Motion and Resistance of a Low-Waterplane Catamaran 



then the motion x of the mass at the natural frequency u can be 

 expressed by 



x 



O o, c 



n 



In the case of ship motion, F corresponds to the wave exciting force 

 and is proportional to Jc as shown by Newman (1962). Thus we 

 have x q ~q -_1_ . This means that a reduction in damping at the natu- 

 ral frequency could result in a large motion. However, the natural 

 period may be increased by proper design to such a magnitude that 

 the corresponding wavelengths may not be frequently encountered by 

 ships in the ocean. Furthermore, the concern for an expected high- 

 peaked resonant motion resulting from a reduction of wave damping of 

 the system may not be serious because of an augmentation of viscous 

 damping due to an increased wetted surface on the LWP catamarans. 



Although reduction of motions of catamarans may be accom- 

 plished through SWATHS configurations, such configurations present 

 formidable structural problems. The decrease in waterplane area re- 

 duces the restoring buoyancy, and this, in turn, makes the LWP cata- 

 marans weight sensitive. The limited tolerance for additional weight 

 requires a narrow margin for safety factors on structural weights. 

 An additional complication to the structural problem is the lack of 

 data for wave loading. The wave loading includes the contribution from 

 impinging waves as well as from motion-generated inertial and hydro- 

 dynamic forces. To obtain an accurate wave loading the effect of the 

 wave diffraction by two hulls and of the motion of the body should be 

 taken into account in the theoretical analysis. 



In this work an analytical method has been developed for 

 predicting characteristics of motion and hydrodynamic loads of cata- 

 marans, either conventional or SWATHS. The equations of motion for 

 catamarans are derived in the frequency domain under an assumption 

 of linear excitation-response relationship. The hydrodynamic coeffi- 

 cients involved in the equations of motion are determined from strip 

 theory, assuming slender geometry of each hull of the catamaran. 

 The effect of forward speed on the hydrodynamic coefficients is treat- 

 ed as if there were no perturbation on the fluid due to a translation of 

 the ship. 



An apparent underestimation of damping by potential theory 

 results in an unrealistically large motion amplitude at the resonant 



467 



