Mooring and Positioning of Vehicles in a Seaway 



Newman's method [ 17] » based on slender body theory, does 

 show some comparison with very limited experimental work for 

 lateral drift force and yaw moment which indicates rough agreement. 

 His results for longitudinal force, for which no experimental com- 

 parison is given, indicate that this force in head seas generally 

 exceeds the lateral forces for a given wave length condition. Further- 

 more, these results indicate that the maximum lateral force occurs 

 in bow waves (P «^ 45°), with the force going to zero in both head and 

 beam waves . 



The results of Hu and Eng [16] include the effects of sway, 

 yaw and roll motions, with no influence of heave and pitch included 

 (as to be expected for thin ship analysis) while Newman [ 17] only 

 accounts for heave and pitch motion effects without any influence of 

 the three lateral degrees of freedom. Thus there is a question as 

 to the proper representation of the drift forces that would reflect 

 the influence of the important dynajnic motions that produce these 

 forces. The analysis by Maruo [15] presents a final expression for 

 the average lateral drift force in beam seas that depends upon the 

 reflected wave cimplitude , which in turn is defined in terms of the 

 relative motion between the incident wave and the resulting heave 

 motion. The presence of sway motion has no effect on the lateral 

 drift force since the body acts like a wave particle in beam seas 

 and no relative motion occurs (to that order), A similar result is 

 indicated for submerged cylinders in the work of Ogilvie [ 18] , 

 where the average lateral force identically vanishes. 



In all of these hydrodynamic studies, the force is found to be 

 proportional to the square of the incident wave amplitude, since the 

 nonlinear pressures are represented in terms of squares of generated 

 wave amplitudes, squares of fluid velocities , and products of first 

 order oscillatory displacements with derivatives of fluid velocities.*- 

 While the previous hydrodynamic analyses have been concerned with 

 the average drift force for a regular sinusoidal wave, it is Important 

 also to determine the actual time histories of these forces, especially 

 for the case of an irregular incident wave system. In that case it is 

 expected that the drift force will be a slowly varying function, in 

 terms of the frequencies contained in the defining incident wave band- 

 width, and it is of interest to determine the basic representation of 

 the forces, the response of floating vessels to such forces, the 

 statistical properties , etc. 



In order to illustrate the basic characteristics of these forces, 

 particular attention will be given to the case of the lateral drift force 

 acting on a vessel in beam seas. Using the results of Maruo [ 15] , 

 the later drift force acting on a cylinder (in the two-dimensional case) 

 is given by 



^ = i PgA'|z-ri|' = ^ Pga'A.'l ^- 1 |' (123) 



1069 



