Saramsha

No. 029  ·  15 October 2026

The Water It Displaces

A solid steel bar sinks. The same steel, hammered into a hollow hull, floats — same weight, same material, nothing different but the shape of what it pushes out of the way. Pick a material, then flatten the block into a hull and watch exactly how much water it needs to displace before it can rest.

About this piece

The cavity floats too, as long as it stays dry

Archimedes' principle says a floating object displaces exactly its own weight of water — push down with a force equal to your weight, and the water pushes back with a buoyant force equal to the weight of the water that used to occupy the space you now occupy. People usually picture that space as the solid material itself, which is why "a steel hull floats" sounds like a contradiction: steel is nearly eight times denser than water, so a lump of it should always sink. The resolution is that the space a hull displaces is not the space its steel occupies. It is the space its outer shape occupies, right down to the waterline — including the hollow, air-filled hold inside it. That hold is sealed off from the water by the hull's walls, so as far as Archimedes is concerned, the trapped air is pushing the water aside exactly as effectively as solid steel would.

That is the whole trick this page lets you perform. Pick a dense material and leave the hull shape solid, and you are building a plain bar: all of its volume is steel, so the amount of water it can ever displace is capped at the volume of that steel, and if steel is heavier than that same volume of water — which it always is — the bar sinks no matter how you orient it. Now drag the shape slider toward "hollow": the same amount of steel gets pressed into thinner walls around a bigger empty middle. The steel hasn't changed, and neither has its weight. What changed is the outer envelope, which can now enclose far more volume than the steel alone ever could. Somewhere along that slider, the hull becomes tall enough that it only needs to dip a shallow depth into the water — well short of its own rim — to displace a weight of water equal to the steel's weight. At that depth it floats, with the rest of its height standing in dry air as freeboard.

Why some materials can't be saved by shape

The slider has limits for a reason: a hull can only be made so thin before it has almost no material left to resist bending or puncturing, so this page caps how extreme the hollowing can go. Within that cap, light materials — a foam, a pine plank, river ice — float as a solid bar already, no hollowing required, because they are less dense than water to begin with. Aluminium and steel need real hollowing: enough that ordinary ships are built from steel plate wrapped around mostly empty cargo holds, not solid steel blocks, which is the entire reason a steel ship is viable and a steel anchor is not. Lead and gold, on the far end, are dense enough that even the thinnest hull this page allows still cannot enclose enough volume to out-displace their weight — which is also why no one builds a lead-hulled ship. There is nothing special about the number; a thin enough shell of literally any material can in principle enclose enough air to float, which is the same reason a sheet of lead foil, folded into a wide enough boat shape, can be made to float on a pond despite lead sinking instantly as a block.

One more detail worth noticing: once a floating hull is pushed deep enough that water finally spills over its rim, the game changes completely. The hold floods, the air that used to displace water escapes or dissolves into bubbles, and the hull is suddenly only displacing its own material's volume again — which is why ships that swamp do not settle a little lower and stop; they go down, and stay down, the same as the solid bar would have from the start.

The simulation treats the hull as a uniform 2D cross-section — a flat floor plus two side walls of equal thickness, extruded one metre into the page — with a fixed amount of material regardless of shape, so hollowing it out always means thinner walls and a taller outer envelope, never more or less steel. Densities are real values in kg/m³ at room temperature; water is fixed at 1000 kg/m³ and g at 9.81 m/s², so the weight and buoyant-force bars are genuine force-per-metre figures in kilonewtons, not illustrative units. Surface tension, hull strength, wave action and the weight of trapped air itself are all ignored.