Figures 33 and 34 Indicate the allowable frequency of an Input oscillation at 

 various amplitudes of this oscillation as a function of the cable length, such that the 

 stipulated maximum dynamic stress is not exceeded. Alternatively, they indicate 

 the maximum amplitude of an input oscillation at a particular frequency such that a 

 maximum dynamic stress Is not exceeded. 



One of the most important problems in the Interpretation of these graphs is the 

 selection of appropriate input conditions, | Uq | and CO, corresponding to the response 

 of the vessel used for the lowering or raising operation of the sea state in which the 

 operation Is carried out. 



It is apparent that the frequency range given In Figures 33 and 34 is far greater 

 than that which would be expected under operational conditions. Data Is available 

 In the literature (Kaplan and Putz, 2 Plerson and Holmes*') on the response of the 

 Cuss-I drilling barge to various sea states. In sea state 5, the range of frequencies 

 of oscillation in heave Is 0.40 to 1.40 radians per second with root -mean -square 

 values of heave of 1. 8 and 1.3 feet at headings of 90 degrees and degrees to the 

 wind respectively. These values imply expected maximum amplitudes of oscillation 

 of 7.2 and 5.2 feet during a 4-hour period on station (Plerson and Holmes). It should 

 be noted, however, that combinations of heave and roll oscillations could easily pro- 

 duce oscillations greater than this If the load-lowering operation is carried out using 

 the boom over the side of the vessel. The above values are used here to illustrate 

 the interpretation of Figures 33 and 34. 



Referring to Figure 33 for the design example using a polypropylene cable. 

 It can be seen that for a heave amplitude of 7.2 feet at frequencies of 1.40 and 

 0.40 radians per second — to cover the entire frequency range — the design dynamic 

 stress will be exceeded at a cable length of less than 200 feet for co = 1.40. For 

 frequencies less than 1.40 radians per second down to 0.40 radian per second. It Is 

 estimated from the curves that the design dynamic stress will be exceeded at cable 

 lengths which gradually decrease from 200 feet. Thus the operation will be unsafe 

 relative to the prescribed maximum dynamic stress for a cable length of less than 

 200 feet. This condition has been fully recognized In the design of various lowering 

 operations conducted by this laboratory. The dynamic stress will then be less than 

 the design stress until the length of the cable reaches a value of approximately 

 5,000 feet. According to the results obtained above the operation will then become 

 unsafe. If the frequency is 1.40 radians per second and the amplitude Is 7.2 feet.* 

 For a frequency of 1.00 radian per second the operation becomes unsafe at a depth 

 of 7,000 feet. The reasons for this result are difficult to visualize, but may be 

 explained from both the mathematical and physical points of view. In terms of the 

 numerical computations carried out as shown in Table VI, the regression of the curves 

 given in Figures 33 and 34 is due to the fact that when the maximum dynamic stress. 



* These comments are based on an approximate Interpolation between the curve 

 labeled 6 feet and 10 feet in Figure 33 for I Uq I =7.2 feet. 



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