Vessel Metacentric Height and Righting Arm

GM is KM minus KG: KM comes off the hull's hydrostatic curves at the loaded draft and is a property of the hull form, while KG is the vertical centre of gravity of everything aboard and is the number a refit changes. Because GM is a DIFFERENCE between two numbers of similar size, a modest change in KG is a large percentage change in stability -- which is why a refit adding a few hundred pounds high can matter more than one adding a ton low, and why the percentage is reported here rather than only the new value. Every weight added moves the centre of gravity toward it, so a radar arch, an enclosure, a tender on the cabin top, or ice on the rigging all raise KG and reduce GM directly. Free surface is the effect that surprises people, because it depends on the tank's WIDTH CUBED and not on how much liquid is in it. A wide shallow tank half full costs far more stability than a narrow deep one holding the same volume, and a tank that is nearly empty is nearly as bad as one that is half full. The correction is a moment divided by displacement and it reduces the effective GM, which is why it is applied here after the weight addition rather than before. A negative GM is not a small problem. The vessel does not simply feel tender: it is unstable upright and lolls to an angle of heel where the righting arm becomes positive, and it can flop from one side to the other. The sign is therefore a computed verdict here rather than a number for the reader to interpret, and the righting arm is reported as meaningless when GM is negative. This is a SMALL-ANGLE screen: GZ = GM sin(theta) holds only while the metacentre is effectively stationary, which is roughly the first ten to fifteen degrees, and beyond that the real righting arm comes from a full cross-curves calculation. It does not compute KM, which needs the hull form; it does not compute the free surface moment, which needs each tank's geometry; and it does not evaluate the stability CRITERIA any authority applies, which are about the area under the righting arm curve rather than about GM alone. The vessel's own stability booklet, a naval architect, and the applicable rules govern.

GM = KM - KG; a weight addition gives new KG = (W KG + w kg) / (W + w); the free surface correction is the free surface moment over displacement and reduces the effective GM; and the righting arm at a small angle is GZ = GM sin(theta).

The small-angle stability relations as naval architecture states them. KM comes off the hull's hydrostatic curves at the loaded draft and is ENTERED; the free surface moment needs each tank's geometry and is ENTERED. A SMALL-ANGLE screen only, valid while the metacentre is effectively stationary, roughly the first 10 to 15 degrees. It does not compute KM, does not compute the free surface moment, and does not evaluate the stability CRITERIA any authority applies, which concern the area under the righting arm curve rather than GM alone.

One difference and one moment balance; no hydrostatic table is reproduced.

Estimate. AHJ and licensed professional govern.

Field names used by the API: km_ft, kg_ft, displacement_lb, added_weight_lb, added_kg_ft, free_surface_moment_ftlb, heel_angle_deg, gm_ft, new_kg_ft, new_gm_ft, gm_loss_pct, weight_fraction_pct, gz_ft

• KM is entered it is a property of the hull form at the loaded draftthe vessel's hydrostatic curves
• Small angles only beyond roughly 10 to 15 degrees the righting arm comes from cross curvesa naval architect
• Not a criteria check stability rules concern the righting arm curve's area, not GM alonethe applicable rules and the stability booklet