BUOYANCY METACENTRE PDF

Admin 0 Comments Sharing is Caring : - Today we will learn more about buoyancy. In our last article we have discussed about what is buoyancy and buoyancy force which a body experienced when it is submerged or immersed in any fluid. We have also noticed that when we see a ship or boat or any floating body, it oscillate about a point during floating. The point about which it ocsillate is known as Metacenter.

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That frequency is determined like with a metronome by the amount of mass on some length of swing arm being pulled by gravity. In a boat, the swing arm is a distance called "GM or metacentric height", being the distance between two points: "G" the center of gravity of the boat and "M" which is an imaginary point called the metacenter.

Metacenter is determined by a ratio of the inertia resistance of the boat divided by the volume of the boat. The inertia resistance is a quantified description of how the waterline width of the boat resists overturning. Wide and shallow or narrow and deep hulls have high transverse metacenters relative to the keel , and the opposite have low metacenters; the extreme opposite is shaped like a log or round bottomed boat.

Ignoring the ballast , wide and shallow or narrow and deep means the ship is very quick to roll and very hard to overturn and is stiff. And log shaped round bottomed means slow rolls and easy to overturn and tender.

The bottom point of the swinging pendulum arm, "G", is the center of gravity. An ideal boat strikes a balance. Very tender boats with very slow roll periods are at risk of overturning and have uncomfortable feel for passengers. However, vessels with a higher metacentric height are "excessively stable" with a short roll period resulting in high accelerations at the deck level.

When a ship is heeled, the centre of buoyancy of the ship moves laterally. 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. The metacentre remains directly above the centre of buoyancy regardless of the tilt of a floating body, such as a ship.

In the diagram to the right the two Bs show the centres of buoyancy of a ship in the upright and heeled condition, and M is the metacentre. KM is the distance from the keel to the metacentre. When the deck is flooded, the stability arm rapidly decreases. The centre of buoyancy, is the centre of the volume of water which the hull displaces.

This point is referred to as B in naval architecture. The centre of gravity of the ship is commonly denoted as point G or VCG. When a ship is stable, the centre of buoyancy is vertically in line with the centre of gravity of the ship. 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 metacentre is commonly designated as point MT in naval architecture. The distance between the centre of gravity and the metacentre is called the metacentric height. This distance is also abbreviated as GM. This creates a righting moment a kind of torque which rotates the hull upright again and is proportional to the horizontal distance between the centre of gravity and the metacentre. The metacentric height is important because the righting force is proportional to the metacentric height times the sine of 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: KB - Centre of Buoyancy KMT - Transverse Metacentre Righting arm Distance GZ is the righting arm: a notional lever through which the force of buoyancy acts.

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.

This is expressed as the righting arm known also as GZ — see diagram : the horizontal distance between the centre of buoyancy and the centre of gravity. 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 A ship with a small GM will be "tender" - have a long roll period.

It also puts the vessel at risk of potential for large angles of heel if the cargo or ballast shifts, such as with the Cougar Ace. A ship with low GM is less safe if damaged and partially flooded because the lower metacentric height leaves less safety margin. For this reason, maritime regulatory agencies such as the International Maritime Organization specify minimum safety margins for sea-going vessels.

A larger metacentric height on the other hand can cause a vessel to be too "stiff"; excessive stability is uncomfortable for passengers and crew. This is because the stiff vessel quickly responds to the sea as it attempts to assume the slope of the wave. An overly stiff vessel rolls with a short period and high amplitude which results in high angular acceleration.

This increases the risk of damage to the ship and to cargo. In contrast a "tender" ship lags behind the motion of the waves and tends to roll at lesser amplitudes. 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. The period of roll can be estimated from the following equation [2] Where g is the gravitational constant , k is the radius of gyration about the longitudinal axis through the centre of gravity and is the stability index.

Damaged Stability If a ship floods, the loss of stability is caused by the increase in B, the centre of buoyancy, and the loss of waterplane area - thus a loss of the waterplane moment of inertia - which decreases the metacentric height.

The range of positive stability will be reduced to the angle of down flooding resulting in a reduced righting lever. 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. This is known as the free surface effect. Free surface effect Further information: Free surface effect 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 results in a displacement of the centre of gravity of the tank or space relative to the overall centre of gravity. The effect is similar to that of carrying a large flat tray of water. When an edge is tipped, the water rushes to that side, which exacerbates the tip even further. The significance of this effect is proportional to the square of the width of the tank or compartment, so two baffles separating the area into thirds will reduce the displacement of the centre of gravity of the fluid by a factor of 9.

This is of significance in ship fuel tanks or ballast tanks, tanker cargo tanks, and in flooded or partially flooded compartments of damaged ships.

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. Transverse and longitudinal metacentric heights There is also a similar consideration in the movement of the metacentre forward and aft as a ship pitches.

Metacentres are usually separately calculated for transverse side to side rolling motion and for lengthwise longitudinal pitching motion. 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.

Measurement 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. This can also be done when a ship or offshore floating platform is in service. It can be calculated by theoretical formulas based on the shape of the structure. The angle s obtained during the inclining experiment are directly related to GM. See also.

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Differentiate Centre Of Gravity, Centre Of Buoyancy And Metacentre?

See Article History Metacentre, also spelled metacenter, in fluid mechanics , the theoretical point at which an imaginary vertical line passing through the centre of buoyancy and centre of gravity intersects the imaginary vertical line through a new centre of buoyancy created when the body is displaced, or tipped, in the water, however little. The centre of buoyancy of a floating body is the point about which all the body parts exactly buoy each other—in other words, the effective centre of the displaced water. The metacentre remains directly above the centre of buoyancy regardless of the tilt of a floating body, such as a ship. The centre of gravity is the point in a body about which all parts of the body balance each other. When a vessel tilts, one side displaces more water than does the other, and the centre of buoyancy moves and is no longer directly under the centre of gravity, but, regardless of the amount of the tilt, the centre of buoyancy remains directly below the metacentre.

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Metacentric height

KM is the distance from the keel to the metacentre. In a boat, the equivalent of the spring stiffness is the distance called "GM" or "metacentric height", being the distance between two points: "G" the centre of gravity of the boat and "M", which is a point called the metacentre. Metacentre is determined by the ratio between the inertia resistance of the boat and the volume of the boat. The inertia resistance is a quantified description of how the waterline width of the boat resists overturning. Wide and shallow or narrow and deep hulls have high transverse metacenters relative to the keel , and the opposite have low metacenters; the extreme opposite is shaped like a log or round bottomed boat. Ignoring the ballast , wide and shallow or narrow and deep means that the ship is very quick to roll and very hard to overturn and is stiff. A log shaped round bottomed means that it is slow to roll and easy to overturn and tender.

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Metacentre

Mecholic No Comments Centre of gravity Centre of gravity is an imaginary point at which the weight of body can be assumed to act. For a uniformly distributed mass, the centre of gravity will be same as the geometrical centre of that object. The concept of centre of gravity helps us to design of static objects, predict the behaviour of moving objects. Buoyancy and centre of Buoyancy Buoyancy is defined as the upward force exerted on a body by a fluid when body immersed in the fluid. Force of buoyancy is equal to the weight of the fluid displaced by the body. Negative Buoyancy: the weight of object greater than the buoyant force.

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