What if a boat carried too much cargo?

Boats carry people, boxes and food across the water.

Each thing we add makes the boat heavier. What if we add too much?

Cargo boats carry huge loads across rivers and oceans, and they still float. Yet a boat made of steel is made of a material that is much denser than water. So how much can a boat carry, and what happens if it is loaded with more than that?

In this lab, Olly loads cargo into a small model steel boat, a little at a time, and watches how it floats.

A steel ship floats because of its shape: as a hollow hull it can push aside far more water than the steel alone would. But that capacity is finite. Every kilogram of cargo must be matched by another kilogram of displaced water.

This lab uses a buoyancy model to load an open steel hull, 1 m long, 0.5 m wide and 0.4 m tall, and asks two questions: how does its draft change with each kilogram, and what is the most it can carry before it goes under?

Olly's little steel boat is empty. It floats!

Part of it is under the water, and part sticks up above.

Olly's model boat is an open steel box with walls 1 centimeter thick. Empty, it has a mass of about 130 kilograms. Steel sinks as a solid lump, but as a hollow boat it floats, sitting 0.26 meters deep with 0.14 meters of its side above the water.

It floats because water pushes up on it. The push equals the weight of the water the boat moves aside, and the empty boat only has to move aside 130 kilograms of water to balance its own weight.

Empty, the hull's steel walls and floor total 129.9 kg. In fresh water (1,000 kg/m³) it floats at a draft of 0.26 m, about 65% of its height under water, leaving 0.14 m of freeboard.

Archimedes' principle states that the buoyant force on an object equals the weight of the fluid it displaces. A floating object settles where those are equal: draft d = m ÷ (ρ·L·W). The same steel as a solid block would weigh 1,570 kg and could displace at most 200 kg of water, so it sinks.

Olly adds some cargo. The boat sinks a little lower.

He adds more and more. The water creeps up the side. Then the water spills in!

Now add cargo. In the model, every 10 kilograms pushes the boat 2 centimeters deeper. With 50 kilograms on board, only 4 centimeters of the side is left above the water.

At 70 kilograms the water is right at the rim. The model says this boat can carry about 70 kilograms in fresh water. Try 75 kilograms and it sinks: water pours over the rim and the boat fills. With 400 kilograms, the plan's big load, it goes straight to the bottom.

The hull's waterplane area is 0.5 m², so each 10 kg of cargo adds 10 ÷ (1,000 × 0.5) = 0.02 m of draft. At 50 kg the draft is 0.36 m with 0.04 m of freeboard; at 70 kg it is 0.40 m, with the rim at the waterline.

The largest mass the hull can float is ρ·L·W·H = 200 kg, so it can carry 70.1 kg of cargo. At 75 kg it sinks. With 400 kg on board the total, 529.9 kg, is far beyond what the hull could ever displace, and once the rim goes under the hull floods and only the steel itself still displaces water.

Water pushes up on a boat. A boat sinks deeper until the push is big enough.

A full-to-the-top boat can't sink any deeper and still float. Too much cargo, and down it goes.

Water pushes up on a boat with a force equal to the weight of the water it pushes aside. When you add cargo, the boat sinks a little deeper, pushes aside a little more water, and balances again.

But a boat can only push aside so much water: the amount that would fill its whole shape up to the rim. Once the cargo needs more than that, there is no deeper level where it can balance, and it sinks. In sea water, which is a little denser, the same boat can carry about 75 kilograms instead of 70.

Floating requires m_total ≤ ρ_liquid·V_hull, where V_hull is the hull's full outside volume (0.2 m³ here). Below that limit there is always a draft where buoyancy equals weight; above it there is none. The spare capacity, here 70.1 kg in fresh water and 75.1 kg in sea water at 1,025 kg/m³, is a reserve of buoyancy, the principle the IMO says the first international load-line rules of 1930 were based on.

The model's limits: a box-shaped hull that stays level, cargo with no volume of its own, calm water, and flooding only when the rim goes under. It does not model tipping (stability), waves, leaks or the stress that overloading puts on a real hull.

Big cargo ships have a special mark painted on their side.

It shows how deep the ship may sit in the water. Loading past the mark is not allowed.

Real cargo ships carry a mark on their side called a load line, or Plimsoll line, after Samuel Plimsoll, who campaigned for it. In 1875 a British law required every cargo ship to show how deep it could safely be loaded. Other countries followed, and an international agreement came in 1930.

Today's rules, from the International Maritime Organization, set how much of the hull must stay above water, depending on the ship, the ocean area and the season. They keep a safety margin of buoyancy, just like stopping well before Olly's boat reaches its rim.

Britannica records that the Merchant Shipping Act of 1875 required a load line on every British cargo ship, marking the maximum safe loading depth, and that an International Load Line was adopted by 54 nations in 1930. The International Maritime Organization's 1966 Load Lines Convention, in force since 21 July 1968, sets minimum freeboards.

IMO notes that the 1930 rules rested on reserve buoyancy, and also aimed at adequate stability and avoiding excessive hull stress from overloading. The rules vary with ocean zone and season, and the lines must be marked amidships on each side of the ship.