How is the Stability of floating bodies maintained? | (equilibrium of a floating ship)

How is the stability of floating bodies maintained? The stability of stationary floating bodies is maintained when the conditions of floating are satisfied. But when a floating body like a ship is tilted then it can get back its stability (through stable equilibrium) if the couple created by its downward weight and the upthrust working on it counterbalance the tilting action, provided the Center of gravity (C.G.) of the ship is below the metacenter of the ship.

For example, the equilibrium of a floating ship is maintained just in this way, as said above. Now, let’s find out in detail the conditions of floating and how actually the state of equilibrium is affected when a ship gets tilted. We will also go deeper to understand the concepts like (i) stable equilibrium, (ii) unstable equilibrium, & (iii) neutral equilibrium.

Two conditions of floating

Here to discuss the stability of floating bodies we will consider a stationary ship floating in the water. Since it’s floating it satisfies the following two conditions:

1] The weight of the ship is equal to the weight of the water displaced by the immersed part of the ship.

2] The center of gravity of the ship (C.G.) and the center of buoyancy(B), which is the center of gravity of the displaced water, lie on the same vertical line.

This vertical line that connects the C.G. of the ship and the center of buoyancy(B) is called the centerline. (figure 1)

How is Stability of floating bodies maintained?Two conditions of floating and stable equilibrium of a ship
figure 1

When the Ship is tilted – what may happen to the state of equilibrium of the ship?

Now if the ship is caught in turbulent waters or storms, then it may tilt.

In this situation, the second condition stated above will not be satisfied as the position of the center of Buoyancy (B) will change to B1. And the vertical line from B1 intersects the centerline at a point and this point of intersection is known as the Meta Center (M).

The weight W of the ship through G and the upthrust FB acting on it through the new center of Buoyancy (B1) act in opposite directions.

Their lines of action are also parallel. Therefore these two forces tend to set up a couple. This couple can be either clockwise or anticlockwise depending on the position of M with respect to the C.G. (G). This determines the state of equilibrium of the ship, in tilted conditions.

When the ship is tilted, the state of equilibrium of the ship may be in (1) Stable equilibrium or (2) Unstable equilibrium or (3) Neutral equilibrium.

Stable equilibrium of the ship

1] Stable equilibrium: When G lies below M, like the case shown in figure 2, when the ship is tilted in the anti-clockwise direction, the couple made by W and FB is set up in the clockwise direction which restores the ship to its original position.

Stable equilibrium: When G lies below M
figure 2

Similarly, if the tilt was in the clockwise direction, with G below M, an anticlockwise couple would be created by W and FB. This also restores the ship to its original position.

This condition when the original position is restored is said to to be stable equilibrium.

Note that, stable equilibrium (with G below M) is possible if the lower part of the ship is made heavy as that lowers its C.G.

Unstable equilibrium of the ship

2] Unstable equilibrium: When G lies above M, like the scenario shown in figure 3, with the ship tilted in the anti-clockwise direction, the couple gets set up in the same direction (here anticlockwise). This increases the tilt of the ship and eventually sinks it.

Unstable equilibrium: When G lies above M
figure 3

Similarly if the tilt was in the clockwise direction, with the G above M, a clockwise couple would be created increasing the tilt and eventually sinking the ship again.

This condition when original position can’t be restored is said to to be unstable equilibrium.

Note that, unstable equilibrium (with G above M) is possible if the top of the ship is made heavy.

To avoid this unstable equilibrium situation, the bottom of the ship is usually filled with sandbags and weights to lower the CG.

There is a line marked on the lateral side of the ship called ‘water line’ and every ship has to float up to this line for stability and this helps in safe sailing.

Neutral equilibrium of the ship

3] Neutral Equilibrium: This situation arises when G and M coincide (see figure 4). In this case, if the ship is tilted, no couple is generated. As a result, the ship neither tilts further nor does it come back to its original position. This is known as Neutral Equilibrium.

Neutral Equilibrium: This situation arises when G and M coincide
figure 4

Conclusion:

So here we have discussed the 2 conditions of floating for a ship.

Also, we have discussed three types of equilibrium for a tilted ship among which stable equilibrium can bring back the tilted ship to its original position.

During the discussion, we came across related terms like metacenter, centerline, and couple.

The readers of this post also read the following topics:

Buoyancy

Equilibrium

Couple

Center of Gravity

Buoyant force

How is the Stability of floating bodies maintained? | (equilibrium of a floating ship)
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