The arclength s would be fixed when the array was assembled. The 

 height d would be measured during the operation using an acoustic pirujer 

 attached to the cable. For a given arclength and height, the horizontal 

 length x of the cable is: 



where: y = c 



(2) 



The horizontal distance x between the anchor and sentinel would 

 be determined from positions acquired using acoustic transponder navigation. 

 A transponder was attached at the sentinel location. This value was, there- 

 fore, an input to the calculations. However, should the transponder fail 

 to operate the parameter could be calculated using equation (2). Further- 

 more, the measured value could be used as a check of the analysis by comparing 

 it with the calculated value. 



The tension at the bottom of the catenary is given by: 



H = cw (3) 



where: w = linear density of cable 



The tension at the top of the catenary is: 



T = yw (4) 



The weight of the catenary is the linear density times the length: 



W = sw (5) 



Summing forces in the x and y directions and dividing yields the 

 angle between the tension vector and the horizontal at point B: 



9 = tan"^ ^ (6) 



A free-body diagram of point B, where the sentinel weight attaches 

 to the two cable segments, is depicted in figure 11. In this figure, P 

 represents the sentinel weight, T and 9 represent the tension and its 

 direction in the lower catenary cable segment, and T' and represent the 

 tension and its direction in the upper catenary cable segment. Summation 

 of forces in equilibrium yields: 



and 



T. = I^ 



Tcos 9 



T' - T sin 9 + P f^. 



