A detailed exposition of the kinematics of the transverse plane motions of ships is provided, with particular attention to the important process of total transverse acceleration in vessel coordinates. The loci of sway, sway velocity and sway acceleration are shown to follow hyperbolic distributions with respect to elevation in both regular and irregular waves. In regular waves the transverse acceleration in earth-fixed and vessel-fixed coordinates are shown to be congruent with a vertical shift in elevation of g/ω2 = λ/(2π). Expressions are given for the elevations minimizing transverse plane processes in regular and irregular waves. In long waves the elevation minimizing total transverse acceleration in vessel coordinates is shown to be g/ωn2 = g[Tn/ /(2π)]2 below the waterline. This is the roll center, which should be used in the traditional analysis of foundation loads. Its location, far below the keel for most vessels, is surprising. The elevation (OP) of the roll axis, which must be used when solving the one-degree-of-freedom equation for roll, is given and is shown to require hydrodynamic coefficients for sway as well as roll. In general, OP does not correspond to an elevation that minimizes any of the transverse plane processes. The effect of hull form, transverse stability and natural roll period on transverse plane motions are examined in an attempt to resolve the dichotomy of views between those who favor ships with low GMT and long natural roll periods and those who favor high GMT with short natural roll periods. It is demonstrated that large values of the beam-to-draft ratio (6/7) with low natural roll periods are advantageous at modest elevations above the waterline. This explains the favorable offshore experience in vessels meeting this description, such as tugs, supply vessels and fishing vessels. At higher elevations long natural periods are shown to present a clear advantage, which supports the preference for low GMT for large passenger vessels, containerships and ships with deck-loads of logs. The trends identified would seem to support the conjecture that, with regard to natural roll period, there is a "forbidden middle" that should be avoided in design.
Implementation of latching control in a numerical wave tank with regular waves