Pien and Lee 



surface beneath it. The relative velocity will also be needed to deter- 

 mine the threshold velocity for slamming. 



Let us consider a situation in which a ship is perfectly con- 

 touring with the wave so that no chance of slamming may occur. 

 When it comes to the working efficiency of the ship crew, contouring 

 performance of the catamaran may not necessarily be the favorable 

 condition because frequent oscillation of a ship can be quite a deter- 

 rent to easy movement. In this respect, we would like to reduce the 

 absolute vertical motion with respect to the calm water level. Thus, 

 a study on both absolute and relative vertical motions along the length 

 of catamarans is important. 



Among various sea conditions that most unfavorable one to 

 a ship would be a periodic swelled sea, having an encountering pe- 

 riod lying in the resonance band of the ship. Although sinusoidal wa- 

 ves may not correctly represent the swell condition, an application 

 of sinusoidal waves for a qualitative study of slamming characteris- 

 tics of a catamaran cross-deck will be made; then the study will be 

 extended to irregular sea conditions. 



The absolute vertical displacement of a station at x is 

 obtained by 



^ = { 30 " X «50 < 14 > 



where £oq and £ en ar e the complex motion amplitudes of heave 

 and pitch, respectively, and the pitch angle is positive when the bow 

 is down. The relative vertical displacement of the same station with 

 respect to the incoming wave surface is given by 



:r) _ t (a) 



30 30 * w0 



*w B * w _ r _ (15) 



where the free- surface elevation f n is given by 



3 Deformation of the free surface is caused not only by the incoming 

 waves but also by the ship-generated waves. An evaluation of local 

 free -surface disturbance due to an oscillating ship with a forward 

 speed is an extremely difficult task to achieve. The difficulty is more 

 so for the region between the two hulls of a catamaran. Thus, the 

 present analysis should be regarded as a gross estimate. 



476 



