11G() THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 



covering the bottom, it would seem difficult for them to provide exact 

 enough data for the control of cable laying. 



At the same time we have seen that if the bottom contour is known 

 in advance, then for a given ship speed one can compute the required 

 cable pay-out rate. Also with foreknowledge of the bottom, one can 

 anticipate steep bottom ascents and decrease the ship speed accordingly. 

 Such a purely kinematic attack on the cable laying problem would seem 

 more fruitful than an attack which depends on measurements of ship- 

 board cable tensions. 



Possibly the simplest way of measuring the bottom contour is by 

 means of a fathometer located at the ship. Since the cable ship is nor- 

 mally far forward of the touchdown point of the cable, one could in 

 theory obtain in this manner the reciuired advance knowledge of the 

 contour. In present practice, a taut piano wire is used to obtain the 

 ground speed of the ship. We examine briefly the accuracy of this method 

 in the next section. 



6.2 Accuracy of the Piano Wire Technique 



The taut wire is laid simultaneously with the cable, but under a con- 

 stant mean shipboard tension. If the bottom is perfectly horizontal, the 

 speed of the wire coincides with the ground speed of the ship. However, 

 when the bottom depth is variable and the wire is laid up and down hill, 

 the wire's pay-out speed deviates from the ship speed. By (31), it is seen 

 that the error in the ship speed which is indicated by the wire is just 

 equal to the slack e with which the wire is paid out. This slack, which 

 may be positive or negative, can in turn be estimated by the methods of 

 the previous sections. 



Consider the beginning (denoted by (1) in Fig. 24) and end (denoted 

 by (2) in Fig. 24) of a downhill lay of the piano wire. As before we neglect 

 the tangential drag force. Then, the condition that the tension at the ship 

 remains constant gives, by (21), 



(Tn)i + wh, = (Toh + wh2 , (39) 



where the subscripts 1 and 2 refer to the configurations at the beginning 

 and end of the downhill lay. If e is the average slack or error of the piano 

 wire during the descent, then (1 + e)F is its average pay-out rate, and 

 we have by Fig. 24, 



S, -f (1 -f e)Vt = ^-^^-1^ + .S'2 , (40) 



sm /3 



