high metacentric ( GM ) is the initial static stability measurement of the floating body. This is calculated as the distance between the center of gravity of a ship and its metacenter. The larger metacentric height implies greater initial stability against the somersault. Metacentric altitude also affects the natural period of gastric rolling, with very high metallic altitudes associated with shorter roll periods that are uncomfortable for passengers. Therefore, adequate, but not very high, metacentric height is considered ideal for passenger ships.
Video Metacentric height
Metacentre
Whenever the body, floating in a fluid, given a small angular displacement, begins to oscillate about some point. In essence, where the body begins to oscillate, it is called Metacentre.
When the heels of the ship, the center of buoyancy moves sideways. It may also move up or down against the waterline. The point at which the vertical line through the center of buoyancy from floating across the line through the original vertical buoyancy center is metacentre. The metacentre stays just above the buoyancy center by definition.
In the diagram, two B shows the center of buoyancy of a vessel in vertical and heterogeneous conditions, and M is metacentre. The metacentre is considered fixed for a small angle of heel; However, at a larger angle than the heel, the metacentre can no longer be considered fixed, and the actual location must be found to calculate the stability of the vessel.
Metacentre can be calculated using the formula:
Where KB is the center of buoyancy (the height above the bottom), I is the second moment of the plane area in meters 4 and V is the displacement volume in meters 3 . KM is the distance from settlement to metacentre.
Stable floating objects have natural winding frequencies, as do loads on springs, where the frequency increases as the springs become stiff. In boats, the equivalent of spring stiffness is the distance called "GM" or "metacentric height", being the distance between two points: the "G" center of gravity of the boat and "M", which is the point called metacentre.
Metacentre is determined by the ratio between boat inertia resistance and boat volume. (Inertial resistance is a quantifiable description of how the waterline width of the boat refuses to overturn.) The wide and shallow or narrow and deep stomach has a high transverse metacenter (relative to hull), and otherwise has a low metaspor; the very opposite is shaped like round wood or a flattened boat.
Ignoring ballast, wide and shallow or narrow and deep means the ship is very quickly rolled over and very difficult to be turned upside down and stiff. Spherical round-shaped log means slow to roll and easily reversed and soft.
"G", is the center of gravity. The "GM", the stiffness parameters of a vessel, can be extended by lowering the center of gravity or altering the shape of the hull (and thus changing the abandoned volume and second moment of the plane plane) or both.
The ideal boat strikes the balance. A very soft boat with a very slow roll period is risked upside down, but comfortable for passengers. However, ships with higher metacentric grades are "too stable" with short roll periods resulting in high acceleration at the deck level.
Cruise cruises, especially racing yachts, are designed to be rigid, which means the distance between the mass center and the metacentre is enormous to withstand the effects of wind limping on the screen. In such vessels, twisting is uncomfortable due to the high pole inertia moment and aerodynamic damping on the screen.
Maps Metacentric height
Different center
buoyancy center is at the center of the mass of water volume moved by the stomach. This point is referred to as B in the naval architecture. The center of gravity of a ship is usually denoted as a point G or VCG . When a ship is at equilibrium, the floating center is vertically aligned with the ship's center of gravity.
The metacentre is the point at which the line intersects (at an angle?) From the power to the buoyancy? Ã, Â ± d?. When the ship is vertical, the metacentre is located above the center of gravity and moves in the opposite direction from the heel when the ship is rolling. This distance is also abbreviated as GM . As the vessel rises, the center of gravity generally remains on the vessel because it depends only on the weight and shipload position, but the surface area increases, increasing the BM? Work must be done to roll the stomach stable. This is converted into potential energy by increasing the center of gastric mass with respect to the water level or by lowering the buoyancy center or both. This potential energy will be released to repair the stomach and the stable attitude will be in the smallest place. This is the potential energy and kinetic energy interactions that result in the ship having a natural winding frequency. For a small angle, the metacentre, M ?, moves with the lateral component so it is no longer directly above the center of mass.
The right pair on the ship is proportional to the horizontal distance between two equal forces. This is the force of gravity that acts down at the center of mass and the same magnitude of force that acts upward through the center of buoyancy, and through the metasenter on it. The proportional attachment pair with the metacentric height is multiplied by the sinus from the heel angle, hence the high importance of metacentric to stability. As a right hull, work is done either by the center of the falling mass, or by falling water to accommodate increased buoyancy, or both.
For example, when the roll of the cylinder rolls is perfect, the center of buoyancy remains on the axis of the cylinder at the same depth. However, if the center of mass is below the axis, it will move to one side and rise, creating potential energy. Conversely if the stomach has a perfectly rectangular cross section having its center of mass at the waterline, the center of mass remains at the same height, but the buoyancy center falls as the heel of the stomach, again storing the potential energy.
When assigning general reference to center, the printed line (in plates or planks) paid off ( K ) is generally selected; thus, the reference height is:
KB - to Power Center
KG - to Gravity Center
KMT - to Metacentre Crossing
Right arm
The metacentric height is the estimate for the stability of the vessel at a small angle (0-15 degrees) from the heel. Outside the range, the stability of the ship is dominated by what is known as the direction of the direction. Depending on geometry, the Naval Architects must be iterating to calculate the center of buoyancy at the enhancement of the heel angle. They then calculate the activation moment at this angle, determined by using the equation:
Where RM is the right moment, GZ is the straightening arm and ? is a transfer. Due to the constant transfer of the vessels, the common practice is to simply draw a straight arm against a heel angle. The right arm (also known as GZ - see diagram): horizontal distance between the floating and gravitational lines.
- on a small heel corner
There are several important factors that must be determined with regard to straightening the arm/moment. This is known as the maximum coronation arm/moment, the deck sinking point, the downflooding angle, and the point of loss of stability. When the maximum splicing is the maximum moment that can be applied to the ship without causing it to be reversed. Deck soaking point is the angle at which the first main deck will face the sea. Similarly, the downflooding angle is the angle at which water will be able to flood more deeply into the ship. Finally, the point of disappearance of stability is an unstable equilibrium point. Any smaller heel from this angle will allow the vessels to support themselves, while any larger heel from this angle will cause negative binding moments (or sudden moments) and force the ship to roll over. When the vessel reaches the heel equal to the point of loss of its stability, any external force will cause the ship to be inverted.
Sailing vessels are designed to operate with higher heel levels than motorized ships and pointing moments at extreme angles are essential.
Monohulled sailing ships should be designed to have a positive right arm (positive positive stability limit ) to at least 120 Â ° from the heel, although many sailing yachts have a stability limit of up to 90 Â ° (poles parallel to the water surface). Because the displacement of the stomach at a certain list level is disproportionate, computation can be difficult, and the concept was not formally introduced into the naval architecture until about 1970.
Stability
GM and scrolling period
The metacentre has a direct relationship with the rolling period of the ship. A ship with a small GM will be "tender" - has a long roll period. GMs that are either too low or negative increase the risk of an upside-down ship in bad weather, such as HMS Captain or Vasa . It also places the vessel at a potential risk for a large angle of heel if the cargo or ballast shifts, as with Ace Cougar. A ship with a low GM is less safe if it is damaged and partially flooded due to the low metacentric height leaving less security margin. For this reason, maritime regulatory bodies such as the International Maritime Organization set minimum safety limits for sailing vessels at sea. The greater metacentric altitude on the other hand may cause the ship to be too "stiff"; excessive stability is not convenient for passengers and crew. This is because the stiff boats quickly respond to the ocean as it tries to assume the tilt of the waves. An overly rigid vessel curls with short periods and high amplitudes that produce high angular acceleration. This increases the risk of damage to the ship and the charge and may cause excessive roll in special circumstances where the eigenperiod of the wave coincides with the eigen period of the ship's roll. Roll damping by the hull of a ship size keels sufficiently reduces the danger. Criteria for the effects of dynamic stability are still being developed. In contrast, the "tender" vessels lag behind the wave motions and tend to roll with lower amplitude. A passenger ship will usually have a long rolling period for convenience, maybe 12 seconds while the tanker or freighter may have a rolling period of 6 to 8 seconds.
Periode roll dapat diperkirakan dari persamaan berikut ini
di mana g adalah percepatan gravitasi, k adalah jari-jari lingkaran tentang sumbu longitudinal melalui pusat gravitasi dan adalah indeks stabilitas.
Stabilitas yang rusak
If the ship is flooded, the loss of stability is due to an increase of KB , the buoyancy center, and the loss of the airplane area - resulting in the loss of the airplane inertia moment - which lowers high metacentricity. This additional mass will also reduce the freeboard (the distance from water to the deck) and the angle of the ship from the lower flood (minimum angle of heel where water will flow to the hull). The positive stability range will be reduced to the lower flood angle thus reducing the reducing lever. When the vessel is tilted, the liquid in the stagnant volume will move to the lower side, shifting its center of gravity toward the list, further extending the heeling power. This is known as free surface effect.
Free surface effects
In a tank or space partially filled with liquid or semi-liquid (fish, ice, or grain for example) as the tank tends to surface liquid, or semi-fluid, fixed level. This results in the displacement of the center of gravity from the tank or space relative to the center of gravity as a whole. The effect is similar to carrying a large water tray. When the tip ends, the water flows to the side, which exacerbates the tip even further.
The significance of this effect is proportional to the cube width of the tank or compartment, so that two baffles separating the area into three parts will reduce the displacement of the gravity center of the fluid by a factor of 9. This is the significance in the ship's fuel tank or ballast tank, the tank charge tank, and in the compartment flooded or partially damaged. Another worrying feature of the free surface effect is that a positive feedback loop can be formed, in which the roll period is equal or nearly equal to the period of movement of the center of gravity in the liquid, so that each winding increases in magnitude until the loop is broken or the vessel is overturned.
This has been significant in historic capsizes, especially MSÃ, Herald of Free Enterprise and MSÃ, Estonia. .
Metallic transverse and elongated altitudes
There are also similar considerations in the movement of advanced metacentre and stern as pitches of ships. Metacentres are usually separately calculated for circular motion (side to side) and for longitudinal motion lengthwise extending. This is known as and , GM (t) and GM (l) , or sometimes GMt and GMl .
Technically, there are different metacentric altitudes for each combination of pitch and roll motion, depending on the moment of inertia of the water vessel area of ​​the vessel around the rotation axis in consideration, but they are usually only calculated and expressed as specific values ​​to restrict pitch motion and pure rolls.
Measurement
Metacentric altitude is usually estimated during ship design but can be determined with a slope test after it is built. This can also be done when ships or floating platforms are offshore in service. This can be calculated by theoretical formulas based on the shape of the structure.
The angle (s) obtained during the skewed experiment is directly related to GM. By using a skewed experiment, an as-built 'gravity center' can be found; obtain GM and KM with experimental measurements (using the measurement of the pendulum swing and draft readings), the center of gravity KG can be found. Thus KM and GM become known variables during inclination and KG is the desired calculated variable (KG = KM-GM)
See also
References
Source of the article : Wikipedia
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