A METHOD OP DETERMINING OPTIMUM LENGTHS OP TOWING CABLES 



t>y 



Leonard Pode 



INTRODUCTION 



A problem that arises frequently in connection with the design of 

 towing arrangements is that of choosing the design variables so that the size 

 of equipment and the magnitude of the forces involved are kept to a minimum. 

 Usually the preliminary choice of the design variables has been merely a guess 

 and the improvement of the guess has depended upon the results of extensive 

 exploratory calculations. Tables and charts are presented here which, for the 

 most frequent design problems, will help to reduce the labor of such calcula- 

 tions and to enable the designer to determine optimum conditions in a straight- 

 forward manner. 



STATEMENT OP PROBLEM 



Suppose that it is desired to tow a body at a stated depth, y, using 

 a specified cable. Since the hydrodynamic behavior of the cable may be as- 

 sumed to be known, the length of cable needed to reach the required depth and 

 the tension at the upper end of the cable are determined when the direction 

 and magnitude of the force that the towed body applies to the lower end of the 

 cable are known. The question of interest to the designer is the manner in 

 which the tension at the upper end of the cable, which is the greatest tension 

 in the cable, will vary with the direction and magnitude of the force applied 

 by the towed body. 



A force of given magnitude may best be used to attain depth by ori- 

 enting it as nearly as possible in the direction of gravity because the com- 

 ponent of force perpendicular to the direction of gravity increases the ten- 

 sion in the cable without contributing to the attainment of the required depth. 

 The angle, <t> , that the force applied by the towed body makes with the direc- 

 tion of stream— which is equal, for equilibrium, to the angle that the cable 

 makes with the stream at the point where the cable meets the body— is there- 

 fore made as close to rr/2 as possible. If the downward force of the body is 

 developed by means of lifting surfaces, the angle <t> is limited by the lift- 

 drag ratios which such surfaces can attain; if the downward force is derived 

 from the weight of the body, the angle <j> Q is limited by the relationship of 

 the weight of. the body to its drag. Since the weight of the body is constant, 



