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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### To Determine The Metacentric Height Of a Ship Model

Metacentres are usually separately calculated deterkination transverse side to side rolling motion and for lengthwise longitudinal pitching motion. Hence, the -coordinate of the metacenter is. This is converted to potential energy by raising the centre of mass of the hull with respect to the water level or by lowering the centre of buoyancy or both. The range of positive determiination will be reduced to the angle of down flooding resulting in a reduced righting lever.

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.

For this reason, maritime regulatory agencies such as the International Maritime Organization specify minimum safety margins for seagoing vessels. Technically, there are different metacentric heights for any combination of pitch and roll motion, depending on the moment of inertia of the waterplane area of the ship around the axis of rotation under consideration, but they are normally only calculated and stated as specific values for the limiting pure pitch and roll motion.

Roll damping by bilge keels of sufficient size will reduce the hazard. However, the center of buoyancy lies a depth below the surface of the water which corresponds to the plane.

Coast Guard Technical computer program support accessed 20 December A larger metacentric height on the other hand can cause a vessel to be too “stiff”; excessive stability is uncomfortable for passengers and crew. Then I brought the body in the water tube and changed the horizontal moving load distance first towards right. 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.

Such a block can be thought of as a very crude model of a ship. When the vessel is inclined, the fluid in the flooded volume will move to the lower side, shifting its centre of gravity toward the list, further extending the heeling force. Retrieved from ” https: However, if the centre of mass is below the axis, it will move to one side and rise, creating potential energy.

Tonnage Gross tonnage Compensated gross tonnage Net tonnage. Work must be done to roll a stable hull. When a ship is at equilibrium, the centre of buoyancy is vertically in line with the centre of gravity of the ship.

This is known as the free surface effect. Stable floating objects have a natural rolling frequencyjust like a weight on a spring, where the frequency is increased as the spring gets stiffer.

Hence, the new submerged volume is. As is easily demonstrated, the body’s new draft becomes.

## Stability and Metacentric Height

Deter,ination righting arm known also as GZ — see diagram: The angle s obtained during the inclining experiment are directly related to GM.

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. As an example, consider a uniform rectangular block of specific gravity floating such that its sides of length, and are parallel to the – – and -axes, respectively.

It is easily demonstrated that. KM is the distance from the keel to the metacentre. Experimental study of Laminar, Transitional and Turbulent Flow. Any heel lesser than this angle will allow the vessel to right itself, while any heel greater than this angle heighr cause a negative righting moment or heeling moment and force the vessel to continue to roll over.

It is calculated as the distance between the centre of gravity of a ship and its metacentre. It might also move up or down with respect to the water line.

Hence, a sufficiently, but not excessively, high metacentric height is considered ideal for passenger ships. From Wikipedia, the free encyclopedia.

### Metacentric height – Wikipedia

Now, is the height of the metacenter relative to the center of buoyancy. The effect is similar to that of carrying a large flat tray of water. However, vessels with a higher metacentric height are “excessively stable” with a short roll period resulting in high accelerations at the deck level. The righting couple is proportional to the metacentric height multiplied by the sine of the angle of heel, hence the importance of metacentric height to stability.

Consider the stability of heigt block to small amplitude angular displacements about the -axis. This is because the stiff vessel quickly responds to the sea as it attempts to assume the slope of the wave. Metacentric height MH Y2. The metacentre is considered to be fixed for metadentric angles of heel; 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.

A ship with low GM is less safe if damaged and partially flooded because the lower metacentric height leaves less safety margin. An Experiment on Hydraulic Jump.