Why Ships Don't Sink

Where ground robots move by wheel torque, vessels are governed by the forces of water — they float, roll, and right themselves. The starting point for maritime simulation is a single question: "Why doesn't a ship sink?" The answer is buoyancy, and from there the story extends to stability and damping.

The Upward Force — Buoyancy

The weight of water displaced by the submerged volume, pushing upward — that is buoyancy (Archimedes' principle). The depth at which the ship's weight (gravity, downward) and buoyancy (upward) are in equilibrium is the waterline, and that is where the ship floats.

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💡 What happens if you disable buoyancy in simulation? — Without the buoyancy term, only gravity remains and the vessel sinks straight down. This happened in practice: a missing buoyancy setup caused seven vessels to plunge to −2989 m. Buoyancy is not a nice-to-have — it is the fundamental skeleton of any vessel simulation.

The Righting Force — Stability (GM)

When a wave heels a ship, the reason it returns upright is stability. The metacentric height (GM), determined by the relationship between the center of gravity (G) and the center of buoyancy (B), governs this. When GM is positive, heeling generates a buoyancy moment that restores the ship.

• GM > 0 — Stable. Returns upright after heeling.
• GM ≤ 0 — Unstable. Continues to heel and capsizes.

⚠️ Too much stability is also a problem — Excessive GM makes a ship too stiff, eliminating natural trim responses. The balance between "good righting" and "flexible motion" varies by vessel type.

The Settling Force — Radiation Damping

When waves keep a ship oscillating in heave, roll, or pitch, radiation damping gradually attenuates those oscillations. The effect arises from the waves the ship generates as it moves, carrying energy away from the hull.

💡 Large ships should be steady; small boats should rock — that's normal — Applying identical damping to a 100-tonne patrol vessel and a 12-tonne boat would make the large ship pitch like a dinghy. Damping must scale proportionally to mass so that large vessels feel heavy and small ones feel nimble — matching reality.

Surface and Subsurface Behave Differently

Surface ships float at the waterline, but submarines regulate buoyancy to control depth (z). Achieving neutral buoyancy (buoyancy = gravity) allows hovering at any depth; a small imbalance causes ascent or descent. The same buoyancy physics is the starting point, but with depth control added as an extra dimension.

In a nutshell

📌 The skeleton of vessel simulation is buoyancy (upward force) + stability GM (righting moment) + radiation damping (oscillation decay). Removing buoyancy causes sinking; negative GM causes capsize; damping must scale with mass to produce a realistic contrast between large and small vessels. Submarines add depth control on top of all of this.