Why a ship lists, and when it could be too much
In the wake if the INS Brahmaputra's listing, a look at the physics involved in what makes a ship float upright and what causes it to list or heel.
The warship INS Brahmaputra, which caught fire last week and where a sailor has died, is now resting on its side at the Mumbai naval dockyard after having listed towards port, or the left side as viewed by someone facing the front of the ship. Listing refers to a ship tilting under the influence of internal forces, as opposed to heeling in which external forces such as winds cause this.
So, what causes a ship to list? The intuitive answer is that a ship tilts (whether listing or heeling) when something has disrupted the factors that were keeping it upright in the first place. Those factors lie in the domain of classical physics at a very fundamental level, taking us back to Archimedes and Newton.
When an object is submerged in a liquid, it is subjected to two forces. One is a gravitational force, acting downwards and equal to the object’s weight; the other is a buoyant force, acting upward and equal to the weight of the water displaced by the object. The two forces are equal and opposite. This is essentially the Archimedes principle explained with Newtonian concepts.
The dynamics of floating — and tilting — involve several variables in addition to these two forces, and a complete graphical representation would require several points of varying significance. The mechanics can, however, be kept simple by looking at just the two equal and opposite forces and two points: the ship’s centre of gravity (a point at which we imagine the ship’s weight to be concentrated) and the centre of buoyancy (the centre of the volume of water displaced by the ship). In an upright ship, these two points lie on the same vertical line — and it is along this imaginary line that the gravitational force acts downwards passing through the centre of gravity, and the buoyant force acts upwards passing through the centre of buoyancy.
A ship tilts when either or both of these two points are displaced. If it is a case of listing, it begins when there is a change in the distribution of weight across the ship, which shifts the centre of gravity towards the weightier side. This sets off a chain of dynamics that shifts the centre of buoyancy, seeking to realign it vertically below the centre of gravity’s new position.
It should be mentioned that a ship can stay afloat even after listing, remaining in equilibrium in its new position if uncomfortably so. Trouble could begin, however, if the wind or waves shift the centre of buoyancy even farther, because now the forces of gravity and buoyancy would together tend to rotate the ship.
The general question to ask, therefore, is: will the rotation of the centre of gravity and the centre of buoyancy bring the ship back to the upright position, will it tilt the ship more and more towards the horizontal, or will the list be so high that the ship will eventually keel over?
“If the rotational motion brings the ship back to the vertical position, the ship will become stable. If it makes it more and more inclined, it becomes unstable and may go down,” said Professor Amol Dighe, a physicist at the Tata Institute of Fundamental Research, Mumbai.
The situation could get complicated even further if the ship is partly filled with water, in which case any tilting changes the centre of gravity further. The presence of water is of key importance. If the listing is caused merely by the shifting of cargo from one part to another, the ship can be brought back upright by redistributing the weight and restoring the centre of gravity to its original position. Water, on the other hand, has been known to contribute to extreme listing.
As reported by HT earlier, the Navy has suggested that water used to douse the fire on the INS Brahmaputra may have caused the warship to list. And over a century ago, it was seawater that caused the Titanic to list first one way and then another before eventually sinking.
After the hull of the Titanic struck an iceberg in 1912, seawater entered and flooded six compartments that lay under the surface on the starboard side (the right side when you are facing the front). This caused the ship to list on that side. Once these compartments at the front were flooded, the water rose to decks above and sought routes to flow through. According to recreations of the disaster, there were two routes, both leading to rear of the ship, one on the starboard side and one on the port side. The starboard passage, however, was partially blocked, so much of the water rushed through the port side. The ship then listed towards port before ultimately sinking.
If the listing of the INS Brahmaputra was indeed caused by water, it could explain why setting it upright has been difficult. “If some solid metal had been placed on the starboard or right side, you could just take it and move it to the left side, and the centre of gravity would shift. But water, being a liquid, would be much more difficult to move, I think,” Dighe said.