Then s = ^-^ — x^ Is a unit vector normal to both the cable and the stream, and 

 ^ ^ ^ sin (f> 



n = r X s is a unit vector that is normal to the cable, lying in the plane 



that includes the direction of the cable and the direction of the stream. The 



-► ->• ->■ 

 three unit vectors f , s, and n then define a rectangular Cartesian reference 



frame which shall be called Reference Frame II. When the hydrod3niamic force 

 acting on a unit length of cable is resolved in this reference frame the com- 

 ponents will be designated P, S, and N respectively. 



It is the component N v;ith which the sine-squared law has been as- 

 sociated. The main hypothesis which is being investigated here is that the 



coefficient C = -:; — ^^, (where p is the density of the water, U the speed of 

 n |pU^d 



the stream and d the diameter of the cable) may be written C = C sin^ 0. 

 where C does not vary with <f>. 



The component S is zero for a smooth round cable or for any cable 

 that presents a sjnranetrical profile to the stream. The fact that a stranded 

 cable does not present a symmetrical profile is apparent from Figure 1 , which 

 shows the cross-section of a stranded cable in an inclined plane. It is the 

 existence of this S component which is responsible both for the yawing of 

 stranded cables and for the fact that stranded cables often tow closer to the 

 surface of the waterthan smooth round cables of the same diameter and weight. 



Figure 1 - Profile of a Stranded Cable 



This sketch shows the asymmetrical profile of a l/8-lnoh stranded 

 cable of 7 X 19 construction which Is out in a plane that Is inclined 

 at an angle to the axis of the cable. 



