Experimental and Theoretical Study of Motion
Authors: Muga Bruce J. 
Published: October 2008

ABSTRACT
A 100-ft-square construction-type platform excited by unidirectional random surface gravity waves was studied in the field, at reduced sr.ale in the laboratory, and by using the linear theory of rigid ship's motion. The platform was spread-moored in about 165 ft of water in the open Pacific Ocean. Water-level variations at three locations, ship rotations and accelerations, mooring forces, and wind velocity were measured in sea states 2 and 3 [Neumann wind model]. A sea state 4 was simulated in the laboratory. Three recordings each [representing nearly beam-on, quartering, and stern-on seas] of the prototype and model tests were analyzed using time-series techniques to provide amplitude-response operators for all of the ship's motions and mooring forces. The amplitude-response operators were computed from a linear theory based on the slender body approximation. The in-line coupled equations of motion are formulated for the 6° of freedom and solved literally and numerically. The results in the form of complex-response operators are compared with those obtained from the prototype and model measurements. Generally, the agreement in both amplitude and phase is excellent for the surge, sway, roll, heave and pitch motions. Discrepancies which are found to exist for certain heading and wavelength or wave frequency combinations are easily explained by the presence of crosscoupling terms or values of damping coefficients.
It is found that the linear theory of ships motion using the slender body approximation is an adequate tool for predicting the behavior of moored platforms in sea states of up to 3.

INTRODUCTION
Ships of conventional design seldom operate at practically zero speed in significant waves. As a consequence, only a trivial amount of data has been published on the motions of ships at zero speed. Zero-speed studies of models in the laboratory are difficult to conduct because of the requirement of eliminating wave reflections from the tank sides. Data on the behavior of moored ships, barges and special purpose platforms is scarcer even than that for models. Nevertheless, the recent and continuing demands for ocean construction underline the need for knowledge in this area. The present study is intended to contribute pertinent information.
Briefly, the present study consists of:Analysis of the measurements of the motions induced on an instrumented prototype barge by irregular waves as moored in the open Pacific Ocean in approximately 165 ft of water off San Clemente Island.Analysis of the measurements of the motions induced on a dynamically similar reduced scale model barge by irregular waves.Determination of the motion response of the barge to representative sea states by application of the linear theory of ships motion.Selected comparisons of the results obtained from 1, 2 and 3 above.
Interest usually centers on the forces induced in the mooring lines. These forces may be obtained from the motions, once the latter are determined.

Prototype
The craft studied is a special purpose construction-type platform designated as Fishhook, as shown in Fig. l. The hull outline is that of two standard [34 ft x 110 ft]