Kaplan 



smaller magnitude than the linear wave force, produce large motions 

 of moored vessels by causing resonant responses with the low fre- 

 quency modes introduced by the moorings. 



If the two responses given in Fig, 15 and 16 were linearly 

 combined, as in the realistic case at sea when both forces are 

 generated simultaneously, the total output would represent the actual 

 motion of the moored vessel. The resulting large motions would 

 cause significant stretching of the mooring cables, leading to larger 

 forces in the cables than indicated by the linear wave effects above 

 (e.g. as shown in Fig, 13). Thus proper consideration of the non- 

 linear wave forces and their influence must be included in any 

 analytical estimation of expected motions and forces of moored 

 vessels, thereby requiring further effort at understanding and simu- 

 lating these effects. 



As an aid in obtaining further insight into the characteristics 

 of the lateral drift force in this case, an evaluation was made of the 

 power spectrum of this force using the expressions given in Eq. (136) 

 for the part that represents the random variations of this force 

 about its mean value (the convolution integral term). The result 

 of this evaluation is shown in Fig. 17, and when considering the 

 effect of the low pass filter, all values for w > 1.0 will be eliminated. 

 Thus it can be seen that the drift force itself is concentrated at low 

 frequencies, and that the response of a dynanmic system with a very 

 low natural frequency (i.e. the ship sway motion) will result in a 

 response spectrum concentrated at an even smedler low frequency 

 band. This is what is usually found in the results of model tests and 

 full-scale experience, and thus an explanation is provided by the 

 preceding analysis. 



X. APPLICATION TO DYNAMIC POSITIONING 



When considering the case of dynamic positioning, various 

 forces act on a free vessel in the open sea that cause it to move from 

 its required position. These forces are the relatively steady forces 

 due to wind and due to current, the oscillatory-type forces due to 

 waves and the drift forces. The wind generates forces and moments 

 because of its impingement upon the above water surfaces of the hull 

 and superstructure, while the current forces act on the underwater 

 hull (and any submerged drilling equipment, if that is the purpose for 

 the vessel). These steady forces can be overcome by the generation 

 of steady forces by some type of thruster mechanism that will act to 

 maintain the ship more-or-less in its desired location. 



The OS dilatory- type forces due to waves are very large, and 

 no force-generating system installed on a vessel is expected to be 

 able to overcome such effects. The ship will therefore oscillate 

 "back- and- forth" in response to these large wave forces with 

 essentially no net deviation of significance from its average position. 



1076 



