Mooring and Positioning of Vehicles in a Seaway 



dT = [ - G(<f>)(l + e) + Wj, sin 4>] ds . (50) 



The summation of forces normal to the cable axis yields: 



F(^)(l + e) ds + Wg ds cos (i> - (T - dT) sin (d^) = 



and with d^ -* , we can approximate sin (d^) by d^. Neglecting 

 higher order terms involving products of differentials , results in an 

 equation for the differential angle: 



d^ = 1 [ F(^)(l + e) + Wc cos 4.] ds. (51) 



The strain, or cable elongation, is obtained from the following simple 

 relationship for an elastic cable material: 



where 



Ag = cable (load-bearing) cross section area 



Eg = effective static elastic modulus of cable material. 



Associated with these equations is the representation of the 

 forces and moments acting on the buoy due to the wind and the cur- 

 rent (not considered here, but discussed in [ 10] from which the 

 present analysis is abstracted). All of these effects are considered 

 to be in equilibrium with the weight, buoyancy, and cable forces. 



All the forces and moments acting on the buoy due to current 

 and wind are considered to be in equilibrium with the weight, buoyancy 

 and cable forces. At the surface buoy we then have: 



Dq + Dg = T cos ^ 



Lg + B(e,h) = W + T sin (j) (53) 



Mj, + Mg = T(i^ + z^^)'^^sin (<^ + 9 - tan |£) + B(e,h)'^(e,h) 



where 



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