On the Slow Motions of Tankers Moored to Single-Point Mooring Systems
Authors: Wichers J.E.W. 
Published: December 2007

This paper discusses dynamic stability and natural frequencies of the modes of motions of a tanker in the horizontal plane, including the effect of system parameters. A procedure is described to obtain practical values of added mass and damping to calculate stability and natural frequencies. Calculations compared with results of model tests show reasonable agreement.

Introduction
A single-point mooring (SPM) system used by a tanker generally is designed for a maximum operational seastate condition. The sea state at which the down-time starts (disconnecting bow hawser and floating hoses) is determined for the most part by the force level in the bow hawser.
The behavior of a tanker moored to an SPM system is determined mostly by the slow motions of the tanker in the horizontal plane. Because of this slow-motion behavior (fish-tailing and galloping) of the tanker, a slowly varying force occurs in the bow hawser. Superimposed on this force in the hawser are the forces caused by buoy and tanker motions with wave frequency. The combination of these forces can lead to high peak loads in the bow hawser force.
These phenomena that occur while the tanker is moored are complicated and will be influenced by many parameters, such as the size of the tanker and its loading parameters, such as the size of the tanker and its loading conditions, the elastic properties of the buoy and bow hawser, the length of the hawser, and the forces on the vessel exerted by wind, current, waves, astern propulsion, and the underkeel clearances. propulsion, and the underkeel clearances. Model tests were conducted to illustrate slow-motion behavior in the horizontal plane of a ballasted or fully loaded tanker moored to an SPM system with steady wind and current and irregular waves. The behavior of the ballasted tanker is shown in Fig. 1 and that of the fully loaded tanker in Fig. 2. Weather conditions are given in the figures.
In Figs. 1 and 2, the positions of the tanker are shown at the times that maximum bow-hawser forces occur. The times at which peak values occur also are indicated. For some oscillations, the registration of the force in the how hawser as a function of time is shown in Fig. 3. Spring characteristics of the hawsers were nonlinear. Compared with those induced by the ballasted tanker, the hawser loads of the fully loaded tanker are lower. Also, me amplitude and frequency of the slow motions for the fully loaded tanker are smaller.
Hermans and Remery showed that the slowly oscillating character of the surge motion of a moored vessel in head waves (one-dimensional direction) is in resonance when wave groups encounter the vessel with a period near the natural period of the mooring system. Pinkster found that in the same sea state for a vessel moored in head seas with a linear mooring system, using different values for the mooring stiffness, the low-frequency surge motions were resonant, demonstrating that low-frequency wave excitation in irregular waves includes the entire range of normal frequencies of a moored vessel. Both examples dealt with vessels having 1 degree of freedom only. A vessel moored to an SPM, however, has degrees of freedom for horizontal motions of surge, sway, and yaw.
When solving the general SPM problem, it is necessary to knowthe state of the dynamic stability andthe range of the natural frequencies of these modes of motions in the horizontal plane of the tanker in steady conditions.
JPT
P. 947