# DETERMINATION OF METACENTRIC HEIGHT PDF

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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First of all I adjust the movable weight along the vertical rod at a certain position and measured the distance of center of gravity by measuring tape. Stay informed – subscribe to our newsletter.

## Metacentric height

KM is the distance from the keel to the metacentre. This is because the stiff vessel quickly responds to the sea as it attempts to assume the slope of the wave.

In the diagram, the two Bs show the centres of buoyancy of a ship in the upright and heeled conditions, and M is the metacentre. It is calculated as the distance between the centre of gravity of a ship and its metacentre. Such a block can be thought of as a very crude model of a ship. Where KB is the centre of buoyancy height above the keelI is the Second moment of area of the waterplane in metres 4 and V is the volume of displacement in metres 3.

Let and be the mean centers of these two volumes, and that of the whole volume. Tonnage Gross tonnage Compensated gross tonnage Net tonnage. Because the vessel displacement is constant, common practice is to simply graph the righting arm vs the angle of heel.

When setting a common reference for the centres, the molded within the plate or planking line of the keel K is generally chosen; thus, the reference heights are:.

An ideal boat strikes a balance. Consider the stability of the block to small amplitude angular displacements about the -axis. A log shaped round bottomed means that it is slow to roll and easy to overturn and tender.

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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. As the hull rights, work is done either by its centre of mass falling, or by water falling to accommodate a rising centre of buoyancy, or both.

Stable floating objects have a natural rolling frequencyjust like a weight on a spring, where the frequency is increased as the spring gets stiffer. Similarly, the downflooding angle is the angle at which water will be able to flood deeper into the vessel. 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.

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 The range of positive stability will be reduced to the angle of down flooding resulting in a reduced righting lever.

The cross-sectional area of the block at the waterline is. The angle s obtained during the inclining experiment are directly related to GM. Thus, the center of buoyancy lies a depth below the surface of the water. The point though which the force of buoyancy is supposed to pass is called as the center of buoyancy.

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

In tanks or spaces that are partially filled with a fluid or semi-fluid fish, ice, or grain for example as the tank is inclined the surface of the liquid, or semi-fluid, stays level. This is of significance in ship fuel tanks or ballast tanks, tanker cargo tanks, and in flooded or partially flooded compartments of damaged ships. Hence, the submerged volume is. Roll damping by bilge keels of sufficient size will reduce the hazard.

Very tender boats with very slow roll periods are at risk of overturning, but are comfortable for passengers. A simple extension of the previous argument reveals that if the body turns through a small angle about the -axis then the metacentric height is. Experimental study of Laminar, Transitional and Turbulent Flow. Subscribe to our Newsletter. 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.

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Water Hammer – Definition and Factors Affecting it. The period of roll can be estimated from the following equation [2]. Whenever a body, floating in a liquid, is given a small angular displacement, it starts oscillating about some point. The metacentric height GM is a measurement of the initial static stability of a floating body.

Principles of Naval Architecture. Now, is the deterrmination of the metacenter relative to the center of buoyancy. Hence, the new submerged volume is. Geometric centers Buoyancy Ship measurements. Experiment – Various Parts of Hydraulic Bench. It might also move up or down with respect to the water line. This results in a displacement of the centre of gravity of the tank or space relative to the overall centre of gravity.

The piston tilted and suspended rod gave the angle of head, I noted the angle for respective displacements. Then I brought the body in the water tube and changed the horizontal moving load distance first towards right.

The metacentric height is normally estimated during the design of a ship but can be determined hfight an inclining test once it has been built. Builder’s Old Measurement Moorsom System. 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.

When an edge is tipped, the water rushes to that side, which exacerbates the tip even further. Hence, and. Deterkination point is referred to as B in naval architecture. An overly stiff vessel rolls with a short period and high amplitude which results in high angular acceleration. Calibration Of Rectangular Notch.