DYNAMICS AND KINEIVIATICS OF SUBIVLIRINE CABLE 1169 



knowledge of the frictional properties of the bottom. For an H value of 

 25.0 degree-knots, (37) indicates that suspensions will occur for ship 

 speeds V greater than V = 25.0/7, where V is in knots and the ascent 

 angle 7 is in degrees. Hence, for a typical laying speed of 6 knots, ascent 

 angles greater than 4.2 degrees will cause suspensions of the piano wire. 

 These magnitudes indicate that suspensions of the piano wire probably 

 actually develop in practice. 



It is seen from Fig. 25 that for the usual small ascent or descent angles, 

 the piano-wire technique is quite accurate, while for large bottom slopes 

 it can be considerably in error. Again, however, if the bottom contour is 

 known in advance, these errors can be estimated in the cases plotted in 

 Fig. 25 and therefore can be corrected for. In this manner, the piano 

 wire could be improved to give accurate ground speeds in all two-dimen- 

 sional situations, with the exception of the case of a suspension caused by 

 a too steeply ascending bottom. Such suspensions can be avoided only 

 by maintaining a sufficiently slow ship speed. However, as seen by the 

 small computed H value of 25.0 degree-knots, the ship speeds recjuired 

 to avoid piano wire suspensions on uneven bottoms are probably pro- 

 hibitively slow. Hence, for steeply ascending bottoms it is likely that 

 some other means of determining the ship ground speed is necessary. 



VII. THREE-DIMENSIONAL STATIONARY MODEL 



7.1 General 



Thus far we have assumed that the cable lies entirely in the plane 

 formed by the ship's velocity vector and the gravity vector. Because of 

 the symmetry of the cable cross-section, this assumption seems reason- 

 able.* However in certain cases, as for example in the presence of ocean 

 cross-currents, the assumption of a planar configuration is clearly un- 

 tenable. We consider therefore the case where the cable configuration 

 is not necessarily planar but is still time independent with respect to a 

 reference frame translating with the constant velocity of the ship. In 

 analogy with previous terminology, Ave call this the three-dimensional 

 stationary model. 



Assume there is a constant velocity ocean current in each of a finite 

 number of layers. Let the vector Vw denote the ocean-current velocity 

 in a reference layer. In the stationary situation the velocity of the cable 



* Because of asymmetries caused by the helical armor wire or because of minor 

 out-of -roundness, it is conceivable that a sidewise drag force might develop which 

 would cause the cable to move out of the ship's velocitj'-gravitN' phme. For a re- 

 port of experimental observations of such jawing in wire stranded cables, see Ref- 

 erence 11. 



