APPENDIX 1 
THE CONFIGURATION AND TENSION OF A LIGHT FLEXIBLE 
CABLE IN A UNIFORM STREAM 
The problem of determining the shape and tension of a light flexi- 
ble round cable in a uniform stream was treated in a previous report (4). 
The same problem is treated here, but a modified law due to Reber (5) for 
the hydrodynamic force acting on an element of cable is assumed. The weight 
of the cable is neglected. The quadratures that arise in the solution of the 
differential equations that describe the cable configuration and tension 
thereby become explicitly integrable, so that the configuration and tension 
can be expressed by functions that have been tabulated. Consequently the 
results are easy to apply to problems involving cables whose parameters dif- 
fer from those of a round cable, provided, of course, that the same law of 
force holds. In particular, the method can be applied to problems that in- 
volve faired cables. 
The hydrodynamic force acting on an element of cable is assumed to 
lie in the plane containing the direction of the stream and the direction of 
the element of cable and is assumed to depend only on the angle between these 
directions. Consequently the entire configuration of the cable lies ina 
plane. 
The following law of force is assumed; see Figure 16. The hydro- 
dynamic force acting on an element of cable is considered to consist of two 
parts: 
1. <A profile drag that acts normal to the cable and varies as the 
square of the sine of the angle that the element makes with the stream. 
2. A frictional drag that acts in line with the stream and has a mag- 
nitude that is independent of the angle that the element makes with the 
stream. 
Choose a point O on the cable as origin of a rectangular coordinate 
system; see Figure 1/7. In general, the angle to the stream and the tension 
in the cable at this point will be known. The X-direction is taken as the 
direction of motion of the cable. The Y-direction is taken as positive to- 
ward that side of the x-axis wnich is reached by proceeding along the cable 
upstream from the origin, O. An arbitrarily chosen point P on the cable is 
thus assigned coordinates 2, y. 
When the cable forms a loop and the origin of the coordinate system 
is chosen as the point where the cable is normal to the stream, any movement 
