Ship Buoyancy and Stability: Archimedes, Draft and the Metacentre

Floating is a balance of two forces

A ship floats because the water it displaces weighs exactly as much as the ship itself. This is Archimedes' principle: the upward buoyant force on a submerged or partially submerged body equals the weight of the fluid it displaces. A steel hull is denser than water, but a hull is mostly air-filled hollow space, so the ship as a whole — steel plus cargo plus air — has a lower average density than water, and it settles until it has pushed aside enough water to support its own weight.

Draft, freeboard and the load line

The depth a hull sinks to is its draft. As you add cargo, the ship sinks deeper until the extra displaced water again balances the extra weight. The vertical distance from the waterline to the deck is the freeboard, and it cannot shrink below a legal minimum — the Plimsoll line painted on a ship's hull marks exactly how low it may safely sit, adjusted for season and water density (seawater is denser than fresh water, so a ship floats slightly higher in the ocean than in a river).

weight of ship + cargo = weight of water displaced
     m * g       =  rho_water * V_displaced * g
=>   V_displaced =  m / rho_water

Stability: why shape matters as much as weight

Floating is not the same as floating upright. A ship's stability depends on the relationship between two points: the centre of gravity (G), where its weight effectively acts, and the centre of buoyancy (B), the centroid of the displaced water volume, where the buoyant force effectively acts. When a ship heels over, B shifts toward the low side as the underwater hull shape changes; the vertical line through the new B crosses the ship's centreline at a point called the metacentre (M). If M sits above G, the buoyant force creates a righting moment that pushes the ship back upright; if M falls below G, the ship is unstable and will keep rolling.

A wide, flat-bottomed hull raises the metacentre and gives strong initial stability — good for cargo ships and ferries. A narrow, deep-keeled hull lowers the centre of gravity instead, which is why sailboats carry heavy ballast keels: they trade some initial stiffness for the ability to right themselves even after being pushed far over by wind.

What happens when you overload it

Add too much weight and two things go wrong at once: the draft increases until freeboard disappears and water washes over the deck, and the extra high-up cargo weight raises the centre of gravity, shrinking or eliminating the GM distance that provides righting stability. Historically, both failure modes have sunk ships independently — the Vasa capsized from a too-high centre of gravity on her maiden voyage in 1628, while countless overloaded vessels have simply swamped as their freeboard vanished.

Frequently asked questions

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