ABSTRACT 



Supplementary tables of the cable functions used for determining the shape 

 and tension of a flexible cable imnersed in a uniform stream are presented. The 

 tables cover the range of critical angles from to 10 degrees in increments of 

 one degree. In the neighborhood of the critical angle, values of the functions are 

 given at intervals of 0.5 degree. 



INTRODUCTION 



An extensive set of tables of functions which may be used to compute the configuration 

 and tensions in a flexible heavy cable immersed in a uniform stream has been published in 

 TMB Report 687. These tables give values of the functions for critical angles from to 180 

 degrees in increments of 5 degrees. However, it has been found that problems involving 

 critical angles in the range from to 10 degrees occur most frequently and that tables cover- 

 ing this range in more detail would be desirable. Therefore, the present supplementary work 

 was undertaken. It provides tables for critical angles in the range from to 10 degrees in 

 increments of one degree. More closely spaced intervals of the independent variable cfy in the 

 vicinity of the critical angle ^^ are also provided. 



DEFINITION OF THE CABLE FUNCTIONS 



The theory of flexible cables immersed in a uniform stream and the application of the 

 cable functions is given in TMB Report 687 and will not be repeated here. The notation used 

 in this supplement is identical to that used in Report 687 but is repeated for convenience as 

 is Figure 1. Equations [16a, b, c, d] of Report 687, which define the cable functions t, a, ^, 

 and T] are also repeated as follows: 



I 



cos (h 



f + w sin <^ 



^2^_^L : d^ [la] 



sin ^ |sin cf)\ + w cos 



J - sin |sin cf)\ + 



w cos 



[lb] 



1 



cos (h r, , 



^ d(f> [Ic] 



- sin (p |sin (p\ + w cos 

 



