Engineering

Why a ship rolls back upright, until the cargo goes too high: the metacentre and the righting arm

A box-shaped ship heeled over in water, with arrows showing weight pulling down at its centre of gravity and buoyancy pushing up from a shifted centre of buoyancy
30seconds
The 30-second version

A loaded ship that leans over usually rolls back upright, because the water's upward push shifts sideways and twists her straight. But raise the cargo high enough and the same twist works the other way.

This article builds the idea from two points, the centre of gravity and the centre of buoyancy, introduces the metacentre, and lets you drag a box barge over, gust it, and slide its cargo from the hold to a tall stack while a live curve shows when she stops pushing back.

It ends with the Vasa, which sank on her maiden voyage in 1628 with a centre of gravity set too high.

Deep dive · 4 min

More in Engineering

View all →
Why a falling pole can be held up: feedback, and the PID controller A pole on a cart wants to fall, and a controller that watches the lean and shoves the cart can hold it up. But how hard it pushes matters: too weak and it… Engineering4 min read Why a dam is fat at the bottom: water's push grows with depth squared, its tipping with depth cubed A dam is fat at the bottom and slim at the top because water pressure grows with depth, so the push grows with depth squared and the tipping effect with depth… Engineering5 min read Why bridges are made of triangles: a square folds, a triangle cannot A square made of four pinned rods folds flat at the slightest push, but a triangle of three rods cannot change shape at all. That one fact is why bridges… Engineering3 min read Why Taipei 101 hangs a 660-tonne ball in its upper floors: the tuned mass damper At the top of Taipei 101 a 660-tonne steel ball hangs in plain view. It is not decoration: it is a tuned mass damper that swings against the building and can… Engineering4 min read Why airliner windows have no corners: stress piles up at the tightest curve Cut a hole in a stretched plate and the force has to squeeze past it, so the metal beside the hole carries far more stress than the rest. For a round hole in a… Engineering5 min read Why steel beams are shaped like an I: the same steel, 25 times stiffer Put a beam across a gap and it sags: the top edge is squeezed, the bottom stretched, and the steel in the middle does almost nothing. That is why girders are… Engineering4 min read