Vessel metacenter definition. Lateral stability

Asia

With regard to surface ships (vessels), due to the elongation of the shape of the ship's hull, its longitudinal stability is much higher than the transverse one, therefore, for the safety of navigation, it is most important to ensure proper transverse stability.

Depending on the magnitude of the inclination, stability is distinguished at small angles of inclination ( initial stability) and stability at large angles of inclination.

Depending on the nature active forces distinguish between static and dynamic stability.

Static stability- is considered under the action of static forces, that is, the applied force does not change in magnitude. Dynamic stability- is considered under the action of changing (that is, dynamic) forces, for example, wind, sea waves, cargo movement, etc.

Initial lateral stability

With a roll, stability is considered as initial at angles up to 10-15 °. Within these limits, the restoring force is proportional to the angle of heel and can be determined using simple linear relationships.

In this case, the assumption is made that deviations from the equilibrium position are caused by external forces that do not change either the ship's weight or the position of its center of gravity (CG). Then the immersed volume does not change in magnitude, but changes in shape. Equal-volume inclinations correspond to equal-volume waterlines, cutting off equal-sized immersed hull volumes. The line of intersection of the waterline planes is called the axis of inclination, which, with equal volume inclinations, passes through the center of gravity of the waterline area. With transverse inclinations, it lies in the diametrical plane.

Free surfaces

All the cases discussed above assume that the ship's center of gravity is stationary, that is, there are no loads that move when tilted. But when such weights are present, their influence on stability is much greater than the others.

A typical case is liquid cargoes (fuel, oil, ballast and boiler water) in partially filled tanks, that is, having free surfaces. Such loads are capable of overflowing when tilted. If the liquid cargo fills the tank completely, it is equivalent to a solid fixed cargo.

If the liquid does not fill the tank completely, that is, it has a free surface that always occupies a horizontal position, then when the vessel is tilted at an angle θ the liquid overflows in the direction of inclination. The free surface will take the same angle relative to the design line.

Levels of liquid cargo cut off equal volumes of tanks, that is, they are similar to waterlines of equal volume. Therefore, the moment caused by the transfusion of liquid cargo when heeling δm θ, can be represented similarly to the moment of shape stability m f, only δm θ opposite m f by sign:

δm θ = − γ x i x θ,

where i x- the moment of inertia of the area of the free surface of the liquid cargo relative to the longitudinal axis passing through the center of gravity of this area, γ- specific gravity of the liquid cargo

Then the restoring moment in the presence of a liquid load with a free surface:

m θ1 = m θ + δm θ = Phθ − γ x i x θ = P(h − γ x i x /γV)θ = Ph 1 θ,

where h- transverse metacentric height in the absence of transfusion, h 1 = h − γ g i x /γV- actual transverse metacentric height.

The influence of the overflowing load gives a correction to the transverse metacentric height δ h = − γ x i x /γV

The densities of water and liquid cargo are relatively stable, that is, the main influence on the correction is the shape of the free surface, or rather its moment of inertia. This means that the lateral stability is mainly affected by the width, and the longitudinal length of the free surface.

The physical meaning of the negative value of the correction is that the presence of free surfaces is always reduces stability. Therefore, organizational and constructive measures are being taken to reduce them:

full pressing of tanks to avoid free surfaces
if this is not possible, filling under the neck, or vice versa, only at the bottom. In this case, any inclination sharply reduces the free surface area.
control of the number of tanks with free surfaces
breakdown of tanks by internal impenetrable bulkheads in order to reduce the moment of inertia of the free surface i x

Dynamic stability

Unlike static, the dynamic effect of forces and moments imparts significant angular velocities and accelerations to the ship. Therefore, their influence is considered in energies, more precisely in the form of the work of forces and moments, and not in the efforts themselves. In this case, the kinetic energy theorem is used, according to which the increment in the kinetic energy of the ship's inclination is equal to the work of the forces acting on it.

When a heeling moment is applied to the ship m cr, constant in magnitude, it receives a positive acceleration with which it begins to roll. As the inclination increases, the restoring moment increases, but at the beginning, up to the angle θ st, at which m cr = m θ, it will be less heeling. Upon reaching the angle of static equilibrium θ st, the kinetic energy of rotational motion will be maximum. Therefore, the ship will not remain in the equilibrium position, but due to kinetic energy it will roll further, but slowly, since the restoring moment is greater than the heeling one. The previously accumulated kinetic energy is repaid by the excess work of the restoring moment. As soon as the magnitude of this work is sufficient to completely extinguish the kinetic energy, the angular velocity will become equal to zero and the ship will stop heeling.

The largest angle of inclination that the ship receives from the dynamic moment is called the dynamic angle of heel. θ dyn. In contrast to it, the angle of heel with which the ship will sail under the action of the same moment (according to the condition m cr = m θ), is called the static bank angle θ st.

Referring to the static stability diagram, work is expressed as the area under the restoring moment curve m in. Accordingly, the dynamic bank angle θ dyn can be determined from the equality of areas OAB and BCD corresponding to the excess work of the restoring moment. Analytically, the same work is calculated as:

A θ = ∫ 0 θ m θ ∂ θ (\displaystyle A_(\theta )=\int _(0)^(\theta )m_(\theta )\partial \theta ) ,

on the interval from 0 to θ dyn.

Reaching dynamic bank angle θ dyn, the ship does not come into equilibrium, but under the influence of an excess restoring moment, it begins to straighten rapidly. In the absence of water resistance, the ship would enter into undamped oscillations around the equilibrium position when heeling θ st with amplitude from 0 to θ dyn. But in practice, due to the resistance of the water, the oscillations quickly die out and it remains to float with a static heel angle. θ st.

The dynamic effect of the heeling moment is always more dangerous than the static one, as it leads to more significant inclinations. Within the rectilinear portion of the static stability diagram, the dynamic bank angle is approximately twice the static angle: θ dyn ≈ 2 θ st.

§ 12. Seaworthiness of ships. Part 1

Seaworthiness must be possessed by both civilian ships and warships.

The study of these qualities with the use of mathematical analysis is carried out by a special scientific discipline - ship theory.

If a mathematical solution to the problem is impossible, then they resort to experience in order to find the necessary dependence and verify the conclusions of the theory in practice. Only after a comprehensive study and testing on the experience of all the seaworthiness of the vessel, they begin to create it.

Seaworthiness in the subject "Ship Theory" is studied in two sections: ship statics and dynamics. Statics studies the laws of equilibrium of a floating vessel and the qualities associated with it: buoyancy, stability and unsinkability. Dynamics studies the vessel in motion and considers its qualities such as handling, pitching and propulsion.

Let's get acquainted with the seaworthiness of the ship.

Vessel buoyancy called its ability to stay on the water at a certain draft, carrying the intended cargo in accordance with the purpose of the ship.

There are always two forces acting on a floating ship: a) on the one hand, weight forces, equal to the sum of the weight of the ship itself and all cargo on it (calculated in tons); the resultant force of the weight is applied in ship's center of gravity(CG) at point G and is always directed vertically down; b) on the other hand sustaining forces, or buoyancy forces(expressed in tons), i.e., the pressure of water on the submerged part of the hull, determined by the product of the volume of the submerged part of the hull and the volumetric weight of the water in which the ship floats. If these forces are expressed by the resultant applied at the center of gravity of the underwater volume of the vessel at point C, called center of magnitude(CV), then this resultant for all positions of the floating vessel will always be directed vertically upwards (Fig. 10).

Displacement is the volume of the immersed part of the body, expressed in cubic meters. Volumetric displacement serves as a measure of buoyancy, and the weight of the water displaced by it is called weight displacement D) and is expressed in tons.

According to the law of Archimedes, the weight of a floating body is equal to the weight of the volume of fluid displaced by this body,

Where y is the volumetric weight of outboard water, t / m 3, taken in calculations equal to 1.000 for fresh water and 1.025 for sea water.

Rice. 10. Forces acting on a floating ship, and points of application of the resultant of these forces.

Since the weight of a floating vessel P is always equal to its weight displacement D, and their resultants are directed oppositely to each other along the same vertical, and if we denote the coordinates of the point G and C along the length of the vessel, respectively, x g and x c, in width y g and y c and along height z g and z c , then the equilibrium conditions for a floating ship can be formulated by the following equations:

P = D; x g \u003d x c.

Due to the symmetry of the ship with respect to the DP, it is obvious that the points G and C must lie in this plane, then

Y g = y c = 0.

Usually the center of gravity of surface vessels G lies above the center of gravity C, in which case

Sometimes it is more convenient to express the volume of the underwater part of the hull in terms of the main dimensions of the vessel and the coefficient of overall completeness, i.e.

Then the weight displacement can be represented as

If we denote by V n the full volume of the hull to the upper deck, subject to the watertight closing of all side openings, we get

The difference V n - V, representing a certain volume of a waterproof hull above the load waterline, is called the buoyancy margin. In the event of an emergency ingress of water into the vessel's hull, its draft will increase, but the vessel will remain afloat due to the buoyancy margin. Thus, the reserve of buoyancy will be greater than more height free water impenetrable side. Therefore, the reserve of buoyancy is an important characteristic of the vessel, ensuring its unsinkability. It is expressed as a percentage of the normal displacement and has the following minimum values: for river vessels 10-15%, for tankers 10-25%, for dry cargo ships 30-50%, for icebreakers 80-90%, and for passenger ships 80-100%.

Rice. 11. Drill on the frames

The weight of the vessel P (weight load) And the coordinates of the center of gravity are determined by a calculation that takes into account the weight of each part of the hull, mechanisms, equipment, supplies, supplies, cargo, people, their luggage and everything on board. To simplify calculations, it is planned to combine individual items by specialty into articles, subgroups, groups and sections of the load. For each of them, the weight and static moment are calculated.

Given that the moment of the resultant force is equal to the sum of the moments of the component forces relative to the same plane, after summing the weights and static moments over the entire ship, the coordinates of the ship's center of gravity G are determined. the height from the main line z c is determined from the theoretical drawing by the trapezoid method in tabular form.

For the same purpose, auxiliary curves are used, the so-called drill curves, also drawn according to the theoretical drawing.

There are two curves: drill along the frames and drill along the waterlines.

Drilling on frames(Fig. 11) characterizes the distribution of the volume of the underwater part of the hull along the length of the ship. It is built in the following way. Using the method of approximate calculations, the area of the submerged part of each frame (w) is determined from the theoretical drawing. On the abscissa axis, the length of the vessel is plotted on the selected scale, and the position of the frames of the theoretical drawing is plotted on it. On the ordinates recovered from these points, the corresponding areas of the calculated frames are plotted on a certain scale.

The ends of the ordinates are connected by a smooth curve, which is the drill along the frames.

Rice. 12. Drilling along the waterlines.

Drilling on the waterline(Fig. 12) characterizes the distribution of the volume of the underwater part of the hull along the height of the vessel. To build it according to a theoretical drawing, the areas of all waterlines (5) are calculated. These areas, on a chosen scale, are plotted along the corresponding horizontals located according to the ship's drafts, in accordance with the position of a given waterline. The resulting points are connected by a smooth curve, which is the combatant along the waterlines.

Rice. 13. Cargo dimension curve.

These curves serve as the following characteristics:

1) the areas of each of the combatants express the volumetric displacement of the ship on an appropriate scale;

2) the abscissa of the center of gravity of the combat area along the frames, measured on the scale of the length of the ship, is equal to the abscissa of the center of the ship's size x c;

3) the ordinate of the center of gravity of the combat area along the waterlines, measured on the scale of draft, is equal to the ordinate of the center of the ship's magnitude z c . Cargo size represents a curve (Fig. 13) characterizing the volumetric displacement of the ship V depending on its draft T. From this curve, you can determine the displacement of the ship depending on its draft or solve the inverse problem.

This curve is built in a system of rectangular coordinates on the basis of pre-calculated volumetric displacements for each waterline of the theoretical drawing. On the y-axis, on a selected scale, the ship's drafts are plotted for each of the waterlines, and horizontal lines are drawn through them, on which, also on a certain scale, the displacement value obtained for the corresponding waterlines is plotted. The ends of the resulting segments are connected by a smooth curve, which is called the cargo size.

Using the cargo size, it is possible to determine the change in the average draft from the reception or expenditure of cargo, or to determine the draft of the vessel from a given displacement, etc.

Stability called the ability of the ship to resist the forces that caused it to tilt, and after the termination of these forces, return to its original position.

Vessel inclinations are possible for various reasons: from the action of oncoming waves, due to asymmetric flooding of compartments during a hole, from the movement of goods, wind pressure, due to the receipt or expenditure of goods, etc.

The inclination of the vessel in the transverse plane is called roll, and in the longitudinal plane - d inferent; the angles formed in this case denote respectively O and y,

Distinguish initial stability, i.e. stability at small angles of heel, at which the edge of the upper deck begins to enter the water (but not more than 15 ° for high-sided surface vessels), and stability at high inclinations .

Let us imagine that under the action of external forces the ship received a roll at an angle of 9 (Fig. 14). As a result, the volume of the underwater part of the vessel retained its value, but changed its shape; on the starboard side, an additional volume entered the water, and on the port side, an equal volume came out of the water. The center of magnitude has moved from the initial position C towards the roll of the vessel, to the center of gravity of the new volume - point C 1 . When the vessel is inclined, the gravity P applied at point G and the support force D applied at point C, remaining perpendicular to the new waterline B 1 L 1, form a pair of forces with the shoulder GK, which is a perpendicular lowered from point G to the direction of the support forces .

If we continue the direction of the support force from point C 1 until it intersects with its original direction from point C, then at small roll angles corresponding to the conditions of initial stability, these two directions will intersect at point M, called transverse metacenter .

The distance between the metacenter and the center of magnitude of the MC is called transverse metacentric radius, denoted by p, and the distance between the point M and the center of gravity of the vessel G - transverse metacentric height h 0. Based on the data in Fig. 14 you can make an identity

H 0 \u003d p + z c - z g.

In a right triangle GMR, the angle at the vertex M will be equal to angle 0. From its hypotenuse and the opposite angle, one can determine the leg GK, which is shoulder m of the restoring pair GK=h 0 sin 8, and the restoring moment will be Mrest = DGK. Substituting the shoulder values, we obtain the expression

Mrest = Dh 0 * sin 0,

Rice. 14. Forces acting when the vessel rolls.

The mutual position of the points M and G makes it possible to establish the following sign characterizing the transverse stability: if the metacenter is located above the center of gravity, then the restoring moment is positive and tends to return the ship to its original position, i.e., when heeling, the ship will be stable, on the contrary, if the point M is located below the point G, then with a negative value of h 0 the moment is negative and will tend to increase the roll, i.e. in this case the ship is unstable. It is possible that the points M and G coincide, the forces P and D act along the same vertical line, there are no pairs of forces, and the restoring moment is zero: then the ship must be considered unstable, since it does not tend to return to its original equilibrium position (Fig. fifteen).

The metacentric height for typical load cases is calculated during the ship design process and serves as a measure of stability. The value of the transverse metacentric height for the main types of ships lies in the range of 0.5-1.2 m, and only for icebreakers it reaches 4.0 m.

To increase the transverse stability of the vessel, it is necessary to reduce its center of gravity. This extremely important factor must always be remembered, especially when operating a ship, and a strict record should be kept of the consumption of fuel and water stored in double-bottom tanks.

Longitudinal metacentric height H 0 is calculated similarly to the transverse one, but since its value, expressed in tens or even hundreds of meters, is always very large - from one to one and a half vessel lengths, then after the verification calculation, the longitudinal stability of the vessel is practically not calculated, its value is interesting only in the case of determining the draft of the vessel bow or stern during longitudinal movements of cargo or when compartments are flooded along the length of the vessel.

Rice. 15. Lateral stability of the vessel, depending on the location of the cargo: a - positive stability; b - equilibrium position - the ship is unstable; c - negative stability.

The stability of the vessel is of utmost importance, and therefore, usually, in addition to all theoretical calculations, after the construction of the vessel, the true position of its center of gravity is checked by experimental inclination, i.e., the transverse inclination of the vessel by moving a load of a certain weight, called roll ballast .

All the conclusions obtained earlier, as already mentioned, are practically valid for the initial stability, i.e., when heeling through small angles.

When calculating transverse stability at large angles of heel (longitudinal inclinations are not large in practice), variable positions of the center of magnitude, metacenter, transverse metacentric radius and restoring moment arm GK are determined for different angles of the ship's heel. Such a calculation is made starting from a straight position through 5-10 ° to the heel angle when the restoring shoulder turns to zero and the ship acquires negative stability.

According to this calculation, for a visual representation of the stability of the vessel at large angles of heel, they build static stability chart(also called the Reed diagram) showing the dependence of the static stability arm (GK) or the restoring moment Mrest on the heel angle 8 (Fig. 16). In this diagram, along the abscissa axis, the roll angles are plotted, and along the ordinate axis, the value of the restoring moments or the shoulders of the restoring pair, since with equal volume inclinations at which the ship's displacement D remains constant, the restoring moments are proportional to the stability shoulders.

Rice. 16. Diagram of static stability.

The static stability diagram is built for each typical case of ship loading, and it characterizes the stability of the ship as follows:

1) at all angles at which the curve is located above the abscissa axis, the righting shoulders and moments are positive, and the ship has positive stability. At those angles of heel, when the curve is located under the abscissa axis, the ship will be unstable;

2) the maximum of the chart determines the limit angle of roll 0 max and the limit heeling moment at the static inclination of the vessel;

3) the angle 8 at which the descending branch of the curve intersects the x-axis is called chart sunset angle. At this angle of heel, the restoring shoulder becomes equal to zero;

4) if an angle equal to 1 radian (57.3 °) is set aside on the abscissa axis, and from this point a perpendicular is erected until it intersects with the tangent drawn to the curve from the origin, then this perpendicular on the scale of the diagram will be equal to the initial metacentric height h 0 .

Stability is greatly influenced by moving, i.e., loose, as well as liquid and bulk cargoes that have a free (open) surface. When the vessel is tilted, these loads begin to move in the direction of the roll and, as a result, the center of gravity of the entire vessel will no longer be at a fixed point G, but will also begin to move in the same direction, causing a decrease in the transverse stability arm, which is equivalent to a decrease in the metacentric height with all the consequences arising from this. To prevent such cases, all cargo on ships must be secured, and liquid or bulk cargo must be loaded into containers that exclude any transfusion or spilling of cargo.

With the slow action of forces that create a heeling moment, the ship, tilting, will stop when the heeling and restoring moments are equal. In the event of a sudden action of external forces, such as a gust of wind, pulling a tug on board, pitching, a side salvo from guns, etc., the ship, tilting, acquires angular velocity and even with the termination of these forces, it will continue to roll by inertia for an additional angle until all of its kinetic energy (live force) of the vessel's rotational motion is used up and its angular velocity becomes zero. This inclination of the ship under the action of suddenly applied forces is called dynamic inclination. If, with a static heeling moment, the ship floats with only a certain roll of 0 ST, then in the case of the dynamic action of the same heeling moment, it can capsize.

In the analysis of dynamic stability for each displacement of the vessel, they build dynamic stability diagrams, whose ordinates represent, on a certain scale, the areas formed by the curve of the moments of static stability for the corresponding heel angles, i.e., they express the work of the restoring pair when the vessel is tilted at an angle of 0, expressed in radians. In rotational motion, as you know, the work is equal to the product of the moment and the angle of rotation, expressed in radians,

T 1 \u003d M kp 0.

According to this diagram, all issues related to the determination of dynamic stability can be solved as follows (Fig. 17).

The angle of heel with a dynamically applied heeling moment can be found by plotting the graph of the heeling pair on the diagram on the same scale; the abscissa of the point of intersection of these two graphs gives the required angle 0 DIN.

If in a particular case the fixing moment has a constant value, i.e. M kr \u003d const, then the work will be expressed

T 2 \u003d M kp 0.

And the graph will look like a straight line passing through the origin.

In order to build this straight line on the dynamic stability diagram, it is necessary to plot an angle equal to a radian along the abscissa axis and draw an ordinate from the obtained point. Having plotted on it, on the scale of ordinates, the value of M cr in the form of a segment Nn (Fig. 17), it is necessary to draw a straight line ON, which is the desired work schedule for the heeling pair.

Rice. 17. Determination of the angle of heel and the limiting dynamic inclination according to the diagram of dynamic stability.

The same diagram shows dynamic inclination 0 DIN, defined as the abscissa of the intersection point of both graphs.

With an increase in the moment M cr, the secant ON can take the limiting position, turning into an external tangent FROM drawn from the origin to the diagram of dynamic stability. Thus, the abscissa of the point of contact will be the original dynamic limiting angle of dynamic inclinations 0 The ordinate of this tangent, corresponding to the radian, expresses the limiting heeling moment at dynamic inclinations M krms.

When sailing, a ship is often subjected to dynamic external forces. Therefore, the ability to determine the dynamic heeling moment when deciding on the stability of the vessel is of great practical importance.

The study of the causes of the loss of ships leads to the conclusion that ships are mainly lost due to the loss of stability. To limit the loss of stability in accordance with various navigation conditions, the Register of the USSR developed the Stability Standards for ships of the transport and fishing fleet. In these standards, the main indicator is the ability of the vessel to maintain positive stability under the combined action of rolling and wind. The vessel meets the basic requirement of the Stability Standards if, under the worst case scenario of loading, its M CR remains less than M ODA.

In this case, the minimum overturning moment of the ship is determined from the diagrams of static or dynamic stability, taking into account the influence of the free surface of liquid cargo, rolling and elements of calculating the ship's windage for various cases of loading the ship.

The standards provide for a number of stability requirements, for example: M KR

the metacentric height must have a positive value, the angle of sunset of the static stability diagram must be at least 60°, and taking into account icing - at least 55°, etc. Mandatory observance of these requirements in all cases of loading gives the right to consider the vessel stable.

Unsinkable ship called its ability to maintain buoyancy and stability after the flooding of a part interior spaces water coming from overboard.

The unsinkability of the vessel is ensured by the reserve of buoyancy and the preservation of positive stability with partially flooded premises.

If the vessel has received a hole in the outer hull, then the amount of water Q flowing through it is characterized by the expression

where S is the area of the hole, m²;

G - 9.81 m/s²

H - distance of the center of the hole from the waterline, m.

Even with a slight hole, the amount of water entering the hull will be so large that the bilge pumps are not able to cope with it. Therefore, drainage means are placed on the ship based on the calculation of only the removal of water that enters after the hole has been sealed or through leaks in the joints.

To prevent the spread of water flowing into the hole through the vessel, constructive measures are provided: the hull is divided into separate compartments watertight bulkheads and decks. With such a division, in the event of a hole, one or more limited compartments will be flooded, which will increase the vessel's draft and, accordingly, the freeboard and buoyancy of the vessel will decrease.

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The definition of metacentric height can be formulated as follows. What is it? This is the center of gravity and the metacenter of the ship. The definition itself is not very clear, and therefore it is worth adding that very often this height is expressed through the stability of the vessel. This is because the metacenter is the main criterion for determining this very stability.

General concepts

As previously stated, the metacentric height is the elevation of the center of gravity above the metacenter of the ship itself. It is important to know here that the greater the value of this characteristic, the greater will be the initial stability of the vessel. If, for some reason, this height deviates towards a negative value, this indicates that the ship will not be able to sail without a roll. What does it mean? Negative values of the metacentric height should never be allowed. Although ... It is definitely impossible to get an exact answer to the question of whether a vessel with a negative value of this height will capsize. Since the theory of stability applies only to the inclinations of ships that do not exceed 10 degrees.

Rules and powers

It is important to note that there are rules of the Classification Societies that monitor the technical operation of ships. These documents describe that only ships with a metacentric height of at least 0.2 meters can be operated. To understand how a body with zero height would behave, we can imagine a barrel floating in water. This parameter of this body will be equal to 0, and its movement will occur along the longitudinal axis every time it is affected by any external force, for example, a wave or wind.

Another basis that allows a ship to float is gravity. And also the Archimedean force. Naturally, gravity will pull the ship down, that is, to the bottom. The numerical value of this characteristic is equal to its weight, and it is applied to the center of gravity of the ship. The Archimedean force, or, as it is also called, the buoyancy force, pushes a sea vessel out of the water. The force of this effect is equal to the displacement of the ship, which is applied in the center of the underwater volume.

The work of forces

With the "direct" position of the vessel, it turns out that these two forces balance each other and are in the same vertical plane. Because of this, the ship is able to move through the water. In the event that a ship roll occurs, the center of the underwater volume of the CV shifts towards the ship's inclination. The displacement occurs due to the fact that the shape of the underwater part of the hull changes. In addition, when the CV is displaced to one side, a restoring moment arises, which will counteract the roll of the sea vessel. When a tilt occurs, the CV, as it were, begins to rotate around a point, which is conditionally called the metacenter m.

The distance from this conditional point of the meteorological center m to the center of gravity of the DH vessel will be its height. For example, for a conventional rowboat, the numerical value of the metacentric height, which will be sufficient for people to safely sit down and stand up, is 0.3 m. In principle, nothing complicated.

How to ensure stability

Knowing everything that has been described above, the obvious question arises of how to assess the safety of a boat, sailing yacht, ship, etc.? How to understand how great are the chances of the ship to return from the "keel up" position to the normal, direct state?

In order to achieve this, it is necessary to improve the stability of the vessel. There are several proven methods for this. Sufficiently high stability can be ensured due to the fact that a fixed ballast will be placed on board the ship. However, here it must be taken into account that the center of gravity of the vessel will decrease with additional load. Shipbuilders, sailors and everyone who is familiar with maritime affairs have this rule: every kilogram of cargo located under the waterline will increase the stability of the ship, but every kilogram above this line will worsen the position of the ship.

Vessel recovery

In order to increase the weight, for example, of a yacht, it is equipped with such a thing as a fixed ballast keel. But, it is important to note here that it can only be placed on a classic type of yacht. Any other species with such a keel would be too heavy. Classic yachts are the absolute stability of a riverboat, as it is called. The thing is that this category of ships can straighten up after almost any roll. The angle of heel, which is necessary for the vessel not to recover, is 155 degrees. This is the parameter of a yacht such as the Contessa 32. In other words, a riverboat of this class will be able to recover to a straight position even after it capsizes with the keel up.

It is important to understand here that large vessels have greater dimensional stability initially due to their size. Another important point is that outboard water should not get inside the ship when heeling through any hatches or openings. If this happens, the liquid that is on board can negate all stability. This will happen due to the fact that the weight of the water that has entered will make the ship heavier. The metacentric height will be violated due to the displacement of the center of gravity. And the ship will begin to sink.

Vessels with superstructure

There is a type of ship that has a waterproof superstructure. Naturally, water will not be able to get inside such a ship, which means that stability will remain at the same level even with a large roll. This principle became fundamental in the invention of tumbler lifeboats. There are life rafts and lifeboats that are considered to be practically incapable because of their design. Such categories of ships are able to recover even after they have completely capsized.

You can take, for example, which has one tricky way to increase the stability of the vessel. The method is called tilting. And its essence lies in the fact that when tilted, the weight of the crew, ballast or swinging keel will move across the entire width of the vessel. There are many different types of moveable ballast in use today. And also there is one newest, which is the presence of underwater controlled wings.

Experimental height

Further. In order to experimentally calculate the metacentric height of the ship, you can move a large load around the ship. The movement of the load must occur at a certain distance Q from the place where it was originally located. Also, when moving an object, it is necessary to measure a small angle of rotation, which is denoted as af. The numerical value of this characteristic will correspond to the angle of the ship.

This is how the transverse metacentric height will look like in the formula:

h 0 \u003d 0.525 (W / T) 2, m

B is the ship's breadth, to be measured in meters, and T is the roll period, to be measured in seconds.

It was this method of calculation, as well as the experimental method of determining, that became the main provisions that made it possible to take the height of the metacenter of the ship as the main criterion for its stability.

Sailing ships

Currently, they are one of the most dangerous in terms of operation, as well as the most demanding in terms of stability. The thing is that with the wind the sail of such a vessel will be constantly exposed to strong air, which in such conditions will be the main point that creates the possibility of a roll. It is because of the presence of a sail that vessels with large and long masts and, as a result, large sails, need additional heavy fixed ballast, which will greatly reduce the center of gravity of the vessel, thereby creating a greater metacentric height.

It is very important to note that quite often they make such a mistake as assessing the stability of a ship only by its metacenter. Of course, this height will be the main criterion. However, the advantages that are available throughout the static stability diagram cannot be ignored. It includes not only the height of the metacenter.

Cases of instability

There are three cases of vessel instability. Let's consider them in more detail.

The first case occurs when the height h>0. This is due to the fact that the center of gravity is higher than the center of magnitude. If these conditions are met and the ship is tilted to either side, the line of action of the support force will cross the diametrical plane higher than the center of gravity.

The second case of instability will occur when the metacentric height is zero. In this case, practically, as in the previous one, the center of gravity will be higher than the center of magnitude. And when the ship is tilted, it will happen that the CG line will run along the magnitude line. In this case, the center of magnitude will always be located in the same vertical with the center of gravity. With this arrangement of forces, the restoring pair that levels the ship will simply be absent. Without the influence of any external forces, the ship will not be able to return to its original, straight position.

The third case occurs if h<0. В данном случае ЦТ будет находиться выше, чем центр величины, а в наклонном положении линия действия силы поддержания будет пресекать след диаметральной плоскости ниже ЦТ. В таком случае при малейшем наклоне будет образовываться отрицательная пара сил, воздействующая на судно и приводящая к его опрокидыванию.