Ship Roll Period & GMT Stability Calculator
Intact ship hydrostatics: Calculate transverse metacentric height (GM_T), roll natural period (T_roll), roll gyration radius (k_xx), and stiff vs tender behavior.
Vessel Geometry & Mass Distribution
Roll Kinematics & Stability Assessment
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Frequently Asked Questions
What is the physical difference between a "stiff" ship and a "tender" ship?
A "stiff" ship has a large transverse metacentric height (GM_T > 2.5 - 3.5 m). It has tremendous restoring righting moments and will not capsize easily, but it snaps upright violently with very short roll periods (7-10 s), throwing crew and failing container lashings. A "tender" ship has a low GM_T (< 0.5 m), producing long, sluggish roll periods (20-30 s); it is gentle on crew but vulnerable to dangerous angles of loll and wind gusts.
How does natural roll period relate to parametric rolling in container ships?
Parametric rolling occurs when a container ship navigates head or following seas with an encounter period (T_e) approximately equal to half the ship natural roll period (T_e ≈ 0.5 * T_roll). As wave crests and troughs pass the ship, the waterplane area changes cyclically, creating an alternating GM_T that pumps roll angles from 5° to over 35° within just a few cycles, often shedding hundreds of containers overboard.
How does cargo distribution affect the roll gyration radius (k_xx)?
The roll gyration radius k_xx reflects mass dispersion from the centerline. Moving heavy weights (such as full wing ballast tanks or outboard container stacks) outward increases k_xx, lengthening the roll period and softening motions. Conversely, concentrating dense cargo (like iron ore) along the centerline drops k_xx, shortening the roll period.