Kaplan 



been carried out, where comparisons between theory, model experi- 

 ment, and (In some cases) prototype behavior were made (see [8] , 

 [9]). The conclusions of those studies were that linear theory 

 produced good predictions of motion response operators; shallow 

 water effects may be easily Incorporated; the effects of other mooring 

 arrangements (such as the usual catenary form of weighted chain 

 cables) can be represented in linear form and produce results agree- 

 ing with theory, within the range of lower sea states. 



While agreement between theory and experiment was generally 

 obtained for alnmost all conditions, some degrees of freedom of the 

 vessels considered in [8] and [ 9] were not properly predicted for 

 irregular sea conditions. The motions of surge, sway, and yaw 

 exhibited large spectral response characteristics at very low fre- 

 quencies where little (if any) wave energy was present, but close to 

 the natural frequencies of those motions (due to the mooring "spring^ 

 forces). Since these motions are very lightly damped, a very small 

 amount of input excitation Ccin still produce relatively large motions 

 at these low frequencies. There are a number of possible explana- 

 tions for this behavior, but the most plausible one is related to the 

 influence of the nonlinear "drift" forces and moments , which will be 

 discussed in a later section when considering dynamic positioning. 



The theory described here supplements what may be known 

 qualitatively for moored vessel behavior by furnishing quantitative 

 estimates for the motions and their Inter- relationships. While the 

 validity of these analytical resialts for any particular vessel is sub- 

 ject to test, the results for other moored vessels using this same 

 analytical procedure give support to the reliability of the predictions. 

 Thus, It Is feasible to treat all six degrees of freedom of a moored 

 ship In a realistic seaway and obtain results for response character- 

 istics of various motions of the ship and any associated load. 



Considering the results and examples concerning the load- 

 lowering operation, there are two main conclusions. First, motions 

 having amplitudes of oscillation or giving rise to forces and accelera- 

 tions sufficiently high to Influence construction operations may occur 

 under certain of the environmental conditions considered In this 

 study, particularly when loads are lowered by means of a boom In a 

 high sea state. Secondly, the violence of these motions, forces, or 

 accelerations may be significantly reduced by the proper choice of 

 vessel heading relative to the wind, and boom azimuth angle. The 

 latter factor regardless of the sea state, has by far the greater effect 

 In minimizing the energy of the fluctuating tension in the lowering 

 line, the vertical acceleration of the load, and Its three displacement 

 components. These results provide useful Information for conducting 

 operations from a moored ship platform, and hence the capability of 

 obtaining guidelines for operating vessels and performing engineering 

 work at sea is available with the tools of theoretical hydrodynamic 

 analysis presented here. 



1052 



