What makes a Ship Float - Archimedes Principle & Buoyancy

It was not without purpose that a genius was so excited as to jump out of his bathtub and run naked on the streets shouting Eureka! Infact so important was that discovery that even the floatation of the huge mass of a ship can be explained like a child’s play.

Introduction

We learnt about the center of gravity and centroid in our previous article. Now we will move a step further and see how a simple principle discovered centuries ago in a bath tub can be applied equally well to the vast oceans in perspective of floatation of a ship.

Archimedes Principle

The science of floatation is simple yet equally interesting to know and let me explain it for you in the simplest manner possible. Now you know that every body or object has got a volume which means that if that object is placed on the surface of the water, it will displace water which is equal in volume to the volume of the object immersed inside the surface of the water (let me add here that I am using the term water in context of sea and ships, otherwise this principle applies to all fluids).

The volume of water that has been displaced certainly possesses a certain amount of mass which is given by

Mass of water displaced = volume of water displaced * density of water

Density of fresh water is normally 1000 kg/m³ and varies slightly whether the water is salt water and so on. Now Archimedes tells us that this mass of water displaced actually acts to push the object upward and it causes and apparent loss of mass of the object placed on water by an amount equal to the mass of water displaced.

The upward force exerted by this displaced volume of water is known as the force of buoyancy. This force can be assumed to act at a single point on the body which is known as the center of buoyancy of the body. And this center of buoyancy of the body is the same as the center of gravity of the part of the body which is immersed inside the water. It is this force of buoyancy which keeps the object pushed upwards and prevents it from sinking.

So Why Don’t All Objects Float?

You can imagine that for an object placed on water it has its weight acting downwards while the force of buoyancy is acting upwards. As the object starts to dip into water the force of buoyancy would obviously rise. At a point where this force is equal (and of course it is opposite) to the mass of the object, the object stops to sink and starts floating at that position. But if the object is not able to displace a mass of water equal to its weight even after full immersion it will sink to the bottom.

Though a ship is made out of several thousand tons of Iron (and other materials) it is shaped in such a way that after some amount of immersion in water it displaces a volume of water sufficient enough to counter its weight, hence the reason for floatation.

Some Terms Associated with Ship Floatation

Here are some of the important terms associated with ship floatation and an accompanying diagram to clarify the same.

• Draft – this refers to the depth from the water surface till the bottom-most section of the ship immersed in water

• Freeboard – this refers to the remaining height of the ship above the water level

• TPC – Tonnes per centimeter refers to the amount of mass which must be added or removed from a ship so that its draft changes by one centimeter.

• WPA – Water plane area of a ship is the area of the ship which the ship occupies when immersed in water at the water plane

• Reserve Buoyancy – a ship is meant to load cargo hence when the ship is empty it must have ample space to take additional weights of cargo etc without sinking and this is known as reserve buoyancy which is defined as percentage of total volume