4r pAlU I 



^ ' °' (11) 



and 



I' 

 max 



377 Mq 



L^d 



^oP 



(12) 



In the A. D. Little report. Equation 7 together with Equations 8, 9, and 10 

 was solved by use of a digital computer to give the maximum dynamic stress as a 

 function of the nondimensional frequency to' for various values of jS and fi- A 

 similar procedure was adopted in this report for two reasons, firstly to investigate 

 the variation of stress over a wide range of to', jS, and pL, and secondly as a means 

 of providing the basis of a design procedure for cables used for lowering or raising 

 heavy loads to or from the deep ocean floor. 



The cable and load system considered herein is a part of the overall lowering 

 system consisting of the vessel from which the operation is performed, its response 

 to the wave action present during the lowering or raising process, and the resulting 

 oscillations of the cable and load. Within existing theoretical limitations of knowl- 

 edge about waves and ship motions, and under the restrictions of a linear theory, the 

 problem of the response of a ship or platform to a particular sea state has been solved 

 in terms of certain probabilistic models by Kaplan and Putz.^ Pierson and Holmes^ 

 in a note on the engineering applications of the Kaplan and Putz report outlined a 

 procedure for the determination of the response of a drilling barge to sea states 3, 4, 

 and 5. The results are obtained in terms of the probability of occurrence of various 

 amplitudes of motion in heave, surge, sway, yaw, pitch, and roll. The Cuss-I 

 ocean-bottom drilling barge was used as an example, but the calculations as carried 

 out by Kaplan and Putz may be applied to other ships or moored platforms, given the 

 use of a digital computer. 



Details of the program, which was written for an IBM 1620 computer, are 

 given in Appendix C. For the purposes of this analysis, the calculations were 

 divided into sections based on the relative values of to' required for prototype 

 computations. 



Equation 6b relates the required range of co' to the length of and velocity of 

 sound in the cable. It is assumed that to, the frequency of oscillation of the cable- 

 suspension point, has a maximum value on the order of 2. 00 radians per second and 

 that the maximum length of the cable is 20,000 feet. Then the required range of co' 

 is determined by the velocity of sound, c, in the cable. For steel and polypropylene 

 cables, c is approximately 12,000 and 2,000 feet per second respectively, resulting 

 in maximum nondimensional frequencies of 3.33 and 20.00. 



