Why do ships float?

If you throw an iron bar into the sea, you will see that it sinks quickly. However, a ship that weighs much more than the iron bar, and that can be made of metal, manages to stay afloat on the water.

The buoyancy is the property that makes boats float and was first described by Archimedes, one of the most important scientists of classical antiquity (287 BC – 212 BC). The buoyancy of a body is determined by what is known as Archimedes' principle. In compressible bodies, the Boyle–Mariotte law which explains how the buoyancy of these bodies changes as their volume varies.

The Buoyancy of Ships and Archimedes' Principle

Archimedes' Principle states: "A body wholly or partially immersed in a fluid at rest is buoyed from bottom to top with a force equal to the weight of the volume of fluid that the body has displaced." This force is known as hydrostatic thrust and is measured, according to the International System of Units, in newtons. The mathematical formulation is:

Archimedean formula


  • AND is he is hydrostatic thrust
  • g is the acceleration due to gravity
  • m mass
  • v is the volume of fluid displaced
  • ρ is fluid density.

The hydrostatic thrust it depends so on the density of the fluid and the volume of fluid displaced (equal to the volume of the submerged object) because on Earth the acceleration of gravity is constant (9.81 m/stwo). When the force of the hydrostatic thrust is equal to the weight of the object, it will stop submerging.

Archimedes is said to have discovered this fact while taking a bath in a bathtub. In that relaxing moment he noticed that when an object is immersed in a fluid, such as bath water, the level of the fluid rises because the object has displaced part of the fluid. Archimedes noticed that any object placed on top of a fluid submerged until the weight of the amount of fluid displaced is equal to the weight of the object.

Different materials, with different densities but the same volume, will have a different buoyancy. Take for example an inflated balloon filled with air and a stone of the same size. Both objects occupy the same volume in space but the stone will sink and the balloon will float. This is due to the higher density of the stone.

Having more density, the weight of the stone is greater than the weight of the water it displaces and the hydrostatic thrust force does not equal the weight of the stone. The stone sinks to the bottom. The stone is said to have a low volume-to-weight ratio, that is low volume and high weight. A ship is essentially a shell filled with air and has a high volume-to-weight ratio, it will rapidly displace a volume of water whose weight is equivalent to the weight of the ship and this is why the ship floats.

Logically, when the boats are loaded the volume-weight ratio decreases and it will submerge more but it will remain afloat as long as it is not overloaded to the point of making the volume-weight ratio too low (little volume for so much weight). Keep in mind that even if the ship is open at the top, the air contained between the walls counts as the volume of the object.

Now that you know how boats float, it will be easier for you to understand and explain how other objects float, including the human body. The volume-to-weight ratio is the key.

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