Why things float, and why they roll over
The most expensive warship of her day sailed about thirteen hundred metres before the sea turned her over. Nothing hit her. She had simply been built with her weight in the wrong place.
On 10 August 1628, the Swedish warship Vasa cast off from below the royal palace in Stockholm on her maiden voyage. She was the pride of the navy: two gun decks, sixty-four bronze cannon, carvings from bow to stern. A crowd watched from the shore. A gust caught her sails and she heeled over. She came back. A second gust laid her over further, water poured in through the open lower gunports, and within minutes she was on the bottom of the harbour, in about thirty metres of water. Some thirty people died.
The inquiry that followed found no one to blame. It turned out that the ship had already failed a test before she sailed. Weeks earlier, with the admiral watching, thirty men had been ordered to run back and forth across her deck to see how she rocked. After three crossings she was rolling so badly that the test was stopped. She sailed anyway.
Vasa had too much weight high up (heavy guns, a tall hull, a lot of ornament) and too little ballast low down. She lay in the cold, brackish harbour mud for 333 years. Then an amateur researcher named Anders Franzén found her in 1956, and in 1961 she was raised almost whole. Today she stands in a museum a short walk from where she sank, still the clearest lesson in naval architecture ever built.
Buoyancy, and the gap between B and G
Buoyancy. Anything in water is pushed up by a force equal to the weight of the water it pushes aside. That's Archimedes' principle. Seawater weighs about 1,025 kg per cubic metre, so every litre of volume you add buys roughly 10 newtons of lift. A vehicle floats, sinks or hovers depending on whether its weight is less than, more than or equal to that push. Hovering, called neutral buoyancy, is what nearly every underwater robot is trimmed for, because then its thrusters only have to steer it, not hold it up.
Two centres. All of a vehicle's weight acts at one point, the centre of gravity (G). All the buoyant push acts at another point, the centre of buoyancy (B), which is the centre of the volume it displaces. When the vehicle tilts, those two forces stop lining up, and they twist it.
Stability. If B sits above G, the twist pulls the vehicle back upright, like a pendulum hanging from its pivot. If G sits above B, the same twist rolls it over. That's why underwater robots carry their foam on top and their batteries and lead on the bottom. The restoring moment is weight × the B–G gap × the sine of the tilt angle, so a few centimetres of separation is the difference between a vehicle that steadies itself and one that has to fight its own body all day. (A surface ship like Vasa also has to deal with a shape that changes as it heels, but the rule is the same: keep the weight low.)
Trim. Real vehicles are trimmed by hand before every dive. Engineers add or remove small lead weights and foam blocks until the vehicle hangs level and barely rises. The Builder on this site shows the same bookkeeping for anything you design: net buoyancy, and the gap between B and G.
A small ROV: fifty litres of foam, frame and housings. Add lead until it hovers, then slide the lead up and down the frame and watch what that does to stability. Then tip it over and let go.
Fly to Stockholm's inner harbour, where Vasa lay in the mud from 1628 until 1961. The Baltic's cold, brackish water had no shipworm to eat her timbers, which is why she survived well enough to be raised.