If the cable has the direction cosines l,m,n{l = cos <i>) in Ref- 

 erence Frame I, the unit vectors of Reference Frame II may be \ijritten 



f = Zi + mj + nk [1 ] 



^ -*- ■*■ "*■ ^ 



s _ i X f _ -nj + mk r2-| 



sin (l> sin </> 



->■->--»• ^ -> ->-->■ „ -»- ->• ^ 



^_ f X (i X f ) ^ i - f • if _ (1 - 1^)1 - Im,] - hik r,-, 

 sin0 sin<^ sin <?!> 



Let the weight in water per unit length of the cable be of magnitude w. Since 

 the weight of the cable acts in the j direction the components of the weight 

 in Reference Frame II are respectively 



Wo = wj-f = wm L4-J 



Wg = wj-s = j^[^ = -w-M. CSC0 [5] 



w^ = w J-t = ^f^ = -wmcot^ [6] 



The equilibrium of forces normal to the cable requires 



S = wn esc 4> [7] 



N = wmcot </> [8] 



so that 



C = ^ , wncsc^ [ya] 



'^ Ipu^d iw^d 



and 



r N _ wm cot <t> ro ■ 



The component of the hydrodynamlc force P and the w^ component of the weight 

 do not cancel but are additive in increasing the tension in the cable. Since 

 the forces acting upon the cable are uniform along the cable, the tension at 

 the upper end may be written 



T = (P + w^)L = (P + wm)L [9] 



where L is the length of the cable. Also, T = D sec ^ , where D is the drag 

 of the cable, so that (P + wm)L = D sec <i> and 



P = ?■ sec ^ - wm= d sec </> - wm, [TO] 



