Motion and Resistance of a Low-Waterplane Catamaran 



r 



wO 



= A e 



j K (x cos B - y sin 6 ) 



where A is the wave amplitude, is the wave heading angle with 

 respect to the positive x-axis, and K = c*) Q /g is the wave number. 

 If we choose the midspan of the cross structure to be the location of 

 our interest, then 



wO 



= A e 



i K x cos 8 

 J o H 



Amplitudes of vertical displacement are obtained by taking 



>■ (A) 



the absolute values of ? 1Q 



and £ 



<Rf 



e. , * 



(A) 



:(RJ 



If we 



and |£ ( 30 



denote the height of the bottom of the cross structure from the calm 

 water level at x by c Q , then we know that when|£' n > c Q , a 

 water contact on the bottom of the cross structure can be made. The 

 water contact establishes only the necessary condition for slamming. 

 The sufficient condition is the magnitude of the relative velocity between 

 the structure and the free surface "period". The criterion of the rela- 

 tive velocity for which the phenomenon of slamming is realized is 

 often called "threshold velocity", denoted by W*; see Ochi (1964). The 

 threshold velocity is a function of geometry of the ship, and no ana- 

 lytical means seems to exist except some empirical values for cer- 

 tain types of monohulls. 



The vertical velocity of the cross structure at x can be 

 obtained by multiplying the vertical displacement by ( -j o> ). Thus, 

 absolute and relative vertical velocities are given, respectively, by 



W 



(A) 

 30 



J 30 



(16) 



W 



(R) 



30 



J 30 



(17) 



Hence, if the following two conditions 



(R) 



30 



and 



> c 



(18) 



W 



(R) 



30 



w- 



(19) 



477 



