The calculated values are used to indicate the tensions in the cable 

 and the geometry of the cable. As previously mentioned, the tension at the 

 ship, T" , and the distances x, X-j- and S^ could be measured inputs. In fact, 

 such measurements could serve as a means of verifying the theory and the 

 calculations. 



Catenary Analysis for Case 2 



We will next consider the case when the sweepline is not horizontal 

 at the anchor. In this case, the sweepline segment forms a portion of a 

 catenary. Development of the analysis can be made along the same lines used 

 for the cable segment BC in Case 1; which is to assume the catenary segment 

 to be extended so the usual catenary calculations may be applied. This is 

 illustrated in figure 14. 



In this case the loading conditions are unknown. For a direct 

 analysis of this situation values for at least two pa rame ters must be assumed, 

 For our purposes the values s, the segment arclength A'B, and 9, the angle 

 of the sweepline at the sentinel, were chosen. The analysis proceeds as 

 follows. 



Select s and 0. Known values are s , the actual length of the sweep- 

 line from anchor to sentinel, and w, the linear density of the cable. The 

 horizontal tension at A', the bottom of the imaginary catenary segment, is 

 calculated from equation (6) by: 



Where W is the weight of the total segment including the imaginary 

 part and is calculated using equation (5). From equation (3) the coordinate 

 system vertical displacement is: 



^-^ (27) 



Using equation (1) the vertical distance from A' to B is: 



d = -c + Vc^ + s^ (28) 



The horizontal distance x is given by equation (2). The tension 

 T at the top of the sweepline is calculated from equation (4). 



Using equation (28) the vertical height of the imaginary segment 



A'A is" 



d' = -c + c^ + s'^ (29) 



Where: 



s' = s - s^ 



a 



