Righting Arm GZ Calculator

Approximate the initial-stability righting arm as GZ = GM sin(heel) for heel angles no greater than fifteen degrees; use a vessel's measured GZ curve at larger angles.

Description

Approximate the initial-stability righting arm as GZ = GM sin(heel) for heel angles no greater than fifteen degrees; use a vessel's measured GZ curve at larger angles.

Righting Arm GZ Calculator is a focused tool for the following task. Approximate the initial-stability righting arm as GZ = GM sin(heel) for heel angles no greater than fifteen degrees; use a vessel's measured GZ curve at larger angles. It reports Righting arm from the values you provide rather than inventing measurements, coefficients, or professional judgment that are not part of the input.

When to use Righting Arm GZ

Use this sailing calculation for planning or education when the vessel, units, reference directions, environmental conditions, and assumptions are explicitly known.

Heel angle (deg)
Required number in deg. Angle of heel from upright.
Metacentric height (ft)
Required number in ft. Metacentric height GM of the vessel.

The cited overview of Ship stability supplies background for the terminology and domain context used by this tool.1

How Righting Arm GZ works

Approximate the initial-stability righting arm as GZ = GM sin(heel) for heel angles no greater than fifteen degrees; use a vessel's measured GZ curve at larger angles. Inputs are interpreted exactly in the displayed units and the calculation returns the following fields without presentation rounding.

Righting arm (ft)
Returned number in ft. Righting arm GZ at the given heel angle.

Limitations and assumptions

  • Vessel design and loading, sea state, wind, current, tide datum, weather, chart accuracy, equipment, crew, and safety margins can make real conditions differ from a simplified result.
  • Heel angle must be at least 0.
  • Heel angle must be no greater than 15.
  • Use finite inputs in the displayed units, preserve source measurements and assumptions, and independently verify consequential decisions.

Alternative or Complementary approaches

Cross-check current charts, tide and weather services, instrument data, vessel manuals, and applicable navigation rules, and retain a conservative alternative plan.

References

  1. Ship stability — Wikipedia contributors

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