In spite of the aforementioned uncertainties, the basic differential 

 equations have been generally accepted and used, but various agencies 

 have developed different expressions for the hydrodynamic loading forces 

 on an element of cable. The two methods most commonly used by the Model 

 Basin to predict the steady-state characteristics of cable-towed body 

 systems are described in References 1 and 7, and are designated herein 

 as Methods 1 and 2 respectively. The two methods are essentially the 

 same but differ in the loading functions which are used. Both methods 

 resolve the hydrodynamic force into normal and tangential components, 

 as shown in Figure 1. The expressions used for the hydrodynamic force 

 components for each method are compared in Table 1. It may be noted 

 that the tangential force in Method 1 is independent of the cable angle, 

 whereas in Method 2 it is a function of cable angle. 



TABLE 1 



Assumed Expressions for Hydrodynamic Force Components Used 

 in Methods 1 and 2 



Method 



Normal Force 



Tangential Force 



1 

 2 



R sin 2 c{> 

 R sin 2 c}> 



. R f 

 R [0,083 cos c|)- 0.035 cos s 4>] 



The Model Basin has a computer program for calculating the equilibrium 

 configuration of a flexible cable in a uniform stream 8 . The program is 

 based on the differential equations of References 1 and 7 which assume 

 that the velocity at the element is constant and is not affected by curvature 

 of the cable. It further assumes that the cable is inelastic and offers no 

 resistance to bending. When the hydrodynamic forces acting on the 

 cable -body system are known, the predicted configuration may be com- 

 puted to an accuracy of ±0.001 percent for each integration step. The 

 exact configuration, then, is primarily dependent upon the accuracy 

 of the input data used in the program. The computer program is set up to 

 allow a choice of the two methods to predict the cable configuration and 

 towline forces . 



DESCRIPTION OF EXPERIMENTAL EQUIPMENT 



The towcable used in this investigation is shown by Figure 2 and a 

 detailed description is given in Reference 9. It is a 0.350 (±0. 005)-inch- 

 diameter, double-armored, electrical cable which consists of two layers 

 of steel armor strands surrounding an eight- conductor (four coax) 

 electrical core. The under layer of armor consists of eighteen strands 

 with a 2.0 (±0.2) -inch right-hand lay. The outer layer consists of 

 twenty-four strands with a 3.0 (±0.2) -inch left-hand lay. Each strand is 

 0. 0375-inch-diameter, Type 304, corrosion- resistant steel. The cable 

 weighs 0. 169 pound per foot in salt water (70 degrees F) and has a 

 breaking strength of approximately 10, 000 pounds. 



