SUMMARY 

 MOORING DYNAMICS SEMINAR McCreight 



The principal question considered during the discussion of the assembly and 

 evaluation of consistent mooring models concerned inclusion of slowly-varying drift 

 forces into the time-domain model. It was quickly agreed that direct evaluation of 

 the double convolution integral model is far too expensive computationally for use 

 in a practical model. Newman's single summation approximation using the steady 

 drift force data appears to be a good model for time-domain simulation of the slowly- 

 varying drift force. 



There are several problems in applying this model, aside from obtaining the 

 steady drift force data in the first place. The principal difficulty is that the 

 coefficients n'^Mwn.'tOn) depend on the first-order motions of the ship, which in 

 turn are affected by the drift force which causes the stiffness and geometry of the 

 mooring system to change as the ship moves in response to the drift forces. The 

 variation of the phase of the wave components with position must also be accounted 

 for. Muga stated that in his experience the drift motions do not change the first- 

 order oscillatory motions sufficiently to significantly affect the results. He 

 attributes this to the relative importance of the diffraction and radiation potentials 

 for the slowly-varying drift force. In general, however, we must allow for the 

 possibility of these effects. There is some data from Stevens Institute for a 

 Series 60 hull which shows quite large differences between drift forces for the 

 fixed and free hull cases, and consequently if the first-order motions are affected 

 by the drift motions there will be a problem if this effect is neglected. 



Methods of including this effect we.re discussed. One approach is an iterative 

 calculation in which the drift force in a given iteration is calculated based on 

 the first-order motions from the previous iteration. This would be a .qui te expens i ve 

 procedure, and convergence is an open question. 



Pauling proposed a method in which time histories of the slowly-varying dJ-ift 

 force are precomputed for a grid of ship positions (surge, sway, and yaw). During 

 the actual run, the slowly-varying drift force would be interpolated using these 

 precomputed time histories. This approach would also avoid the di f f i cul ty of 

 extracting amplitude and phase for each component of the linear response, which 

 is the form in which the first-order responses are actually required as these 

 responses would be computed in the frequency domain using the existing linear 

 frequency-domain model. A possible drawback is that an excessively fine grid may 

 be required for accurate interpolation, which would increase the number of time 

 histories to be precomputed. It is otherwise a rather attractive approach. 



A direct method requiring neither iteration nor multiple precomputed drift 

 force time histories would be very desirable for those cases in which the drift 

 motions do affect the first-order motions. 



The possibility of a second-order frequency domain simulation as an alternative 

 to the time-domain simulation was discussed. If it is possible to extend the 

 linearized cable dynamics model to compute the second-order response to two 

 simultaneous sinusoidal incident waves,' this could be combined with the second-order 



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