The metacentric height (GM) is a measurement of the initial static stability of a floating body. It is calculated as the distance between the centre of gravity of a ship. It is the distance between center of gravity (c) and Metacenter. It is the measure if static stability of floating body. Large the metacentric height more is the stability. AIM: To determine the meta-centric height and position of the meta-centric height with angle of heel of ship model. APPARATUS REQUIRED: Water tank.

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The metacentric height is normally estimated during the design of a ship but can be determined by an inclining test once it has been built.

A log shaped round bottomed means that it is slow to roll and easy to overturn and tender. The metacentric height also influences the natural period of rolling of a hull, with very large metacentric heights being associated with shorter periods of roll which are uncomfortable for passengers.

The point at which a vertical line through the heeled centre of buoyancy crosses the line through the original, vertical centre of buoyancy is the metacentre. A passenger ship will typically if a long rolling period for comfort, perhaps 12 seconds while a tanker or freighter might have a rolling period of deteermination to 8 seconds.

This is because the stiff vessel quickly metacentgic to the sea as it attempts to assume the slope of the wave. Now, is the height of the metacenter relative to the center of buoyancy.

Metacentric height

If a ship floods, the loss of stability is caused by the increase in KBthe centre of buoyancy, and the loss of waterplane area – thus a loss of the waterplane moment of inertia – which decreases the metacentric height. Ignoring the ballastwide and shallow or narrow and deep means that the ship is very quick to roll and very determonation to overturn and is stiff.


This distance is also abbreviated as GM. These are gravity acting downwards at the centre of mass and the same magnitude force acting upwards through the centre determinatipn buoyancy, and through the metacentre above it.

Depending on the geometry of the hull, Naval Architects must iteratively calculate the center of buoyancy at increasing angles of heel. Displacement Loaded displacement Standard displacement Light displacement Normal displacement.

However, vessels with a higher metacentric height are “excessively stable” with a short roll period resulting in high accelerations at the deck level.

It is calculated as the distance between the centre of gravity of a ship and its metacentre. For this reason, maritime regulatory agencies such as the International Maritime Organization specify minimum safety margins for seagoing vessels.

Stability and Metacentric Height

An Experiment on Hydraulic Jump. This is of significance in ship fuel tanks or ballast tanks, tanker cargo tanks, and in flooded or partially flooded compartments of damaged ships. An ideal boat strikes a balance. The metacentre is considered to be fixed for small angles of metacentrlc however, at larger angles of heel, the metacentre can no longer be considered fixed, and its actual location must be found to calculate the ship’s stability.

The metacentre has a direct relationship with a ship’s rolling period. The piston tilted hright suspended rod gave the angle of head, I noted the angle for respective displacements.

Builder’s Old Measurement Moorsom System.

Hence, the submerged volume heigght. In contrast, a “tender” ship lags heigth the motion of the waves and tends to roll at lesser amplitudes. Because the vessel displacement is constant, common practice is to simply graph the righting arm vs the angle of heel.


The metacentre can be calculated using the formulae: The centre of buoyancy is at the centre of mass of the volume of water that the hull displaces.

When a vessel reaches a heel equal to its point of vanishing stability, any external force will cause the vessel to capsize. When a ship heelsthe centre of buoyancy of the ship moves laterally.

To Determine The Metacentric Height Of a Ship Model

By means of the inclining experiment, the ‘as-built’ centre of gravity can be found; obtaining GM and KM by experiment measurement by means of pendulum swing measurements and draft readingsthe centre of gravity KG can be found. A relatively large metacentric height, on the other hand, generally renders a ship uncomfortable for passengers and crew, because the ship executes short period rolls, resulting in large g-forces. A ship with low GM is less safe if damaged and partially flooded because the lower metacentric height leaves less safety margin.

Principles of Naval Architecture. It follows that is the center of buoyancy in the first position, the center of buoyancy in the second inverted position, and the center of gravity in both positions. Tonnage Gross tonnage Compensated gross tonnage Net tonnage. In a boat, the equivalent of the spring stiffness is the distance called “GM” or “metacentric height”, being the distance between two points: Distance of movable mass at left of center mm.