Virtual bottom for ships sailing in restricted waterways (unsteady squat)

The focus of this paper is to update the classic criterion for the determination of the safe keel clearance for ships sailing in restricted waterways. Ship׳s dynamics is taken into account by integrating the notion of the unsteady squat. This paper shows the existence of unstable equilibrium position of the ship during heave motion. Furthermore, it proposes a new mathematical expression to evaluate it as a function of canal and ship parameters. It is shown that this unstable equilibrium position can be considered as a virtual bottom for ship. It should not be reached during ship motion in order to avoid grounding. The importance of this result, confirmed both by an analytical model as well as by a numerical model with Finite Elements Method, lies in the reduction of the safety margin actually allowed for pilots. So this result points out the knowledge of a virtual bottom that could lie above the real nautical bottom.