Kaplan 



Sy = y + |KG|4> (37) 



where x, y, z and ^ are the instantaneous ship motions of surge, 

 sway, heave, and roll, respectively, and KG is the vertical distance 

 between the center of gravity and the keel. 



The tension, T, in the lowering line is given by the relation 



T- W^ =— V =-^z . (38) 



where W_| is the weight of the load, and only vertical effects are 

 considered to affect the tension. At rest, 



T = To = W^ , 



so that upon representing the tens ion as 



T = To + T' = W^ + T' 



where T' is the tension change due to dynamic effects, one obtains 



— = - . (39) 



W, g 



Thus the tension variation due to the dynamics of the ship motion is 

 directly related to the vertical acceleration of the load, and it is also 

 proportional to the weight of the load. 



In the derivation of the formulas given above, it is assumed 

 that the trajectory of the load attached to the line is such that at each 

 instant it is on the vertical line through the point of attachment of 

 the lowering line to the barge. It is also assumed that the elastic 

 effects of the lowering lines may be neglected; the only dynamic 

 influences considered being those due to the ship motions. The 

 neglect of elastic effects in the lowering line appears to be a fairly 

 safe assumption, since the major influence would occur only if the 

 wave frequencies excited the natural frequency of wave propagation 

 in the lowering line. In view of the lack of specification of the line's 

 physiccd characteristics, as well as the expectation of wave-propa- 



1034 



