Parasitic Motions and Capsize Safety of a SWATH-Type Ship
Authors: Smith S.N. 
Published: October 2008

ABSTRACT
This paper presents the experimental results of an investigation into the 'parasitic' motions (parametric rolling in head seas, sub-harmonic rolling in beam seas) and capsize safety of a three-hulled SWATH*-type vessel. The results illustrate the significance of the 2:1 ratio for the heave and roll natural frequencies and the important influence of the hull-shape above the still-water line. Some evidence on the effect of damping is given. Time histories illustrate the build-up of roll motions in regular head seas and intermittent rolling in irregular seas. The results indicate that there is a 'saturation' level, influenced by damping, for the 'parasitic' motion but that the wave frequency motion continues to increase with wave amplitude. The parasitic motions never led to a capsize and, furthermore, it was observed that at large wave amplitudes the parasitic motion could cease completely.
Although the results are limited to only one particular novel configuration of vessel they also shed some light on similar types of motion for other floating vessels.

INTRODUCTION
SWATH vessels have attracted considerable interest for use as ferries, for transporting personnel offshore, as research vessels and for military and other uses. While much of the interest in SWATHs is due to their proven excellent low motion response it has been observed by the author1 that under certain extreme design conditions undesirable parasitic motions can occur. (Herein the term 'parasitic' is used to describe motions at frequencies other than the frequency of encounter). Nakamura2 has also apparently observed such motions in SWATHs, they are known to occur for conventional ships3, and have been investigated for offshore structures such as Tension Leg Platforms4.
* SWATH is an acronym for Small Waterplane Area Twin Hull but the term is used in this paper to include a triple hull vessel of the same family.
Paulling and Rosenberg5 investigated 'unstable' motions for ships resulting from non-linear coupling and conducted experiments on a roll-heave system by forcing the ship model in heave and producing a roll motion at half the forced frequency for certain amplitudes and frequencies corresponding to unstable regions on the Mathieu stability chart. Further extensive experiments in San Francisco Bay3 identified parametric rolling (also called 'low cycle resonance' or 'auto parametrically induced rolling) as an important capsize mechanism.
Theoretical work such as in Refs. 6 and 7 hills also been conducted showing, for instance, the important effect of the 2:1 ratio of the pitch or heave natural frequency to the roll natural frequency and also the occurrence of a 'saturation' phenomenon.

THE MODEL, EXPERIMENTS, AND EXPERIMENTAL CONDITIONS
The model, Fig. 1, was a model of a design proposal for a small three-hulled SWATH inshore research vessel. The model was tested at zero speed in head seas for a number of conditions involving different above-water hull shapes i.e. flared columns, Fig. 2, and two different damping ratios resulting from the inclusion or omission of a flat horizontal brace between the two aft hulls.