a and b (see Table 10). 



Consequently, the resultant hydrodynamic forces and moments 

 may be given as shown in Tables 11 and 12, where the subscript (a + b) 

 for the rigidly coupled bodies is omitted. 



Since the bodies are twin and the incident wave flow consists of 

 part which are symmetric and asymmetric with respect to the vertical 

 z-axis, the odd and even components of the wave-exciting forces and 

 moments on bodies a and b are equal in magnitude, whereas some 

 forces on a,b act in opposite directions. (Table 12) 



These relations which arise due to symmetry afford consider- 

 able simplications for evaluations of catamaran-type configurations. 

 They are exhibited graphically in Figures 14a-d. 



For convenience, the previously defined force and moment coef- 

 ficients C, 8 (Tables 6, 7) will be called the forces and moments. 

 Figure 14a illustrates a typical force system, - induced by the heaving 

 motion of the twin bodies. The heaving motion induces both heaving and 



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