buoyancy, tendency of an object to float or to rise in a fluid when submerged. This fluid can be either a liquid or a gas.

Archimedes’ principle and density

A popular story suggests that the concept of buoyancy was discovered by the Greek mathematician Archimedes while he was taking a bath. He knew that some materials floated in water, while others did not. With more investigation, Archimedes developed the idea that for an object to float in water, the weight of the water that the object displaces when it is placed in water must be greater than the weight of the object itself. This insight became the basis of what is now known as Archimedes’ principle.

Extremely heavy objects can float in water, as long as their shape is carefully crafted to ensure that the displaced weight of the water is greater than the total weight of the object. Fundamental to Archimedes’ principle is the concept of gravity. Fluid pressure increases with depth because of the (gravitational) weight of the fluid above. This increasing pressure applies a force on a submerged object that increases with depth. The result is buoyancy. However, at the time of Archimedes, gravity had yet to be conceptualized.

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skeleton: Buoyancy devices

Today, the concept of forces is used to explain buoyancy. Gravity is a downward force that acts on all objects. When objects are placed in a fluid, the fluid must supply a force equal in magnitude but opposite in direction to the gravitational force for the objects to float. This force is referred to as the buoyant force.

Buoyancy is closely tied to density, which is defined as the ratio of the mass of an object to its volume. The density of an object in comparison to the density of water is called specific gravity. Objects that float when placed in a fluid have a lower specific gravity than the fluid, while objects that sink in a fluid have a higher specific gravity than the fluid. Most buoyant objects are objects that have a relatively large volume and a relatively low density.

Calculation of ship weight and buoyancy volume

Very large cruise ships and cargo ships rely on the concept of buoyancy in their engineering. In early stages of the design, ship weight is estimated as the sum of the weights of the cargo, hull, fittings, equipment, propelling and auxiliary machinery, piping systems, electrical and electronic gear, fuel, water, consumable stores, passengers, and crew, plus a margin of a few percent for weights that are underestimated. At a later stage, the weights are calculated more precisely or are taken from actual weights of similar items. In many cases, the weight estimates are revised constantly as the design proceeds in order to avoid an ultimate overweight that might detract seriously from the ship’s performance.

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The underwater volume of a ship must be adequately sized to displace the weight of water that will support the entire ship. It must also be of adequate length, breadth, and height and so shaped that all other operating and naval architectural requirements are fulfilled. When the ship is built and fully laden, it must float level and upright at no greater depth than the design waterline (typically indicated by a Plimsoll line).

As the underwater and above-water portions of the hull are fashioned, naval architects maintain a running check of the estimated weights and calculated buoyancy volumes. They also track the products of these weights and volumes multiplied by the horizontal fore-and-aft distances of each from the transverse vertical reference plane at mid-length. These distances are also called “moment arms.” The products are known as the longitudinal weight and buoyancy moments.

To carry out these operations systematically, the underwater hull is divided into segments by imaginary transverse planes called stations. There may be 10 such segments for a boat, or 40 or more for a large ship. The volume of each segment is computed together with the position of the centre of volume for each. The forward and after moments of volume are then computed in the same way as the fore-and-aft moments of weight. A summation of the individual segment volumes gives the total underwater hull volume. The fore-and-aft positions of the centres of gravity of the individual weight groups are then estimated. Separate sums are kept of the moments of these groups forward of and behind the mid-length. Dividing the total underwater hull volume by the volume per unit weight of the fresh, brackish, or salt water in which the ship is to run gives the weight of water displaced. This must equal the total weight if the ship is to float at no greater depth than the design waterline. The net weight moment, forward of or abaft the mid-length, is divided by the total weight to give the distance at which the centre of gravity (G) lies forward of or abaft the mid-length. The same operation for the volume moments gives the fore-and-aft position of the centre of buoyancy (B).

Other examples of buoyancy

Fish achieve buoyancy through an organ called a swim bladder. This organ resembles an air-filled balloon that expands and contracts as the fish moves higher or lower in water. When the bladder expands, the volume of the fish increases, while its mass remains the same. This results in a lower specific gravity and the fish moving upward. A decrease in the volume of the bladder results in a higher specific gravity and the fish moving downward.

Submarines dive underwater by allowing water to fill ballast tanks. This increases the weight of the submarine, which makes the average density of the submarine greater than the density of the water. Tanks of compressed air are then used to force the water out of the ballast tanks, making the average density of the submarine less than that of the water. The change in density this causes allows the submarine to surface.

Objects can experience buoyancy in any fluid, so machines like hot air balloons are buoyant in air. Heating the air inside the balloon creates hotter air that is less dense than the surrounding air, pushing the hot air balloon upward. To come back down, the gas heaters are turned off and the air inside the balloon starts to cool. A vent at the top of the balloon is also opened to allow more surrounding cool air to move into the balloon as the hot air cools, increasing the density of the air inside the balloon as the balloon slowly descends toward the ground.