r = 



2m (x) 



n 



cq. (3) becomes, 



\"/7/ 



+ (2 TJ^ 



(4 



'*'^f'^(4' 



(4) 



Maximum line tension can tiien be expressed as, 



n=1 



(5) 



where 



W 



= weight of ALVIN in water 

 = ship heave ampHtude 



= vertical motion at point of lift line suspension due to ship 



roll 

 = vertical motion at point of lift line suspension due to ship 



pitch 



= amplitude ratio evaluated at ship heave, roll, and pitch 

 natural frequencies, respectively 



The natur;d frequencies are defined as follows: 



2-K 



J = iOij = ; T Lj - heave period 



27r ,, • , 



> 2 = ^p> = / T D - loU period 



65 



