Displacement & Hydrostatics

A floating hull displaces its own weight of water, so the whole of hydrostatics starts at ∇ = L·B·T·Cb and Δ = ρ∇. The block coefficient Cb is the fraction of the L×B×T box the hull actually fills, and Cw is the same idea for the waterplane. Both are yours to supply — take them from your own hydrostatics, because a coefficient off someone else's hull is not your hull.

Everything here is exact given those two coefficients. Salt water at 1025 kg/m³ floats a boat 2.5% lighter in draft than fresh at 1000 — which is why a boat launched in a river sits deeper than the same boat at sea.

Hull and waterline

Displaced volume ∇
—
Displacement Δ
—
Waterplane area Aw
—
Tonnes per cm (TPC)
—
Sinkage from the payload
—
Draft at that weight
—

Speed regime

Two Froude numbers matter. On length, Fn = V/√(gL), which governs the wave the hull makes and puts the so-called hull speed at Fn ≈ 0.4. On displacement, Fn∇ = V/√(g∇1/3), which is the one that says whether the boat is floating or flying: under 1 it is a displacement hull, 1–2 semi-displacement, over 2 planing.

Froude number Fn
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Hull speed (Fn 0.4)
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Fn∇ and regime
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Prismatic hydrostatics from the coefficients you supply — it is not a lines-plan calculation, and it knows nothing about trim, LCB or the shape of your sections. Reserve buoyancy here is the deck-edge freeboard against the waterplane, which is the first cut, not a damaged-stability case. A helper, not a substitute for engineering judgment.