What if a boat changed shape?

Steel is very heavy. A steel nail sinks in the bath.

But big ships are made of steel, and they float! What if we changed the shape of the steel?

Steel is much heavier than water for its size, so a steel nail or a steel bolt sinks as soon as you drop it in. Yet huge ships made of steel carry heavy loads across oceans without sinking.

What is the trick? In this lab you start with a solid steel block, then reshape it into a hollow boat hull of exactly the same outside size. Will the steel boat sink like the block, or float?

Steel's density, about 7,850 kg/m³ in the model, is nearly eight times that of fresh water. Any solid piece of it sinks. Yet steel ships float, which tells us that density of the material is not the whole story.

This lab holds the material and the outside dimensions fixed (1 m long, 0.5 m wide, 0.4 m tall) and changes only the shape, from a solid block to an open-topped hull, so you can see what Archimedes' principle says about shape.

Olly puts a solid steel block in the water.

Splash! It sinks to the bottom. The water pushes up, but not hard enough.

Water always pushes up on anything you put in it. That push is called buoyancy, and it equals the weight of the water the object pushes out of the way.

Our solid steel block weighs 1,570 kilograms. Even when it is completely under water, it pushes aside only 200 kilograms of water, because that's all the water that fits in its space. So the upward push is far too small, about one eighth of what it would need, and the block sinks.

The solid block has a mass of 1,570 kg and a weight of about 15,400 N. Fully submerged, it displaces 0.2 m³ of water, 200 kg, so the buoyant force is only 1,962 N, about 13 percent of its weight.

The net downward force is large and the block accelerates to the bottom, slowed only by drag. No change of depth helps: once it is under, the displaced volume can't grow any more.

Now Olly makes the steel into a boat shape. It is hollow, with air inside.

The boat floats! It sits low in the water, but it stays up.

Now choose the boat hull. It has the same outside size as the block, but it is hollow: thin steel walls and a floor, 1 centimeter thick, with air inside. It needs only about one twelfth as much steel, so it weighs about 130 kilograms.

The hull floats with about two thirds of its height under water. Push it down further and it could push aside up to 200 kilograms of water, so it can even carry about 70 kilograms of cargo before the water comes over the side.

With 1 cm walls the hull contains about 0.0165 m³ of steel, roughly 8 percent of the block's, for a mass of 129.9 kg. It floats when its weight equals the weight of water displaced: a draft of 0.26 m, 65 percent submerged, leaving 0.14 m of freeboard. Its maximum displacement is still 200 kg, so it can take 70 kg of cargo.

Thicken the walls to 2 cm and the hull's mass, 252.7 kg, exceeds the 200 kg it can displace, so it sinks. Add 100 kg of cargo to the 1 cm hull and it sinks too.

The boat is mostly air inside. Air is very light.

So the whole boat is lighter than the water it pushes away. The water holds it up.

An object floats if it weighs less than the water it can push out of the way. A solid steel block is all steel, so it is far heavier than the water that would fill its space. A hollow hull is mostly air, so the same space weighs much less.

The water pushing up on the bottom of the boat is what holds it up. Our model is simple: the boat is a box that always stays level. It can't tip over, and water only gets in when the rim goes under.

Floating requires m ≤ ρ_water × V_outside, and the equilibrium draft follows from m = ρ_water × L × W × d. Shape changes V_outside per kilogram of steel: the hull spreads a small mass around a large enclosed volume of air, so its average density, about 650 kg/m³ here, is below water's.

Model limits: a rectangular box with straight sides, kept level; no tipping or stability (metacenter), no waves or leaks, and cargo adds mass but no volume. The settling motion uses a chosen damping force, so it shows how it gets there rather than a measured motion.

Real ships are made of steel, but they are full of air inside.

If a ship carries too much, it sits lower and lower in the water.

OpenStax, a free physics textbook, describes a neat test: drop a lump of clay in water and it sinks, but mold the same clay into a boat and it floats, because the boat shape pushes aside more water. The same is true of steel ships.

Physicists at the University of Illinois explain that a ship floats if it weighs less than the water it would push aside, and real ships have lots of air inside. They add that how much a ship carries and how salty the water is also matter.

Archimedes' principle, as OpenStax states it, says the buoyant force equals the weight of the fluid displaced; a clay boat floats where a lump sinks because it displaces more water, and the same applies to steel ships. University of Illinois physicists answering students note that a ship sinks if its total weight exceeds the weight of water it displaces, and that shape, load and the water it sails in all affect floating.

In the model, sea water (1,025 kg/m³) lets the same hull ride slightly higher, a 0.25 m draft, and carry about 75 kg of cargo instead of 70. Real hull design must also keep a ship from tipping, which this model leaves out.