Generate righting arm curves GZ(θ) from KN(θ) and KG. Optional displacement for righting moment and area checks.
| θ (deg) | KN (m) |
|---|
Max GZ: — m @ —°
Range of positive stability: —°
Vanishing stability angle: —°
Area under GZ: — m·deg | — m·rad
Area limit used: —
Notes: GZ = KN − KG·sinθ | RM = Δ·GZ
The GZ curve, also known as the righting arm curve, is one of the most fundamental stability representations in naval architecture. It describes the vessel’s ability to generate a restoring moment when subjected to heeling forces such as wind, waves, or cargo shift. This calculator generates a full GZ(θ) curve directly from hydrostatic KN values and the vessel’s vertical centre of gravity (KG).
For a given heel angle θ, the righting arm is defined as:
GZ(θ) = KN(θ) − KG · sin(θ)
where KN(θ) is obtained from hydrostatic calculations or cross-curves of stability, and KG represents the vertical position of the ship’s centre of gravity. A positive GZ indicates a restoring lever that tends to return the vessel to upright condition.
This tool allows you to enter a table of heel angles and corresponding KN values, either manually, by editing rows, or by pasting CSV data directly from stability software or hydrostatic tables. The calculator then:
If a downflooding angle is specified, the integration of the GZ curve is automatically limited to this angle. This reflects practical stability requirements where progressive flooding invalidates stability assumptions beyond that point.
When displacement Δ is provided, the calculator can also plot the righting moment curve:
RM(θ) = Δ · GZ(θ)
This is particularly useful for comparing stability capability against external heeling moments from wind, turning, or lifting operations.
The accuracy of the generated GZ curve depends entirely on the quality of the supplied KN data and KG value. This tool does not replace class-approved stability software, but it provides a fast, transparent, and highly practical way to analyse stability trends, verify calculations, and visualise results.