the cable would not change unless a different cable were used. The depth at 

 the anchor point, given to be 4515 meters, was a value that could be changed 

 if required. The depressor and sentinel weights were approximate values 

 that would be refined when the weights were actually constructed, and the 

 length of the sweepline would be fixed at the time the sweepline array was 

 deployed. 



Table 2 lists those parameters that could be measured during the 

 operation. For the catenary calculations these values are redundant and some 

 could serve as inputs for the calculations while the rest provide a means for 

 checking the accuracy of the theoretically computed values. Furthermore, any 

 of these values could be computed from the other inputs using the catenary 

 equations. If any of the instrumentation failed, the analysis provided a 

 means for calculating the missing parameter. 



Table 3 lists some calculated values used in determining the sweep- 

 line and cable geometries. This information would be used to ensure that 

 the sweepline was off the bottom and simultaneously below the MAVA releases. 



Usual catenary calculations employ a coordinate system whose origin 

 is offset some vertical distance from the lowest point of the catenary 

 (i.e., where the catenary becomes horizontal). This is demonstrated in 

 figure 10 where the offset is c. H is the horizontal tension at the bottom 

 and T is the tension at the top of the catenary. The arclength is s and W 

 is the weight of the cable occurring at the midpoint of the arc. 



It could not be assumed that the sweepline would form the geometry 

 depicted in figure 10. If too much cable were payed out, some of the line 

 would lay on the bottom. This would have the effect of moving point A farther 

 down the cable, resulting in a new catenary of, shorter arclength. In this 

 case the standard catenary equations would hold; however, an adjustment in the 

 position of point A and coordinate system would be required. On the other 

 hand, if not enough cable were payed out to achieve the geometry shown, then 

 the assumption that the cable was horizontal at point A would be incorrect. 



This led to two cases for consideration: 



Case 1 - sweepline catenary is horizontal at point A 

 Case 2 - sweepline catenary is not horizontal at point A 



This first case was solved using standard catenary equations. The second case 

 required some additional analysis and introduced new parameters for considera- 

 tion. Both cases will be considered separately. 



C atenary Analysis for Case 1 



Figure 10 can be considered a free-body diagram of the sweepline 

 anchored at point A without the sentinel weight. The vertical coordinate 

 offset c is calculated from: 



where: s = catenary segment arclengtn 



d = height of point B off bottom 



