i? 



" e»' » 



i 



that vsry only in magnitude with depth. The program 

 was written for a surface-buoy system but. with only 

 minor changes, could be rrude applicable to a submerged 

 mooring. A program listing is given in Reference 1 5. 



This program is a zero-order form of a dynamic program 

 for the behavior of surface-buoyed, single-point moorings. 

 The time-dependent terms in the cable equations have been 

 allowed to go to zero and have then been integrated, using 

 a fourth-order Kunge-Kuita integration algorithm. Since 

 the forces on the buoy are a function of cable tension, an 

 iterative solution mu>t be used to match the computed 

 vertical projection of the cable with the depth of water. 

 Program-predicted data &how good agreement with data 

 from shallow- and deep-water, single-point moorings. 



The modeling capability consists of a program for the 

 initial value problem of a single-point mooring and a 

 program for muttilcg mooring systems. The iniii.il value 

 program solves the differential equations for cable equilib- 

 rium using a numerical-integration technique. The output 

 from this program has been shown to be within 10% of 

 cxpeiimtnial towing cable data. The multikg program 

 uses a technique similar to Skop's MIR with "an improved 

 convergence capability." but the program requires that all 

 legs join at one buoy. The programs are considered pro- 

 prietary, and no listings arc available. 



Two steady-state progratns have been developed to evalu- 

 ate the three-dimensional behavior of the single-point 

 mooring. One program (named MR3E) solves the initial 

 value problem of finding the cable scope required to reach 

 a given depth (or depth for a given scope) when the buoy- 

 ancy and drag are specified for the surface buoy. In cases 

 where both the ocean depth and cable scope arc fixed, 

 the correct submergence of the buoy must be determined 

 by iteration. The other program (named iMR3S) incorpo- 

 rates the iteration scheme and simply increases buoy draft 

 if the end of the cable does not reach the scafloor or 

 decreases buoy draft if the cable overshoots the seafloor. 

 Both programs use a Kutia-Mcrson subroutine to integrate 

 the differential equations of cable equilibrium. This pro- 

 gram is being used at the Naval Air Development Center 

 and the Naval Ordnance Laboratory for the analysis of 

 moored systems. Program listings are not given in the 

 references. 



1" 

 < 



C. Cable mass and drag forces are 

 lumped on each cable segment. 



A. Cable is 8 series of straight 

 elements. 



B. Cables are perfectly flexible. 



A. -^^able is i series of straight^ 

 (^ segments. . -^ 



B. Current profile is linear on each 

 scgmeift. 



A. The current profile is assumed to 

 be linear between points of 



£ -i 

 ^ > 



I I g 



a-^i 



1 



I ^ ■ ^ 



1 



I' I, I 



p 



;j 



^ R R 



II 



I I I 



1 ^ 



Single-point 



Single-point 

 moor; Bi- 

 moor; Tri- 



Single-point 



ljf 



- 



V 



E E 



1 S X 



1 

 i tsiH i III J iPPlll 



