Why a Hull Floats

Put an empty bowl on still water and it floats high. Add a few small objects and it settles lower. The bowl has not become a different shape. More of the same shape has entered the water.

A boat behaves similarly. Its hull must occupy enough space in the water to obtain support for the entire load, including the hull itself. To see how that works, it helps to separate three quantities that everyday speech often bundles together: how much space something occupies, its mass, and the force pulling it down.

Space, mass and density

The load’s mass is commonly measured in kilograms; its weight is the downward gravitational force on that mass. A boat specification that gives a “weight” in kilograms is stating mass. Keeping the quantities distinct will let us compare the boat’s load with the water’s supporting force.

Equal-sized objects need not have equal masses. Fill two identical containers with different materials and one may be much harder to lift. Density expresses the comparison as mass per unit volume. A sample with a mass of six kilograms and a volume of three litres has a density of two kilograms per litre. A less dense material needs more volume to hold the same mass. This is why both the material and the space it occupies matter to our load.

Hollowing a trunk removes material while leaving an outer body capable of keeping water out. Building a shell around a frame achieves enclosed space by assembling smaller pieces instead. These methods change the amount of hull material needed to enclose a given volume. They help explain why a watertight hollow vessel can carry a load even when some of its materials, placed in the water alone, would sink.

Weight and the water’s support

The immersed part of the hull occupies space that water would otherwise fill. That amount is the displaced volume. The water exerts an upward force on the immersed body, called buoyancy. Archimedes’ principle gives its magnitude: in water, the buoyant force equals the weight of the water displaced. The principle is associated with Archimedes’ ancient work on floating bodies.

For a boat floating at rest, the upward buoyancy balances the total downward weight. If the total mass is 200 kilograms, the boat must displace water whose mass is also 200 kilograms. Using a rounded fresh-water density of 1,000 kilograms per cubic metre, that is 0.200 cubic metres, or 200 litres: there are 1,000 litres in a cubic metre.

Put a 50-kilogram box aboard. The old immersed volume supplies too little upward force for the new weight, so the hull settles until it displaces another 50 litres in the same water. It now displaces 250 litres. Whether that requires a small or large change in depth depends on the hull’s shape at the surface.

The principle also applies to a body held entirely underwater, but its buoyancy need not equal its own weight. A compact, heavy object can displace water weighing less than it does and sink when released. Equal upward and downward forces are the condition for our freely floating boat at rest, rather than a rule that every immersed object must float.

Two imaginary points help describe the balance. The centre of gravity, usually written G, represents the combined position of the boat’s mass: its weight can be treated as acting down through that point. Moving our box moves G towards the box’s new position. Raising a load raises G.

The centre of buoyancy, B, is the centre of the displaced underwater volume. The combined upward buoyant force acts through it. B follows the shape of the volume under the surface, while G follows the distribution of mass. When a boat inclines, its immersed shape changes, and B can move even though nothing aboard has moved relative to the hull. That difference will become central to understanding how a sailing boat stays upright.

Loading changes the waterline

The waterline is where the hull meets the water’s surface. The box’s added weight moves that line up the hull as the boat settles. Drawings can also use “waterline” for a horizontal reference slice; an actual waterline afloat describes the boat’s present condition.

Measure vertically down from that surface to a stated lowest point and the distance is draught, also spelt draft. A figure for hull draught may stop at the hull itself; an overall draught may include something projecting beneath it. A useful specification identifies what is included.

Measure upwards from the same waterline and freeboard gives the distance to a specified reference, commonly the deck edge. In our open boat, the relevant upper edge helps show how much side remains above the water. Added load generally increases draught and reduces freeboard. The boat can still float while becoming more easily filled by water coming over that edge.

The term displacement commonly gives the mass of the water displaced, equal to the boat’s total mass when it floats at rest. Thus our loaded example has a displacement of 250 kilograms. A description can instead state displacement as a volume, here 250 litres under the stated fresh-water assumption. Mass and volume displacement describe the same condition in different units; converting between them requires the water’s density.

A design waterline, often shortened to DWL, marks where the designer expects a boat to float in a specified loading condition. An actual loaded waterline, or load waterline, belongs to the load it is carrying. It may coincide with the design waterline, but an extra person or empty tank can change it. These lines describe flotation; a permitted carrying capacity needs its own assessment.

Likewise, light displacement describes a defined light condition, whereas loaded displacement includes the load specified for a loaded condition. The words do not provide a universal inventory. Whether a published light figure includes particular equipment or liquids must be checked before comparing it with another boat’s figure. Crew, stores and equipment all contribute to the mass that the water must support.

Move the added box towards the bow without adding or removing anything. The total mass remains 250 kilograms. The boat must still displace the same mass of water, but it may settle differently at its two ends. This fore-and-aft attitude is trim. Loading forward can increase draught at the bow and reduce it aft as the boat finds a new balance. Total displacement tells us how much support is needed; trim helps describe where the immersed volume lies.

There must also be a limit to how far a hull can settle while keeping its useful spaces dry. Watertight volume above the current waterline can enter the water and supply additional support. This available volume is reserve buoyancy. An enclosed, sound part of the hull can contribute as immersion increases. An opening that lets water straight into the boat changes the situation.

Flooding is unwanted water entering spaces intended to remain dry. Swamping describes an open or low-sided boat becoming filled enough to impair its normal flotation or operation. Once water comes over an open edge, a boat can lose usable carrying space rapidly. It may remain partly afloat because of its materials or enclosed buoyant compartments, while no longer carrying its occupants as intended. “Still floating” is a much narrower achievement than “still a useful boat”.

Our box has changed the depth of immersion, the room above the water and, when moved, the balance between the ends. The hull’s outline determines how those changes develop. A broad body and a narrow one can displace the same volume, yet offer very different places for people to sit and very different shapes for water to pass around.