Kaplan 



only for obtaining phase information. 



The ship is assumed to be placed in a currentless seaway, 

 with no wind effects being considered. This may be somewhat un- 

 recdistic from the practical point of view, but since concern here is 

 devoted only to the motions induced by the seaway, this neglect is 

 reasonable (as discussed previously). The ship is assumed to be 

 moored with bow and stern moorings of conventional line and anchor 

 type. The line and anchor mooring system utilized for this study is 

 a particular system especially suited to deep-sea operations [4] , 

 and utilizes a taut line. Other types of mooring lines can be con- 

 sidered as well, but separate analyses to determine the static 

 orientation, restoring force variations, etc, must be carried out. 

 The extent of linearity for these different mooring arrangements 

 must be determined for use in the present type of analysis. The 

 effects of the moorings will be to provide restoring effects in the 

 particular displacements of surge, sway and yaw, thereby providing 

 "spring-like" terms in the equations for these degrees of freedom. 

 As a result, there are certain natursil frequencies associated with 

 these motions, which do not ordinarily occur in case of free (un- 

 moored) ships. The moorings are assumed to have a negligible 

 influence on the motions of heave, pitch, and roll, which have large 

 hydrostatic restoring effects. 



Following the evaluation of the various motions of the moored 

 ship, equations are formulated to determine the forces in the moor- 

 ing cables, and the displacement of and tension in the lowering line, 

 as a function of the different degrees of freedom of the oscillating 

 platform moored in the seaway. The lowering line displacenaent and 

 tension, which are functions of the ship motions are then related to 

 the seaway and all of the resulting spectra determined. Operations 

 on these quantities provide information on expected amplitudes for 

 particular sea states, and in addition the vertical accelerations of 

 the loads are determined and similarly expressed, where this infor- 

 mation is useful for study of impact of the loads on the ocean bottom. 



IV. EQUATIONS OF SHIP MOTION 



The equations of naotion of the moored ship are derived on the 

 basis of linear theory, with the body allowed to have six degrees of 

 freedona, A right-hand cartesian coordinate system is chosen with 

 the axes fixed in the body, and with the origin at the center of gravity 

 of the body. The x-axis is chosen positive toward the bow, the y-axis 

 is positive to port, and the z-aixis is positive upward. These axes 

 are defined to have a fixed orientation, i.e. they do not rotate with 

 the body, but they can translate with the body. The body angular 

 motions can be considered to be small oscillations about a mean 

 position given by the axes. The dynamic variables are the linear 

 displacements x, y, and z along the respective axes, and the 

 angular displacements 4>> 6 and ijj which are defined as positive in 



1022 



