# LCB and LCF – Their Relation To Stability Of A Ship

The LCB, the longitudinal center of buoyancy, and the LCF, the longitudinal center of flotation play a huge role in regard to the stability of a vessel. Firstly, let us take a look into what LCB and LCF are and further proceed with their relation to the stability of a vessel.

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## Centre of Buoyancy – LCB

Assuming you could retain fluid in a fixed form, the center of buoyancy is the point at which all the displaced fluid would stay perfectly balanced if you were to take it and hold it by that point. Also known as the center of mass, this location. An object’s center of buoyancy corresponds to the fluid it displaces the center of mass.

For an item to be stable while floating in a fluid, it is essential to understand where the center of buoyancy lies. When an item is floating in the water, for instance, its weight and the buoyant force acting on it are equal, and these forces are operating through the center of mass and the center of buoyancy, respectively.

## Centre of Flotation – LCF

Typically, the center of flotation is the geometric center of the ship’s water plane area and is the point about which the ship will trim. Let us assume a vessel, in which a weight moves about longitudinally.

The longitudinal center of flotation (LCF), remains and maintains the same position throughout the ship’s length. As the water plane area shifts shape and size with the depth of water that keeps the ship afloat. The position of the longitudinal center of flotation also shifts. Mostly the position of LCF is estimated in hydrostatic data as meters forward of the after perpendicular.

In short, the center of flotation of a ship is very important as, in the face of a drastic wind, the shift in trim must be enhanced to the aft draught and the rest to the forward draught and balance out each other.

## Staying Upright – Buoyancy And Stability Of A Ship

It is still quite a great exchange of engineering that explains the theory behind how a ship, or any large vessel, stays afloat. For instance, it is a simple understanding that, for any object to sink in any liquid, the density of the object must be higher than the density of the liquid.

Using the same explanation, a ship stays upright without sinking as the density of the ship is much lower than the density of the sea. Though this is the reason, when you consider the materials used in the making of a ship, for example-steel, the density of steel is much higher than that of water, but, when you calculate the entire volume of the ship to its weight, the density is much lower.

There are a lot of empty gaps, and air spaces that occupy the vessel, resulting in the vessel having a lower average density than water, despite the heavy metals it is made of and the kind of amenities and facilities provided on bigger vessels and cruises.

In theory, forces like buoyancy that act against gravity help objects such as even a large ship, float on water. This buoyant force creates a displacement where the water(medium) surrounding the ship resembles the weight of the deformed liquid.

This relationship between an object and the medium is immersed in Archimedes’ principle. Thus, in the case of a ship, the submerged part of the ship is lighter than the water that has been displaced, and, the displaced water equals the total weight of the ship.

Though buoyant forces are enough to keep a ship stay upright and afloat, it is not enough to keep the ship sailing through different water plane areas. This is when shipbuilding and design hold importance. In a normal sequence, the following factors ensure stability in a vessel- the hull’s shape and size, its mass and mass distribution, load weight and distribution, dynamic behavior of the ship during changing speeds, cargo movement, etc.

Other external factors such as operating conditions during wind, swell, drift, water density depending on freshwater/salt water, and even icing of the deck surfaces during cold weather, also affect the stability of the ship.

So, what exactly are the fundamental parameters of a ship’s stability? The only factors are the center of gravity, the center of buoyancy, the metacenter, and the metacentric height.

• Centre of gravity: the center of gravity in a ship can be explained as a single point at which the entire downward force or weight of the ship is concentrated. This point remains the same as long as all the masses in the ship remain in the same place. But with motion and shifting of the masses, this point, or the center of gravity also shifts.
• Metacenter: it can be better understood as two lines- the original center of buoyancy and the shifted center of buoyancy, that intersect each other. This intersecting point is the metacenter. As the center of buoyancy shifts laterally or heels over to one side, the metacenter would remain directly above it.
• Metacentric height: The distance between the newly shifted center of buoyancy and the metacenter that stays exactly above it, is known as the metacentric height.

When the ships heel to one side due to rough waters and/or other external factors, the center of gravity and the center of buoyancy does not remain perpendicular to each other. When this happens, the center of gravity is below the metacenter, hence giving rise to righting lever. This righting lever creates a righting moment, in which moment the ship returns to its original position. If the ship returns to an upright position, it is said to be in stable equilibrium, in other cases, they are said to be in either neutral equilibrium or unstable equilibrium.

• Neutral equilibrium: When the metacenter overlaps the center of gravity at vertical positions, a righting lever does not occur during the heel. This means that the heeling moment does not create a righting moment to bring back the ship to its original position. In this situation, the weight of the cargo can increase the heeling angle of the ship, leading to an unstable equilibrium.
• Unstable equilibrium:  Unlike in stable equilibrium, where the center of gravity is above the metacenter. This creates a negative righting lever due to larger healing from momentum. If this state continues and the ship does not come back to a stable equilibrium, the ship will get overturned into the water.

## Summary

The primary forces which act on the hull are the gravitational and buoyant forces, also the location where it acts plays a huge role in determining how the vessel behaves hence there are very important parameters for the stability of the vessel.