Hydrodynamic Coefficients of Mooring Tower
Authors: Chakrabarti S.K. , Cotter D.C. 
Published: October 2008

ABSTRACT
Wave tank tests have been performed on an Articulated tower in order to determine the hydrodynamic coefficients associated with the tower. The tower was a uniform diameter rigid cylinder and incorporated a Localized Load sensing device. It was tested in three different phases:fixed in regular waves,mechanically oscillated in still water, and (J) free to move in regular waves.
Thus, different forma of the Morison equation could be compared. The forces on the small Load sensing segment were measured and the coefficients were correlated with Local values of RC and Re. It is found that the data for hydrodynamic coefficients for the fixed cylinders in waves and the mechanically oscillated cylinder in still water are reasonably applicable to the articulated cylinders in waves.

1. Introduction
The determination of wave loads on offshore structures is based on two major techniques. For large structures, the scattering of the incident waves is considered and a diffraction theory is employed. The wave loads on small members of an offshore structure are generally determined by applying the Morison equation. This equation separates the loads into inertia forces and drag forces. The coefficients associated with these two components of forces are determined experimentally. Many laboratory tests have been conducted in order to evaluate these coefficients. Thesetests have established that the inertia and drag coefficients are functions of the Keulegan Carpenter (KC) number and Reynolds (Re) number (aswell as roughness parameter). One of the drawbacks of laboratory tests is the limited range of Re that can be attained. Nevertheless, these data clearly show the relationship of these coefficients with KG and Re numbers and are useful in the design of offshore structures.
There have been two general types of tests performed to determine hydrodynamic coefficients. Example of this type of test is reported by Chakrabarti (2) in which the hydrodynamic coefficients are given as functions of KC. The second consists of oscillating structures in still water. This type of test has been performed by Garrison, et ale (5) who provide the values of inertia and drag coefficients as functions of KG and Re. Equivalently, water is oscillated harmonically past a fixed structure. Several investigators have followed this method, e.g. Sarpkaya (6) and Bearman and Graham (1). The advantage of mechanical oscillation over oscillatory waves is that the experiment may be more carefully controlled and, thus, the accuracy of the results improves. However, the application of these results to the case of structures in waves is questioned because of the presence of a free surface in waves and the vertical variation (three dimensionality) of the water particle kinematics.
When a structure is moving in waves, the force and the motion are dependent upon the water particle kinematics as well as the velocity and acceleration of the structure itself. In this case, several alternative forms of the modified Morison equation are used. However, because of the lack of data in this area the hydrodynamic coefficients for the analysis of such problems are chosen from studies similar to the ones described in the preceding paragraph.