Hence, Equation [38] > which is valid for the cable -anchor 

 configuration, can ue used to compute the change in tension 

 above the equilibrium value for any point along the cable for 

 a range of input circular frequencies, cd, and input displace- 

 ments, p. 



NUMERICAL EXAMPLES 



Three mooring cable systems, I, II, and III, shown in 

 Figure 3, are invest! gated utilizing the results developed in 

 the previous sectlon.3. Various simplifying assumptions con- 

 cerning the cable systems are made; however, the physical case 

 of anchoring a ship in deep water will probably lie between 

 the two idealized cases. 



In all three examples the cable is assumed tc be subjected 

 to sufficient tension such that the configuration can be approx- 

 imated by a straight line. Because the sag due &o the weight 

 of the cable has been neglected in this analysis, the computed 

 tension variations probably will be larger than actually developed 

 in the real case. The equilibrium configurations for the three 

 examples are presented in Tables 1, 2, and 3 and Figure 3. 



Equation [25] is used to compute -YP for the examples where 

 the lower end of the cable is fixed and Equation [38] is used 

 for the examples where the lower end is free to move. In these 

 computations, the anchor, chain, and concrete clump which com- 

 prise the last 270 feet of the system, are lumped together and 

 considered as a single mass. The numerical values of the con- 

 stants in Equations [d'o] and [38] were taken a3 



A = 0.785 in 2 



E = Ik x 10 6 psl 



a = 1.68 x 10 4 ft/sec 



Figure h shows how the ratio of dynamic tension to static 

 tension varies as a function of frequency of displacement of 

 the upper end. The calculations are for a 1-f oot-harmcnlc 

 displacement of the upper end for each of the three configura- 

 tions with fixed and with free lower ends. The percentage change 

 in the dynamic towline tension for the three example? subject to 

 1 -foot-harmonic displacement of the upper end 13 shovm' In 

 Figure 5. Since AT varies linearily with displacement, the 

 effect of other displacements can be obtained from these curves 

 by multiplication. In Figures h and 5j separate curves are shown 

 for the tension parameter at the upper and lov/er ends. 



