Asymmetric roll center of symmetric body in beam waves

Surprisingly, the so-called roll center is not a concept well defined for rolling ships or platforms that are submitted to a wave field. The paper proposes a definition and shows a methodology to assess this point. For beam wave incidence on a symmetric body, the roll center is not necessarily located at the line of symmetry of this body. For regular waves, the locus of the instantaneous center of rotation is a frequency dependent straight line. This investigation using basic equations of the rigid body kinematics, reports model tests, frequency domain calculations and devises a closed form equation for the instantaneous center of rotation locus. The matching is very clear. For a platform, which will usually operate in beam seas, it does make sense to have non-symmetrical bilge keels width in each board.