The GZ curve is a graph of the righting lever GZ against the angle of heel. Its relevant features are:

• The origin: at zero heel, GZ = 0.
• The initial slope: the tangent to the curve at the origin equals GM (the metacentric height), since GZ = GM sin(theta) for small angles. A steeper initial slope means a larger GM.
• The maximum righting lever (GZ max): the highest point of the curve, and the angle at which it occurs (the angle of maximum stability, typically 25-40 deg).
• The range of stability: the angle from the upright to the angle of vanishing stability (where GZ returns to zero, typically 60-90 deg).
• The area under the curve: proportional to the dynamical stability (the work done in heeling the ship), used to assess stability in a seaway and against wind heeling.
• The angle of loll: if the curve starts below the axis (negative GZ at small angles), indicating a negative GM and an unstable ship that lolls to one side.
• The effect of free surface: the curve is reduced by the free-surface correction.

The curve is obtained from the cross-curves of stability corrected for the actual KG and free-surface effects, and is compared with the statutory criteria.

(i) Increased freeboard: increasing the freeboard raises the deck edge and increases the reserve buoyancy, so the range of stability is increased (the angle of vanishing stability moves to a larger angle) and the area under the curve is increased. The initial slope (GM) is largely unchanged, but the curve is higher and extends further, giving greater dynamical stability and a larger range.

(ii) Increased beam: increasing the beam increases the waterplane area and the BM (BM is proportional to the cube of the beam), so the initial slope (GM) increases and the curve is steeper at small angles. The maximum GZ is increased and occurs at a smaller angle, but the range of stability may be reduced (the angle of vanishing stability decreases) because the ship becomes stiffer and the deck edge immerses earlier. The area under the curve may be reduced at large angles.

(iii) Increased GM: increasing the GM (e.g. by lowering KG) makes the initial slope steeper, so the curve rises more steeply at small angles and the maximum GZ is larger and occurs at a smaller angle. However, the range of stability is reduced (the angle of vanishing stability decreases) and the ship rolls more quickly and with a shorter period, which can be uncomfortable. The area under the curve at small angles increases but the overall range decreases.