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Initial Stability (GM)

Small-angle stability is one line: GM = KB + BM − KG, with BM = I/∇ from the waterplane's second moment. GM is the lever the hull has to right itself, so the righting moment at a small heel is Δ·g·GM·sinθ — and every kilo you put high up comes straight off it.

The values here are exact for the shape they state. KB is T/2 for a box; the waterplane inertia coefficient is 1/12 for a rectangle and lower for any real hull, so it is an input — take both from your own hydrostatics. A slack tank's free surface comes off the top of GM whatever it holds, because what matters is how wide the surface is, not how much is in it.

Hull

Waterline length L (m)

Waterline beam B (m)

Draft T (m)

Block coefficient C_b

KG, centre of gravity above the keel (m)

Waterplane inertia I/(L·B³)

KB above the keel (m, blank = T/2)

Water

Roll radius of gyration / B

Displacement Δ

—

BM = I/∇

—

GM solid

—

Free-surface loss

—

GM corrected

—

Slack tanks

A free surface costs i/∇ of GM, where i is the surface's own second moment — l·b³/12 for a rectangle. The cube is why a baffle down the middle of a tank cuts the loss to a quarter, and why a shallow, wide tank is the dangerous one.

Tank 1: length (m)

Tank 1: width (m)

Tank 1: baffles (bays across)

Tank 2: length (m)

Tank 2: width (m)

Tank 2: baffles (bays across)

What heels her

Weight moved across (kg)

...how far (m)

Beam wind (knots)

Windage area (m²)

Its lever above the water (m)

Drag coefficient

Righting moment at 10°

—

Heel from the weight shift

—

Wind force / moment

—

Heel from the wind

—

Roll period

—

GM if she rolls in…

—

Measured roll period (s)

Small-angle (initial) stability only: it says nothing about the righting arm at large heel, the angle of vanishing stability, downflooding, or damaged stability — and those are what a stability book is for. Wall-sided assumptions, and the empirical inputs (waterplane inertia, roll radius of gyration, drag coefficient) are yours to justify. A helper, not a substitute for engineering judgment.