Mooring and Positioni^tg of Vehicles in a Seaway 



leading to 



TT 3 I I 



M^ = -J pgR a j Jj (y) - JjCy) I cos cot . (84) 



For the surge force due to waves the pressure component in 

 the axial direction is required, and this is found in terms of the 

 axial gradient of the wave anaplitude record along the disc. For a 

 hull of draft d', the surge force due to waves is given by 



X^ = - 2pgd' ^ f(x) -^ Ti{x,t) dx (85) 



which leads to 



Xy, = - 2pg-rTd*RaJ| (y) cos wt. (86) 



Thus the above expressions complete the representation of the terms 

 required for treating the motion of a disc- shaped buoy in regular 

 waves o 



VIII. MOORING DYNAMICS 



The initial treatment of mooring cable dynamics will be based 

 upon a complete formulation of equations of motion for a continuous 

 line that is assumed to be completely flexible and extensible. The 

 analysis is restricted to two-dimensional motion in a single plane, 

 which is coplanar with the oncoming current, and the velocities, 

 etc. are converted from directions along x- and y-axes (fixed in 

 space) to those along the normal to the cable, which leads to con- 

 sideration of the velocities U (normal) and V (tangential) relative 

 to the cable as basic variables. 



The basic equations of motion in the x- and y-directions are 

 ^^lF= If (T8lTTlil)-^G<^^^)^°^* + F(l+e) sin c{> (87) 



^ w= "li- ("^ eifi+il) +^<^"^^^ ^^^^- ^(^"^^^ ^°^ ^- Wc (88) 



where |j. is the sum of the cable mass and added fluid mass per unit 

 length, when considering an elongated element of the cable, of length 

 (1+e) ds. From geometric considerations 



1063 



