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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When a ship is at equilibrium, the centre of buoyancy is vertically in line with the centre of gravity of the ship.

## Metacentric height

The volume of the block is. It is easily demonstrated that. Criteria for this dynamic stability effect remain to be developed. Metacentric height Detsrmination Y2.

Hence, the submerged volume is. As the displacement of the hull at any particular degree of list is not proportional, calculations can be difficult, and the concept was not introduced formally into naval architecture until about Subscribe to our Newsletter. Desirable and Undesirable Characteristics of Offshore Yachts.

## Stability and Metacentric Height

When a vessel reaches a heel equal to its point of vanishing stability, any external force will cause the vessel to capsize. Sailing yachts, especially racing yachts, are designed to be stiff, meaning the distance between the centre of mass and the metacentre is very large in order to resist the heeling effect of the wind on the sails. KM is the distance from the keel to the metacentre.

Sailing vessels are designed to operate with a higher degree of heel than motorized vessels and the righting moment at extreme angles is of high importance. A larger metacentric height on the other hand can cause a vessel to be too “stiff”; excessive stability is uncomfortable for passengers and crew. It might also move up or down with respect to the water line.

A passenger ship will typically have a long rolling period for comfort, perhaps 12 seconds while a tanker or freighter might have a rolling period of 6 to 8 seconds. This page was last edited on 22 Novemberat The point, about which the body starts oscillating, is called Metacentre. This distance is also abbreviated as GM.

It is the interplay of potential and kinetic energy that results in the ship having a natural rolling frequency. The period of roll can be estimated from the following equation [2]. Simple trigonometry reveals that assuming that is small. The righting couple on the ship is proportional to the horizontal distance between two equal forces.

Such a block can be thought of as a very crude model of a ship. The piston tilted and suspended rod gave the angle of head, I noted the angle for respective displacements.

Retrieved from ” https: This potential energy will be released in order to right the hull and the stable attitude will be where it has the least magnitude. When the ship is vertical, the metacentre lies above the centre of gravity and so moves in the opposite direction of heel as the ship rolls.

The metacentric height of a conventional ship whose length greatly exceeds its width is typically much less for rolling i. Because the vessel displacement is constant, common practice is to simply graph the righting arm vs the angle of heel. Any heel lesser than this angle will allow the vessel to right itself, while any heel greater than this angle will cause a negative righting moment or heeling moment and force the vessel to continue to roll over.

Let and be the volumes that are above and below the waterline, respectively, in the first position.

The righting arm known also as GZ — see diagram: This is because the stiff vessel quickly responds to the sea as it attempts to assume the slope of the wave. This is known as the free surface effect. They then calculate the righting moment at this angle, which is determined using the equation:.

Conversely if a hull having a perfectly rectangular cross section has its centre of mass at the water line, the centre of mass stays at the same height, but the centre of buoyancy goes down as the hull heels, again storing potential energy.

When an edge is determinatioon, the water rushes to that side, which exacerbates the tip even further.

### Metacentric height – Wikipedia

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 metacentre remains directly above the centre of buoyancy by definition.

The metacentre has a direct defermination with a kf rolling period. Length overall Length between perpendiculars Length at the waterline. Suppose that the body now turns through a small angle about the -axis. 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.

Another worrying feature of free surface effect is that a positive feedback loop can be established, in which the period of the roll is equal or almost equal to the period of the motion of the centre of gravity in the fluid, resulting in each roll increasing in magnitude until the loop is broken or the ship capsizes. However, if the centre of mass is below the axis, it will move to one side and rise, creating potential energy. The angle s obtained during the inclining experiment are directly related to GM.

Experimental study of Laminar, Transitional determinatjon Turbulent Flow. 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. Tonnage Gross tonnage Compensated gross tonnage Net tonnage.