Glossary term
Righting Arm
Lever arm between buoyancy and weight forces that creates a righting or overturning moment for a heeled floating body.
Definition
quantityRighting arm is the horizontal lever arm between buoyancy and weight forces for a heeled floating body.
Righting arm, commonly written GZ, determines the righting or overturning moment of a vessel or floating platform at a given heel angle. The righting-arm curve is central to intact and damaged stability because it shows reserve stability, maximum righting ability, range of positive stability, and sensitivity to loading condition.
Righting arm is the lever arm that creates a moment between the upward buoyant force and the downward weight force when a floating body is heeled. It is commonly written as GZ. If the lever arm tends to return the body toward upright, it is a righting arm. If it tends to increase heel, it is an overturning arm.
The righting moment is:
where \Delta_m is displacement mass, g is gravitational acceleration, and GZ is righting arm. For small heel angles, righting arm can often be approximated by:
where GM is metacentric height and \phi is heel angle.
Engineering use
The righting-arm curve shows GZ over a range of heel angles. It is more informative than a single initial stability value because it shows maximum righting arm, angle of maximum righting arm, area under the curve, downflooding limits, and range of positive stability.
Righting-arm review is used for vessels, offshore platforms, pontoons, barges, floating cranes, and damaged-condition analysis. It depends on hull form, displacement, center of gravity, free-surface effect, openings, deck immersion, flooding, cargo shift, wind heel, and operating condition.
Common mistakes
A common mistake is using a small-angle approximation at large heel angles. Another is reviewing a righting-arm curve without checking downflooding openings, freeboard, damage condition, or operational loads. A strong righting-arm review states loading condition, displacement, center of gravity, tank status, free-surface correction, water density, heel range, and acceptance criteria.