Righting moment is the actual force tending to rotate a heeled ship back toward upright — the practical, force-based expression of a vessel’s stability at any given angle of heel.
How Righting Moment Is Calculated
Righting moment = Displacement × GZ (righting arm)
Where GZ is the horizontal distance between the vertical lines of action of the ship’s weight (acting through G) and its buoyancy (acting through the shifted B) at a given angle of heel. A larger GZ, at the same displacement, produces a larger righting moment and thus a stronger tendency to return upright.
Righting Moment vs GZ
- GZ (righting arm) — a distance measurement, describing the geometric lever at a given heel angle
- Righting moment — the actual rotational force, obtained by multiplying that lever (GZ) by the ship’s displacement
GZ curves are typically plotted showing how GZ (and therefore righting moment, since displacement is constant for a given loading condition) changes across a range of heel angles — this curve is a core tool in stability assessment.
Why This Matters Practically
The shape of the righting moment/GZ curve across increasing heel angles reveals critical stability information — the maximum righting moment, the angle at which it occurs, and the angle of vanishing stability (where righting moment drops to zero and the ship would no longer naturally return upright) are all read from this curve during a stability assessment.
Exam Relevance
Righting moment calculations and their relationship to the GZ curve are core Ship Stability topics, extensively tested in deck officer competency exams, particularly at Chief Mate and Master level.