Motion and Resistance of a Low- Wat erp lane Catamaran 



1. 253 for mean average 

 C = I Z. for one-third highest average 



2. 546 for one-tenth highest average 



r o * 2 



/(^( aJ o)/ A ( a 'o)) S ( a> ) dco = Variance of motion (11) 



r°° o 2 



E = I ( Wo £° / A) S (w ) dw = Variance of velocity (12) 



•'o 



where A is the wave amplitude and S (w ) is the sea-energy spec- 

 trum. The sea-energy spectrum in this work is that introduced by 

 Pierson and Moskowitz (1964), which is given by 



C -C/c^ 



sk) = -A e (13) 



where u> Q is the wave frequency and C, and C_ are constants 

 which are given by 



2 2 



C = 0. 0081 g and C ? = 33. 56 /(significant wave height in feet) 



1 £ 



The dimension of S ( w Q ) is [ L T ] , and the scaling unit is 

 governed by that used for the gravitational acceleration g. 



Absolute and Relative Vertical Motion. 



One of the important aspects to be examined in catamaran 

 motion is the chance of slamming the bottom of the cross -deck struc- 

 ture. To avoid slamming, it might be desirable to raise the cross- 

 deck structure as high as possible. However, for various reasons 

 such as roll instability, wind resistance, structural problems, and 

 problems caused by a high freeboard, e. g. , recovery operations of 

 divers or objects from the sea, a high cross-deck may be undesira- 

 ble. Hence, the first criterion in determining the height of the cross- 

 deck should be the acceptable minimum deck height from a slamming 

 standpoint. 



To find out the chance of slamming, we first have to know 

 the magnitude of the relative vertical displacement and velocity of 

 the ship with respect to the wave surface. Specifically, we would 

 like to know the vertical amplitude and phase of the forward portion 

 of the cross-deck structure with respect to the motion of the free 



475 



