### Metacentric Height | Metacentric Height Calculation Formula | Buoyant Force | Centre of Buoyancy

# Definition and Application of Metacentric Height | Metacentric Height Calculation Formula | What is Buoyant Force | What is Centre of Buoyancy

## What is Metacentric Height?

The metacentric height is a measure of a floating body’s initial static stability. It is calculated as the distance between a ship’s center of gravity and its metacentre.

Greater initial stability against overturning is implied by a higher metacentric height.

The natural period of rolling of a hull is similarly influenced by metacentric height, with particularly large metacentric heights linked with shorter durations of roll that are uncomfortable for passengers.

As a result, a sufficiently high, but not excessively so, metacentric height is regarded as optimum for passenger ships.

When a ship heels (rolls sideways), the ship’s center of buoyancy moves laterally. It may also move up and down in relation to the water line.

The metacentre is the point at which a vertical line across the heeled center of buoyancy intersects the line through the original, vertical center of buoyancy.

A metacentre is a theoretical point at where an imaginary vertical line intersects the imaginary vertical line through a new centre of buoyancy generated when the body is shifted, or tipped, in the water.

By definition, the metacentre remains immediately above the center of buoyancy.

A buoyant friction is a push that lifts an object upward and is created by displaced fluid.

This force is constant regardless of how far the fluid is moved. The buoyant force increases as more fluid is displaced.

This is why, if you press something that normally floats in water totally beneath the water and then let it go, it will rise up out of the water.

When an object is submerged, more water is displaced, and the buoyant force increases. When you no longer hold the thing down, it begins to speed upwards because the force pulling down is higher than the force pushing up.

M – Metacenter

G – Center of Gravity

B – Center of Buoyancy

K – Keel

## Metacentric Height Calculation Formula

The metacentric height of a ship is generally calculated during its design, although it can be determined after it has been built using an inclining test.

When a ship or offshore floating platform is in service, this can also be done. It can be computed using theoretical calculations depending on the structure’s shape.

An inclining test is a test conducted on a ship to measure its stability, lightship weight, and center of gravity positions.

The test is applied to new completely constructed ships longer than 24m in length, as well as ships that have been altered in ways that may influence stability.

The International Maritime Organization and other international organizations provide inclining test protocols.

By reading draughts and comparing them to established hydrostatic properties, the weight of a vessel can be easily estimated.

The design can approximate the metacentric height, which dominates stability, but an accurate number must be determined by an inclining test.

To achieve precision, the inclining test is normally performed inshore in calm weather, in quiet water, and free of mooring limitations.

Moving weights transversely to produce a known overturning moment in the range of 1-4 degrees, if practicable, determines the metacentric height position.

The metacentric height can be computed by knowing the restorative characteristics (buoyancy) of the vessel from its dimensions and floating position, as well as determining the equilibrium angle of the weighted vessel.

The weight shifts must be known and the angles of tilt must be monitored, just like in a new ship test.

To calculate the average and variance of metacentric height, a series of weight (ballast) movements are used.

## What Is the Buoyant Force?

The buoyant force is created by hydrostatic pressure, or the pressure created by the displaced fluid’s desire to return to its original location.

While it is true that pressure is applied to all sides of the object, the forces operating on the bottom of the object are the most fascinating.

This is due to the fact that the pressures acting on the sides of the object are identical in magnitude but acting in opposite directions, therefore they cancel each other out. This leaves simply the forces acting upward.

## Centre of Buoyancy

The center of buoyancy is located at the center of mass of the volume of water displaced by the hull.

The center of buoyancy is the point at which, supposing you could retain a fluid in a fixed shape, if you took all of the displaced fluid and held it by that point, it would remain perfectly balanced.

This is also known as the center of mass. The center of buoyancy of an object corresponds to the center of mass of the fluid that it displaces.

Understanding where the center of buoyancy is located is critical for an object floating in a fluid’s stability.

When a vessel floats in water, the object’s weight and the buoyant force exerted on the boat are equal, and those forces work through the center of buoyancy and the center of mass.

If those two places are close to each other, the boat’s rocking will be minimized. If the two locations are too far apart, the rocking will grow and the chance of the boat capsizing will increase.

## Metacentric Height FAQs

### What is metacentric height?

Metacentric height is the distance from the center of gravity to the metacenter. Metacentric height can be used as a measure of stability and it influences how much buoyancy force is needed for a ship to remain afloat in shallow water.

The greater the metacentric height, the more stable a vessel will be in high winds or waves.

The most common use of metacentric height concerns ships and boats; determining whether they are stable enough without having too much freeboard.

Metacentrics plays an important role when designing vessels such as ships and boats because its value reflects how well balanced, they are; if there’s not enough balance, then these vessels might capsize over time due to forces that push down on them like wind.

### What are applications of metacentric height?

Metacentric height is a measurement used in ship design. It’s the distance between the center of buoyancy and the center of gravity.

The metacentric height can be adjusted by changing the weight distribution on board or by adjusting ballast. This has applications such as balancing a boat that has taken on too much water, making it more stable for passengers’ safety.

The metacentric height can be adjusted by changing the weight distribution on board or by adjusting ballast.

### What is the purpose of the inclining experiment?

The experiment performed to determine the ship vertical center of gravity. It consists of shifting a series of known weights transversally across the deck when the ship is free to heel.

### What happens when metacentric height increases?

An increase in metacentric height increases the stability of the ship but at the same time, it reduces the period of oscillation.

### What is the difference between centre of gravity and centre of buoyancy?

Center of Gravity is the point in a body where the gravitational force may be taken to act. Center of Buoyancy is the center of the gravity of the volume of water which a body displaces.