The exponents are small ccsapared to unity and can be expanded 



1 - c - ScDx/TqCOs^ "... 

 ^^^(®-^^ = 1+ c+ 2cDx/ToCOS0+ ... 



1-c 

 = 3^(1 - J+cDx/(l-c2)To COS0... . 



Using a first order expression for sin(Q-0) we have 



. Hi 1-c 

 sinB = - — 



1+c 

 and 



o — 

 Q = itcDx/T^Cl+c) cos^ . 



The dependence comes through the factor c/(l+c) cos which can 

 be reduced, on assuming that Oq is small but ^ is not, to the 

 value (l+sin0)/i4-; hence: 



d = Dx(l+sln0)/To 



is the equation defining the shape of the cable. Since is 77«7° 

 in our chosen example we see that the total cable offset is 

 nearly doubled when the cable weight is included in the calculation. 

 The predicted offset is now: 



Y = DX^(l+sin0)/2TQ = 11 ft. in the example. 



The angle of drag on the aoachor is about one degree from the 

 vertical. 



IV. DISCUSSION 



The rather strong dependence of the shape of the anchor line 

 on the relatively small buoyancy/weight forces acting on the cable 

 itself appears surprising. Evidently, the shape of the cable must 

 be viewed as i«,ther weakly enforced by the cable tension and side 

 thrust forces acting alone. It is apparent that minimization of 

 the offset can be accomplished by use of self -buoyant cable or 

 cable with many small buoyant bodies attached (provided they do 

 not increase the drag appreciably). Weighting the cable by attach- 

 ing, for example, heavy electrical cables would greatly increase 

 the offset distances. 



291 



