The data from the DTNSRDC towing experiments are compiled in Table 3.2. In addition to the 

 kind of results already discussed, these experiments reveal a number of interesting phenomena. Con- 

 sider first the data from experiments 10, 7 and 23 in the table. These measurements were obtained on 

 the Double Armor Steel Cable at a relatively low tension, T = 289N (65 lb); this condition 

 corresponds to a slack cable (see Appendix B). The critical tension H below which slack cable effects 

 become important is given by the equation 



//„„= 0.93 (PF2£^) 1/3, (3.1) 



where W is the total weight of the cable in water, E is Young's modulus of the cable material and A is 



the cable's cross-section area. These parameters are all known for the case of the Double-Armored 

 Steel (DAS) cable. The computed and measured natural frequency-tension behavior is shown in Fig. 

 3.9. The critical tension //„,, is in the range 756 to 1112N (170 to 250 lb) based on the EA values 

 given in the figure, so that the conditions for runs 10, 7 and 23 fall well within the slack cable regime. 

 The natural frequency of the DAS cable in water is /„ = 4.2 Hz from Fig. 3.11, which falls within the 

 frequency "crossover" range enclosed by the dashed lines in the figure. This modal crossover is a com- 

 plex phenomenon associated with the dynamics of slack cables with small sag-to-span ratios. At the 

 crossover three modes of the cable have the same natural frequency and include a symmetric in-plane 

 mode, an anti-symmetric in-plane mode and an out-of-plane or sway mode. The symmetric modes con- 

 tain an even number of nodal points along the cable while the anti-symmetric modes contain an -odd 

 number of nodes. The dynamics of slack marine cables are discussed further in Appendix B of this 

 report. 



It is sufficient to note here that although the results of runs 10, 7 and 23 fall within this complex 

 regime, the transverse vibration amplitudes for these runs are comparable to those measured under taut condi- 

 tions. The strumming waveform contains an appreciable in-line component at the transverse vibration 

 frequency and there are large phase differences between the in-line and transverse components. Small 

 or non-existent phase differences were exhibited during the taut cable strumming experiments. 



56 



