Mooring and Positioning of Vehicles in a Seaway 



VII. MOORED BUOY ANALYSIS 



A moored buoy system Is similar in many respects to the 

 moored ship case, and simplifications are made in order to treat a 

 representative problem. The buoy system is assumed to be a single 

 point mooring, with a surface floating buoy hull connected by a 

 flexible line to the ocean bottom. Both slack and taut types of 

 moorings are included in the analysis, and the surface buoy form 

 can be either a ship-like form, a spar shape, or an axisymmetric 

 discus shape. The analysis is restricted to motion in a single plane 

 and the current direction and wave direction thereby lie in this plane, 

 making a two-dimensional problem. Allowance for current magni- 

 tude variation with depth is considered, with its main influence being 

 in the static equilibrium problem (which will not be treated in detail 

 here). 



Considering the static equilibrium problem, a free-body 

 diagram of a differential element of the cable in the plane of interest 

 is shown in Fig. 14. The cable bends and the tension varies along 

 its length so as to keep all the indicated forces in equilibrium. The 

 cable weight acts vertically and the tension forces are directed 

 along the cable axis. The hydrodynamic forces due to the current 

 are resolved into components normal and tangential to the cable 

 direction. These unit forces are represented as follows: 



F(^) = Cn • y pc(Vc sin i^f (48) 



G((j)) = C^ . i pc(V^ cos i^f (49) 



where 



p = mass density of fluid 



c = cable chord length (in current direction) 



and C^, C are appropriate drag coefficients. These coefficients 

 depenci on the cable cross section and surface geometry. 



The sunamation of forces along the direction of the cable 

 axis yields: 



T + G(<^)(1 + €) ds - Wc ds sin (|> - (T - dT) cos (d(|>) = 



For a differential element, d4)-* 0, so that cos (d<|)) -* i.O. This 

 gives the differential equation for cable tension in terms of the inde- 

 pendent variable s, as follows: 



1053 



