Appendix A 

 AN APPROXIMATE STATIC ANALYSIS OF THE SINGLE GUIDELINE SYSTEM 



The orientation of the guide frame depends only on the relative 

 position of the payload and the guideline at the depth in question. 

 Figure A-1 is a plan view of a guideline system at the guide frame. The 

 projected positions of the payload and the guideline supports on a hori- 

 zontal plane are Pq and G^, respectively. The payload position after 

 horizontal displacement is P. The position of the guideline in zero 

 current is G-^ and, if current is present, G. The guide frame is assumed 

 to be pointing to North at the surface. The current direction is \l) from 

 North. The current speed is assumed to be uniform throughout the depth. 

 The guideline anchor has a horizontal offset of L„q in the direction of 

 (fi from the North. The coordinate system on the horizontal plane has an 

 origin at Gq as sho^^ra in Figure A-1 . 



The final orientation of the guide frame may be approximated by the 

 expression (see Figure A-1) 



tan e = 



Xp 



^P 



where 6 = angular displacement of guide frame from North 

 Xp = £p^ sin ^ 



Yp = So + ^pc ^°s * 

 Xg = £gQ sin (f) + £.g^ sin ij; 

 Yg = £gQ cos (|) + £g(, cos \l) 

 S = guide frame length 

 a = horizontal displacement 



The first subscripts p and g indicate the payload at the end of lift line 

 and the guideline, respectively. The second subscripts o and c indicate 

 displacements caused by anchor offset and by current force, respectively. 



All external forces acting on the lift line and the payload are 

 shown in Figure A-2 on a vertical plane. Since the current drag is 

 usually small when compared with the total weight of the payload and the 

 lift line, the curvature in the catenary is small. For a first approxi- 

 mation, the lift line is assumed to be a straight line. The total moment 

 about point is zero, and the payload displacement is 



27 



