In the theory of lateral stability, ship inclinations are considered that occur in the midship plane, and an external moment, called the heeling moment, also acts in the midship plane.

Not limited for the time being to small inclinations of the ship (they will be considered as a special case in the section “Initial stability”), let us consider the general case of the ship’s heeling due to the action of a time-constant external heeling moment. In practice, such a heeling moment can arise, for example, from the action of a constant wind force, the direction of which coincides with the transverse plane of the vessel - the midship plane. Under the influence of this heeling moment, the ship has a constant roll to the opposite side, the value of which is determined by the wind force and the restoring moment from the side of the ship.

In the literature on the theory of the ship, it is customary to combine two positions of the ship in the figure at once - straight and rolled. The banked position corresponds to a new position of the waterline relative to the vessel, which corresponds to a constant submerged volume, however, the shape of the underwater part of the banked vessel no longer has symmetry: the starboard side is submerged more than the port side (Fig. 1).

All waterlines corresponding to one value of the ship's displacement (at a constant weight of the ship) are called equal volume.

The exact image in the figure of all equal-volume waterlines is associated with great computational difficulties. In ship theory, there are several methods for graphical representation of equal volume waterlines. At very small angles of heel (at infinitely small equal-volume inclinations), one can use the corollary from L. Euler's theorem, according to which two equal-volume waterlines that differ by an infinitely small angle of heel intersect along a straight line passing through their common center of gravity of the area (for finite inclinations, this the statement loses force, since each waterline has its own center of gravity of the area).

If we disregard the real distribution of the forces of the ship's weight and hydrostatic pressure, replacing their action with concentrated resultants, then we come to the scheme (Fig. 1). At the ship's center of gravity, a weight force is applied, directed in all cases perpendicular to the waterline. Parallel to it, the buoyancy force acts, applied in the center of the underwater volume of the vessel - in the so-called center of magnitude(dot With).

Due to the fact that the behavior (and origin) of these forces do not depend on each other, they no longer act along the same line, but form a pair of forces parallel and perpendicular to the acting waterline V 1 L 1. With regard to the strength of the weight R we can say that it remains vertical and perpendicular to the surface of the water, and the heeled vessel deviates from the vertical, and only the conventionality of the figure requires that the vector of the weight force be deflected from the diametrical plane. It is easy to understand the specifics of this approach if we imagine a situation with a video camera mounted on a ship, showing on the screen the sea surface tilted at an angle equal to the ship's roll angle.

The resulting pair of forces creates a moment, which is commonly called restoring moment. This moment counteracts the external heeling moment and is the main object of attention in the theory of stability.

The value of the restoring moment can be calculated by the formula (as for any pair of forces) as the product of one (any of the two) forces and the distance between them, called shoulder of static stability:

Formula (1) indicates that both the shoulder and the moment itself depend on the ship's roll angle, i.e. are variable (in the sense of roll) quantities.

However, not in all cases the direction of the restoring moment will correspond to the image in Fig.1.

If the center of gravity (as a result of the peculiarities of the placement of goods along the height of the vessel, for example, with an excess of cargo on the deck) is quite high, then a situation may arise when the weight force is to the right of the line of action of the support force. Then their moment will act in the opposite direction and will contribute to the heeling of the vessel. Together with the external heeling moment, they will capsize the vessel, since there are no other opposing moments anymore.

It is clear that in this case this situation should be assessed as unacceptable, since the ship does not have stability. Consequently, with a high position of the center of gravity, the ship may lose this important seaworthiness - stability.

On displacement ships, the ability to influence the ship's stability, "control" it, is provided to the navigator only by rational placement of cargo and reserves along the height of the ship, which determine the position of the ship's center of gravity. Be that as it may, the influence of crew members on the position of the center of magnitude is excluded, since it is associated with the shape of the underwater part of the hull, which (with a constant displacement and draft of the vessel) is unchanged, and in the presence of a roll of the vessel it changes without human intervention and depends only on draft. Human influence on the shape of the hull ends at the design stage of the vessel.

Thus, the position of the center of gravity in height, which is very important for the safety of the vessel, is in the “sphere of influence” of the crew and requires constant monitoring through special calculations.

For the calculation control of the vessel's "positive" stability, the concept of the metacenter and the initial metacentric height is used.

Transverse metacenter is a point that is the center of curvature of the trajectory along which the center of magnitude moves when the vessel rolls.

Consequently, the metacenter (as well as the center of magnitude) is a specific point, the behavior of which is exclusively determined only by the geometry of the shape of the vessel in the underwater part and its draft.

The position of the metacenter, corresponding to the landing of the ship without a roll, is commonly called initial transverse metacenter.

The distance between the ship's center of gravity and the initial metacenter in a specific loading option, measured in the center line (DP), is called initial transverse metacentric height.

The figure shows that the lower the center of gravity is in relation to the constant (for a given draft) initial metacenter, the greater the metacentric height of the vessel, i.e. the larger is the shoulder of the restoring moment and this moment itself.

Thus, the metacentric height is an important characteristic that serves to control the ship's stability. And the greater its value, the greater at the same roll angles will be the value of the restoring moment, i.e. resistance of the vessel to heeling.

With small ship heels, the metacenter is approximately at the site of the initial metacenter, since the trajectory of the center of magnitude (points With) is close to a circle, and its radius is constant. A useful formula follows from a triangle with a vertex at the metacenter, which is valid for small bank angles ( θ <10 0 ÷12 0):

where is the roll angle θ should be used in radians.

From expressions (1) and (2) it is easy to obtain the expression:

which shows that the static stability arm and the metacentric height do not depend on the weight of the ship and its displacement, but are universal stability characteristics that can be used to compare the stability of ships of different types and sizes.

So for ships with a high center of gravity (timber carriers), the initial metacentric height takes on the values h 0≈ 0 - 0.30 m, for dry cargo ships h 0≈ 0 - 1.20 m, for bulk carriers, icebreakers, tugs h 0> 1.5 ÷ 4.0 m.

However, the metacentric height should not take negative values. Formula (1) allows us to draw other important conclusions: since the order of magnitude of the restoring moment is determined mainly by the displacement of the vessel R, then the static stability arm is a “control variable” that affects the range of torque change M in for this displacement. And from the slightest change l(θ) due to inaccuracies in its calculation or errors in the initial information (data taken from the ship's drawings, or measured parameters on the ship), the magnitude of the moment significantly depends M in, which determines the ability of the vessel to resist inclinations, i.e. determining its stability.

Thus, the initial metacentric height plays the role of a universal stability characteristic, which makes it possible to judge its presence and magnitude, regardless of the size of the vessel.

If we follow the mechanism of stability at large angles of heel, then new features of the restoring moment will appear.

With arbitrary transverse inclinations of the vessel, the curvature of the trajectory of the center of magnitude With changes. This trajectory is no longer a circle with a constant radius of curvature, but is a kind of flat curve that has different values ​​of curvature and radius of curvature at each of its points. As a rule, this radius increases with the roll of the vessel and the transverse metacenter (as the beginning of this radius) leaves the diametrical plane and moves along its trajectory, tracking the movement of the center of magnitude in the underwater part of the vessel. In this case, of course, the very concept of metacentric height becomes inapplicable, and only the restoring moment (and its shoulder l(θ)) remain the only characteristics of the ship's stability at high inclinations.

However, at the same time, the initial metacentric height does not lose its role of being the fundamental initial characteristic of the stability of the vessel as a whole, since the order of magnitude of the restoring moment depends on its value, as on a certain “scale factor”, i.e. its indirect influence on the stability of the vessel at large angles of heel remains.

So, to control the stability of the vessel, carried out before loading, it is necessary at the first stage to evaluate the value of the initial transverse metacentric height h 0, using the expression:

where z G and z M 0 are the applicates of the center of gravity and the initial transverse metacenter, respectively, measured from the main plane in which the origin of the OXYZ coordinate system associated with the ship is located (Fig. 3).

Expression (4) simultaneously reflects the degree of participation of the navigator in ensuring stability. By selecting and controlling the position of the vessel's center of gravity in height, the crew ensures the stability of the vessel, and all geometric characteristics, in particular, Z M 0, must be provided by the designer in the form of graphs from settlement d, called curved elements of a theoretical drawing.

Further control of the ship's stability is carried out according to the methodology of the Maritime Register of Shipping (RS) or the methodology of the International Maritime Organization (IMO).

Restoring moment arm l and the moment M in have a geometric interpretation in the form of a Stability Diagram (DSD) (Fig.4). DSO is graphic dependence of the restoring moment shoulder l(θ) or the very momentM in (θ) from the angle of heel θ .

This graph, as a rule, is depicted for the ship's list only to starboard, since the whole picture for a list to port for a symmetrical ship differs only in the sign of the moment M in (θ).

The value of DSO in the theory of stability is very large: it is not only a graphic dependence M in(θ); The DSO contains comprehensive information on the status of the ship's loading in terms of stability. The DSO of the vessel allows solving many practical problems in this voyage and is a reporting document for the ability to start loading the vessel and sending it on a voyage.

The properties of DSO are as follows:

• DSO of a particular ship depends only on the relative position of the ship's center of gravity G and initial transverse metacenter m(or the value of the metacentric height h 0) and displacement R(or draft d cf) and takes into account the presence of liquid cargoes and stocks with the help of special amendments,
• the shape of the hull of a particular ship is shown in the DSO over the shoulder l (θ), rigidly connected with the shape of the hull contours , which reflects the displacement of the center of magnitude With towards the side entering the water when the ship is heeling.
• metacentric height h 0, calculated taking into account the influence of liquid cargoes and reserves (see below), appears on the DSO as the tangent of the slope of the tangent to the DSO at the point θ = 0, i.e.:

To confirm the correctness of the construction of the DSO, a construction is made on it: the angle is set aside θ \u003d 1 rad (57.3 0) and build a triangle with a hypotenuse tangent to the DSO at θ = 0, and a horizontal leg θ = 57.3 0. The vertical (opposite) leg should be equal to the metacentric height h 0 axis scale l(m).

• no actions can change the type of DSO, except for changing the values ​​of the initial parameters h 0 and R, since DSO reflects in a sense the invariable shape of the ship's hull through the value l (θ);
• metacentric height h 0 actually determines the type and extent of the DSO.

Bank angle θ = θ 3, at which the DSO graph crosses the abscissa axis, is called the sunset angle of the DSO. sunset angle θ 3 determines only the value of the angle of heel at which the weight force and the buoyancy force will act along one straight line and l(θ 3) = 0. Judge the capsizing of the vessel when heeling

θ = θ 3 will not be true, since the capsizing of the vessel begins much earlier - shortly after the maximum point of the DSO is overcome. DSO maximum point ( l = l m (θ m)) indicates only the maximum removal of the weight force from the support force. However, the maximum leverage l m and maximum angle θm are important values ​​in the control of stability and are subject to verification for compliance with the relevant standards.

DSO allows you to solve many problems of ship statics, for example, to determine the static angle of the ship's heel under the action of a constant (independent of the ship's roll) heeling moment M cr= const. This angle of heel can be determined from the condition of equality of the heeling and righting moments M in (θ) = M cr. In practice, this problem is solved as a problem of finding the abscissa of the intersection point of the graphs of both moments.

The static stability diagram reflects the vessel's ability to create a righting moment when the vessel is tilted. Its appearance has a strictly specific character, corresponding to the loading parameters of the vessel only in this voyage ( R = Ri , h 0 = h 0 i). The navigator involved in planning the loading voyage and stability calculations on the ship is obliged to build a specific DSS for the two states of the ship on the upcoming voyage: with the initial position of the cargo unchanged and at 100% and at 10% of ship stores.

In order to be able to build static stability diagrams for various combinations of displacement and metacentric height, he uses auxiliary graphic materials available in the ship's documentation for the project of this vessel, for example, pantokarens, or a universal static stability diagram.

Pantocarenes are supplied to the ship by the designer as part of the stability and strength information for the captain. are universal graphs for a given vessel, reflecting the shape of its hull in terms of stability.

Pantocarenes (Fig. 6) are shown as a series of graphs (at different heel angles (θ = 10,20,30,….70˚)) depending on the weight of the vessel (or its draft) of some part of the static stability arm, called the stability arm forms - lf(R, θ ).

The shoulder of the form is the distance that the buoyancy force will move relative to the original center of magnitude C ο when the vessel rolls (Fig. 7). It is clear that this displacement of the center of magnitude is associated only with the shape of the hull and does not depend on the position of the center of gravity in height. A set of shape shoulder values ​​at different heel angles (for a specific vessel weight P=Pi) are removed from the pantocaren charts (Fig. 6).

To determine the shoulders of stability l(θ) and build a diagram of static stability in the upcoming voyage, it is necessary to supplement the form arms with weight arms l in which are easy to calculate:

Then the ordinates of the future DSO are obtained by the expression:

Having performed calculations for two load states ( R app.\u003d 100% and 10%), two DSOs are built on a blank form, characterizing the ship's stability in this voyage. It remains to check the stability parameters for their compliance with national or international standards for the stability of marine vessels.

There is a second way to build a DSS, using the universal DSS of a given ship (depending on the availability of specific auxiliary materials on the ship).

Universal DSO(Fig. 6a) combines the transformed pantocarenes to determine lf and graphs of weight shoulders lin(θ). To simplify the view of graphical dependencies lin(θ) (see formula (6)) it was necessary to make a change of variable q = sin θ , resulting in sinusoidal curves lin(θ) transformed into straight lines lin (q(θ)). But in order to do this, it was necessary to adopt an uneven (sinusoidal) scale along the x-axis θ .

On the universal DSO, presented by the ship designer, there are both types of graphic dependencies - l f (Р,θ) and l in (z G ,θ). Due to the change in the x-axis, the graphs of the shoulder shape l f no longer look like pantocarenes, although they contain the same amount of information about the shape of the body as pantocarenes.

To use the universal DSO, it is necessary to use a meter to remove from the diagram the vertical distances between the curve l f (θ, P *) and curve l in (θ, z G *) for several values ​​of the ship's heel angle θ = 10, 20, 30, 40 ... 70 0 , which will correspond to the application of formula (6a). And then, on a clean DSO form, build these values ​​​​as the ordinates of the future DSO and connect the points with a smooth line (the axis of roll angles on the DSO is now taken with a uniform scale).

In both cases, both when using pantocaren and when using a universal DSO, the final DSO should be the same.

On the universal DSO, sometimes there is an auxiliary axis of the metacentric height (on the right), which facilitates the construction of a specific straight line with the value z G * : corresponding to some value of the metacentric height h 0 * , insofar as

Let us now turn to the method of determining the coordinates of the ship's center of gravity XG and ZG. In the information about the stability of the ship, you can always find the coordinates of the center of gravity of an empty ship abscissa xG0 and ordinate z G 0.

The products of the ship's weight and the corresponding coordinates of the center of gravity are called the static moments of the ship's displacement. relative to the midship plane ( M x) and main plane ( Mz); for an empty ship we have:

For a loaded ship, these quantities can be calculated by summing up the corresponding static moments for all cargo, tank stores, ballast in ballast tanks, and empty ship:

For static moment MZ it is necessary to add a special positive correction, taking into account the dangerous effect of the free surfaces of liquid cargoes, stores and ballast, available in the ship's tank tables, ∆MZh:

This correction artificially increases the value of the static moment in order to obtain the worst values ​​of the metacentric height, thereby the calculation is carried out with a safety margin.

Sharing now static moments M X and M Z correct for the total weight of the vessel in this voyage, we obtain the coordinates of the center of gravity of the vessel along the length ( XG) and corrected ( Z G correct), which is then used to calculate the corrected metacentric height h 0 correct:

and then to build a DSO. The value of Z mo (d) is taken from the curved elements of the theoretical drawing for a specific average draft.

Stability is the ability of a vessel deviated from the equilibrium position to return to it after the cessation of the forces that caused the deviation.

Vessel inclinations can occur 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 acceptance or expenditure of goods.

The inclination of the ship in the transverse plane is called roll, and in the longitudinal trim. The angles formed in this case are denoted respectively by θ and ψ

The stability that a ship has in longitudinal inclinations is called longitudinal. It is, as a rule, quite large, and the danger of capsizing the vessel through the bow or stern never arises.

The stability of the vessel with transverse inclinations is called transverse. It is the most important characteristic of the ship, which determines its seaworthiness.

There are initial lateral stability at small angles of heel (up to 10 - 15 °) and stability at large inclinations, since the restoring moment at small and large angles of heel is determined in various ways.

initial stability. If the vessel is under the influence of an external heeling moment M KR(for example, wind pressure) will roll by an angle θ (the angle between the original WL 0 and current WL 1 waterlines), then, due to a change in the shape of the underwater part of the vessel, the center of magnitude With move to a point From 1(Fig. 5). Sustaining power yV will be applied at the point C1 and directed perpendicular to the current waterline WL 1 . Dot M located at the intersection of the diametrical plane with the line of action of the supporting forces and is called transverse metacenter. Vessel weight force R stays in the center of gravity G. Together with strength yV it forms a pair of forces that prevents the vessel from tilting by the heeling moment M KR. The moment of this pair of forces is called restoring moment M V. Its value depends on the shoulder l=GK between the forces of weight and support of an inclined vessel: M B \u003d Pl \u003d Ph sin θ, where h- point elevation M above the ship's CG g, called transverse metacentric height vessel.

Rice. 5. The action of forces during the roll of the vessel.

It can be seen from the formula that the value of the restoring moment is the greater, the greater h. Therefore, the metacentric height can serve as a measure of stability for a given vessel.

Value h of a given ship at a certain draft depends on the position of the center of gravity of the ship. If the loads are positioned so that the ship's center of gravity takes a higher position, then the metacentric height will decrease, and with it the static stability arm and the restoring moment, i.e., the ship's stability will decrease. With a decrease in the position of the center of gravity, the metacentric height will increase, the stability of the vessel will increase.

Since for small angles their sines are approximately equal to the angles measured in radians, we can write M B = Phθ.

The metacentric height can be determined from the expression h = r + z c - z g , where z c- elevation of the CV over the OL; r- transverse metacentric radius, i.e., the elevation of the metacenter above the CV; z g- elevation of the ship's CG above the main one.

On a built ship, the initial metacentric height is determined empirically - inclining, i.e., the transverse inclination of the vessel by moving a load of a certain weight, called roll-ballast.

Stability at high angles of heel. As the ship's roll increases, the restoring moment first increases, then decreases, becomes equal to zero, and then not only does not prevent the inclination, but, on the contrary, contributes to it (Fig. 6).

Rice. 6. Diagram of static stability.

Since the displacement for a given load state is constant, the restoring moment changes only due to a change in the transverse stability arm l st. According to the calculations of transverse stability at large angles of heel, static stability chart, which is a graph expressing the dependence l st from the roll angle. The static stability diagram is built for the most typical and dangerous cases of ship loading.

Using the diagram, it is possible to determine the heeling angle from a known heeling moment or, conversely, to find the heeling moment from a known heeling angle. The initial metacentric height can be determined from the static stability diagram. For this, a radian equal to 57.3 ° is laid off from the origin of coordinates, and the perpendicular is restored to the intersection with the tangent to the curve of the stability shoulders at the origin. The segment between the horizontal axis and the intersection point on the scale of the diagram will be equal to the initial metacentric height.

With a slow (static) action of the heeling moment, the state of equilibrium during a roll occurs if the condition of equality of the moments is met, i.e. M KR \u003d M B(Fig. 7).

Rice. 7. Determination of the roll angle from the action of statically (a) and dynamically (b) applied force.

With the dynamic action of the heeling moment (a gust of wind, a jerk of the towing cable on board), the vessel, tilting, acquires an angular velocity. By inertia, it will pass the position of static equilibrium and will continue to heel until the work of the heeling moment becomes equal to the work of the restoring moment.

The value of the angle of heel under the dynamic action of the heeling moment can be determined from the static stability diagram. The horizontal line of the heeling moment is continued to the right until the area ODSE(work of the heeling moment) will not become equal to the area of ​​the figure BOTH(restoring moment work). At the same time, the area OASE is common, so we can restrict ourselves to comparing areas OH YEAH and ABC.

If the area bounded by the restoring moment curve is insufficient, the ship will capsize.

The stability of seagoing vessels must meet the Register requirements, according to which it is necessary to fulfill the condition (the so-called weather criterion): K \u003d M def min / M d max ≥ 1" where M def min- minimum overturning moment (minimum dynamically applied heeling moment, taking into account pitching), under the influence of which the vessel will not lose stability yet; M d max- dynamically applied heeling moment from wind pressure at the worst loading option in terms of stability.

In accordance with the requirements of the Register, the maximum arm of the static stability diagram lmax shall be not less than 0.25 m for vessels of 85 m in length and not less than 0.20 m for vessels over 105 m at an angle of heel θ of more than 30°. The slope angle of the diagram (the angle at which the curve of the stability arms intersects the horizontal axis) for all vessels must be at least 60°.

Influence of liquid cargoes on stability. If the tank is not filled to the top, that is, it has a free surface of the liquid, then when tilted, the liquid will overflow in the direction of the roll and the ship's center of gravity will shift in the same direction. This will lead to a decrease in the stability arm and, consequently, to a decrease in the restoring moment. At the same time, the wider the tank, in which there is a free surface of the liquid, the more significant will be the decrease in lateral stability. To reduce the influence of the free surface, it is advisable to reduce the width of the tanks and strive to ensure that during operation there is a minimum number of tanks with a free surface of the liquid.

Influence of bulk cargoes on stability. When transporting bulk cargo (grain), a slightly different picture is observed. At the beginning of the inclination, the load does not move. Only when the angle of heel exceeds the angle of repose does the cargo begin to spill. In this case, the spilled cargo will not return to its previous position, but, remaining at the side, will create a residual roll, which, with repeated heeling moments (for example, squalls), can lead to loss of stability and capsizing of the vessel.

To prevent spillage of grain in the holds, suspended longitudinal semi-bulkheads are installed - shifting boards or stack sacks of grain on top of the grain poured in the hold (cargo bagging).

Effect of a suspended load on stability. If the cargo is in the hold, then when it is lifted, for example, by a crane, there is, as it were, an instantaneous transfer of the cargo to the suspension point. As a result, the ship's CG will shift vertically upward, which will lead to a decrease in the righting moment arm when the ship receives a roll, i.e., to a decrease in stability. In this case, the decrease in stability will be the greater, the greater the mass of the load and the height of its suspension.

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

The obtained equilibrium conditions of the ship are not sufficient for it to constantly float in a given position relative to the water surface. It is also necessary that the balance of the vessel is stable. The property, which in mechanics is called the stability of equilibrium, in the theory of the ship is usually called stability. Thus, buoyancy provides the conditions for the equilibrium position of the vessel with a given landing, and stability ensures the preservation of this position.

The stability of the vessel changes with an increase in the angle of inclination and at a certain value it is completely lost. Therefore, it seems appropriate to study the stability of the vessel at small (theoretically infinitesimal) deviations from the equilibrium position with Θ = 0, Ψ = 0, and then determine the characteristics of its stability, their permissible limits at large inclinations.

It is customary to distinguish vessel stability at low inclination angles (initial stability) and stability at high inclination angles.

When considering small inclinations, it is possible to make a number of assumptions that make it possible to study the initial stability of the vessel within the framework of the linear theory and obtain simple mathematical dependences of its characteristics. Vessel stability at large angles of inclination is studied using a refined non-linear theory. Naturally, the stability property of the ship is unified and the accepted division is purely methodological.

When studying the stability of a vessel, its inclinations are considered in two mutually perpendicular planes - transverse and longitudinal. When the vessel is tilted in the transverse plane, determined by the angles of heel, it is studied lateral stability; with inclinations in the longitudinal plane, determined by the trim angles, study it longitudinal stability.

If the inclination of the ship occurs without significant angular accelerations (pumping liquid cargo, slow water flow into the compartment), then stability is called static.

In some cases, the forces tilting the vessel act suddenly, causing significant angular accelerations (wind squall, wave surge, etc.). In such cases, consider dynamic stability.

Stability is a very important nautical property of a vessel; together with buoyancy, it ensures the navigation of the vessel in a given position relative to the surface of the water, which is necessary to ensure propulsion and maneuver. A decrease in the ship's stability can cause an emergency roll and trim, and a complete loss of stability can cause it to capsize.

In order to prevent a dangerous decrease in the ship's stability, all crew members must:

Always have a clear idea of ​​the ship's stability;

Know the reasons that reduce stability;

Know and be able to apply all means and measures to maintain and restore stability.

Let us find the condition under which a ship floating in equilibrium without heel and trim will have initial stability. We assume that the loads do not shift when the ship is tilted and the ship's CG remains at the point corresponding to the initial position.

When the vessel is tilted, the force of gravity P and the buoyancy forces γV form a pair, the moment of which acts on the vessel in a certain way. The nature of this impact depends on the relative position of the CG and the metacenter.

Figure 3.9 - First case of vessel stability

There are three typical cases of the state of the vessel for which the influence of the moment of forces P and γV on it is qualitatively different. Consider them on the example of transverse inclinations.

1st case(Figure 3.9) - the metacenter is located above the CG, i.e. z m > z g . In this case, a different location of the center of magnitude relative to the center of gravity is possible.

1) In the initial position, the center of magnitude (point C 0) is located below the center of gravity (point G) (Figure 3.9, a), but when tilted, the center of magnitude shifts in the direction of inclination so much that the metacenter (point m) is located above the center of gravity vessel. The moment of forces P and γV tends to return the ship to its original equilibrium position, and therefore it is stable. A similar arrangement of points m, G and C 0 is found on most ships.

2) In the initial position, the center of magnitude (point C 0) is located above the center of gravity (point G) (Figure 3.9, b). When the ship is tilted, the resulting moment of forces P and γV straightens the ship, and therefore it is stable. In this case, regardless of the size of the displacement of the center of magnitude when tilted, a pair of forces always tends to straighten the ship. This is because the point G lies below the point C 0 . Such a low position of the center of gravity, which provides unconditional stability on ships, is difficult to implement constructively. Such an arrangement of the center of gravity can be found in particular on sailing yachts.

Figure 3.10 - Second and third case of vessel stability

2nd case(Figure 3.10, a) - the metacenter is located below the CG, i.e. z m< z g . В этом случае при наклонении судна момент сил Р и γV стремится еще больше отклонить судно от исходного положения равновесия, которое, следовательно, является неустойчивым. В этом случае наклонения судно имеет отрицательный восстанавливающий момент, т.е. оно не остойчиво.

3rd case(Figure 3.10, b) - the metacenter coincides with the CG, i.e. z m = z g . In this case, when the ship is tilted, the forces P and γV continue to act along the same vertical, their moment is equal to zero - the ship will be in a state of equilibrium in the new position. In mechanics, this is a case of indifferent equilibrium.

From the point of view of the theory of the ship, in accordance with the definition of ship stability, the ship is stable in the 1st case, and not stable in the 2nd and 3rd.

So, the condition for the initial stability of the vessel is the location of the metacenter above the CG. The ship has transverse stability if z m > z g , (3.7)

and longitudinal stability if z m > z g . (3.8)

Hence the physical meaning of the metacenter becomes clear. This point is the limit to which the center of gravity can be raised without depriving the ship of positive initial stability.

The distance between the metacenter and the ship's CG at Ψ = Θ = 0 is called initial metacentric height or simply metacentric height. The transverse and longitudinal planes of inclination of the vessel correspond respectively to the transverse h and longitudinal H metacentric heights. It's obvious that

h = z m – z g and H = z m – z g , (3.9)

or h = z c + r – z g and H = z c + R – z g , (3.10)

h = r – α and H = R – α, 3.11)

where α = z g – z c is the elevation of the CT above the CV.

As you can see, h and H differ only in metacentric radii, because α is the same quantity.

, so H is much larger than h.

α \u003d (1%) R, therefore, in practice, it is believed that H \u003d R.

Ship unsinkability

unsinkability called the ability of the vessel after the flooding of part of the premises to maintain sufficient buoyancy and stability. Unsinkability, unlike buoyancy and stability, is not an independent seaworthiness of a vessel. Unsinkability can be called a property of a ship maintain their seaworthiness when a part of the watertight volume of the hull is flooded, and the theory of unsinkability can be characterized as the theory of buoyancy and stability of a damaged ship.

A ship with good unsinkability, when one or more compartments are flooded, must, first of all, remain afloat and have sufficient stability to prevent it from capsizing. In addition, the ship should not lose propulsion, which depends on draft, roll and trim. An increase in draft, a significant list and trim increase the resistance of water to the movement of the vessel and impair the efficiency of the propellers and ship mechanisms. The vessel must also maintain controllability, which, with a good steering gear, depends on roll and trim.

Unsinkability is one of the elements of the ship's survivability, since the loss of unsinkability is associated with severe consequences - the death of the ship and people, so its provision is one of the most important tasks for both shipbuilders and the crew. In practice, unsinkability is ensured at all stages of the ship's life: by shipbuilders at the stages of design, construction and repair of the ship; by the crew during the operation of an undamaged ship; crew directly in an emergency. From such a division it follows that unsinkability is ensured by three sets of measures:

Structural measures that are carried out during the design, construction and repair of the ship;

Organizational and technical measures that are preventive and are carried out during the operation of the ship;

Measures to combat the unsinkability after the accident, aimed at combating the ingress of water, restoring stability and straightening the damaged vessel.

constructive activities. These measures are carried out at the stages of design and construction of the vessel and are reduced to the appointment of such buoyancy and stability margins so that when a given number of compartments are flooded, the change in the landing and stability of the emergency vessel does not go beyond the minimum allowable limits. The most effective means for using the reserve buoyancy in case of damage to the hull is the division of the vessel into compartments by watertight bulkheads and decks. Indeed, if the ship does not have an internal division into compartments, then in the presence of an underwater hole, the hull will fill with water and the ship will not be able to use the buoyancy reserve. The division of ships into compartments is carried out in accordance with Part V of the “Rules for the Classification and Construction of Sea-Going Ships” of the Maritime Register of Shipping. The waterline of an undamaged ship, used when dividing into compartments, the position of which is recorded in the ship's documentation, is called cargo waterline subdivision. The waterline of a damaged ship after flooding of one or more edema is called emergency waterline. The vessel loses its buoyancy if the damage waterline coincides with limit line of immersion- the line of intersection of the outer surface of the bulkhead deck plating with the outer surface of the side plating at the side. The greatest length of the part of the ship below the margin line is length of division of the vessel into compartments. Under bulkhead deck understand the uppermost deck, to which transverse watertight bulkheads are brought across the entire width of the vessel.

The amount of water poured into the damaged compartment of the ship is determined using room permeability coefficientμ is the ratio of the volume that can be filled with water when the compartment is flooded to the total theoretical volume of the room. The following permeability coefficients are regulated:

For premises occupied by mechanisms - 0.85;

For premises occupied by goods or stocks - 0.6;

For residential premises and premises occupied by cargoes with high permeability (empty containers, etc.) - 0.95;

For empty and ballast tanks - 0.98.

An important characteristic of the ship's unsinkability is maximum flood length, which is understood as the maximum length of the conditional compartment after the flooding of which, with a permeability coefficient of 0.80, with the draft of the corresponding cargo waterline of dividing the vessel into compartments and in the absence of an initial trim, the emergency waterline will touch the limit line of immersion.

An important constructive measure to ensure unsinkability is the creation of durable and watertight closures (doors, hatches, necks) installed along the contour of the watertight compartment, which should work well when heeling, trimming and sea waves. For all sliding and hinged type doors in watertight bulkheads, indicators shall be provided on the navigation bridge to indicate their position. The watertightness and strength of the vessel must be ensured not only in the underwater part, but also in the surface part of the hull, since the latter determines the buoyancy margin consumed in case of damage.

For the active struggle of the crew for unsinkability, the ship also provides for:

Creation of ship systems (heeling, trim, drainage, drainage, pumping liquid cargo, flooding, descent and bypass, ballasting);

Supply of emergency equipment and materials.

Such closures, systems and mechanisms must be appropriately marked to ensure their correct use with maximum efficiency. Emergency staging areas are called emergency posts. These can be special rooms or pantries, boxes and shields on the deck. Devices for remote start-up of ship systems can be brought to such posts.

Organizational and technical measures. Organizational and technical measures to ensure floodability are carried out by the ship's crew during operation in order to prevent water from entering the compartments, as well as to maintain the landing and stability of the ship, preventing it from flooding or capsizing. These activities include:

Proper organization and systematic training of the crew for the struggle for unsinkability;

Maintenance of all technical means of struggle for unsinkability, emergency supply in a condition that guarantees the possibility of their immediate use;

Systematic monitoring of the condition of all hull structures in order to check their wear (corrosion), replacement of individual structural elements during current or medium repairs in case of exceeding the established wear standards;

Planned painting of hull structures;

Elimination of distortions and sagging of watertight doors, hatches and windows, their systematic pacing and maintenance of all battening devices in good condition;

Control of outboard openings, especially when docking a vessel;

Strict observance of the instructions for the reception and consumption of liquid fuels;

Fastening cargo in a stowed manner and preventing their movement during pitching (especially across the vessel);

Compensation for stability losses caused by icing of the vessel by taking liquid ballast and taking measures to remove ice (chipping, washing with hot water);

Fight for invincibility. The struggle for unsinkability is understood as a set of actions of the crew aimed at maintaining and possibly restoring the reserves of buoyancy and stability of the vessel, as well as bringing it into a position that provides propulsion and controllability.

The struggle for unsinkability is carried out immediately after the ship receives damage and consists of combating incoming water, assessing its condition and measures to restore stability and straighten the ship.

Fighting incoming water consists in detecting the ingress of water into the ship, taking possible measures to prevent or limit the ingress and further spread of outboard water through the ship, as well as to remove it. At the same time, measures are being taken to restore the impermeability of the sides, bulkheads, platforms, and ensure the tightness of emergency compartments. Small holes, open seams, cracks are sealed with wooden wedges and plugs (chops) (Figure 3.11). Larger holes are covered with a hard metal patch or mat, pressed down with a shield.

Figure 3.11 - Wooden wedges and plugs: Figure 3.12 - Clamping bolts:

a, b, c - wedges; d, e - plugs a - with a folding bracket; b, c - hook.

For their fastening, the emergency equipment kit includes special bolts and clamps, spacer bars and wedges (Figure 3.12 3.15). Sealing the hole in the described ways is a temporary measure. After pumping out the water, the final restoration of the tightness is carried out by concreting the hole - placing a cement box. The success of sealing small holes depends on their location (surface or underwater), on the accessibility of the hole from inside the vessel, on its shape and the location of the edges of the torn metal (inside the hull or out).

Figure 3.13 - Metal patches:

a - valve; b - with clamping bolt; 1 - box-shaped body; 2 - stiffeners; 3 - socket for sliding stop; 4 - branch pipes with plugs for rods of hook bolts; 5 - valve; 6 - eyelets for fastening the tail ends; 7.8 - clamping bolt with a folding bracket; 9 - nut with handles; 10 - pressure disk.

Figure 3.14 - Metal sliding stop:

1.8 - thrust bearings; 2,3 - nuts with handles; 4 - pin; 5 - outer tube; 6 - inner tube; 7 - hinge

In the premises adjacent to the emergency compartment, water can enter as a result of its filtration through various leaks (violation of the tightness of the bulkhead glands of pipelines, cables, etc.). In such cases, the tightness is restored with caulking, wedges or plugs, and the bulkheads themselves are reinforced with emergency bars to prevent them from buckling or destruction.

Figure 3.15 - Emergency clamp: a - with grips for channel-type frames; b - grip for bulb type frames; 1 - clamp; 2 - clamping screw; 3 - clamping screw handles; 4 - nut-slider; 5 - locking screws; 6 - bolts fastening two

channel bars; 7- capture

Figure 3.16 - Soft patches

a - educational; 1 - canvas; 2 - firmware; 3 - lyktros; 4 - corner thimbles; 5 - krengels for the control end; b - stuffed: 1 - two-layer canvas cover; 2 - stuffed mat; 3 - firmware; 4 - angular thimble; c - lightweight: 1 - angular thimble; 2 - lyktros; 3 - pocket for rail; 4 - spacer rail from the pipe; 5.7 - layers of canvas; 6 - felt pad; g - chain mail: 1.2 - double layer of canvas cushion; 3 - patch lyktros; 4 – grid ring; 5 - canvas washer; 6 - mesh lyktros

Soft plasters (figure 3.16) are the main means for temporary sealing of holes, as they can fit snugly along the contours of the ship's hull in any place.

Literature:: p.36-47; : p.37-53, 112-119: : p.42-52; : with. 288-290.

Questions for self-control:

1. What are the main dimensions of the vessel?

2. Define the seaworthiness of a vessel?

3. Vessel's buoyancy?

4. Give a definition of all the volumetric operational characteristics of the vessel?

5. Draw a load line and decipher the letters at the comb?

6. What is called the unsinkability of the vessel?

7. What organizational and technical measures ensure unsinkability?

8. What is called the stability of the vessel?

9. Give the definition of metacentric height?

Steering gear

Rudder designs

A modern ship's rudder is a vertical wing with internal reinforcing ribs, rotating around a vertical axis, the area of ​​\u200b\u200bfor sea vessels is 1/10 - 1/60 of the area of ​​the submerged part of the DP (the product of the length of the vessel and its draft: LT).

The shape of the rudder is significantly influenced by the shape of the aft end of the vessel and the location of the propeller.

According to the shape of the feather profile, the rudders are divided into flat and profile streamlined. The profile rudder consists of two convex outer shells with ribs and vertical diaphragms on the inside, welded to each other and forming a frame to increase rigidity, which is covered on both sides with steel sheets welded to it.

Profile rudders have a number of advantages over lamellar ones:

Higher value of the normal force of pressure on the steering wheel;

Less torque required to turn the steering wheel.

In addition, the streamlined rudder improves the propulsion qualities of the vessel. Therefore, he found the greatest use.

The inner cavity of the rudder blade is filled with a porous material that prevents water from entering inside. The rudder blade is attached to the ruderpiece along with the ribs (Figure 4.1). Ruderpieces are cast (or forged) together with hinges for hanging the rudder on the ruder post (casting is sometimes replaced by a welded structure), which is an integral part of the sternpost.

The size of the rudder blade area depends on the type of vessel and its purpose. For an approximate assessment of the required rudder area, the S / LT ratio is usually used, which is 1.8-2.7 for sea transport ships with one rudder, and 1.8-2.2 for tankers;

for tugboats - 3-6; for coastal navigation vessels - 2.3-3.3.

By connection method with body and number of supports pen passive rudders are divided into:

Simple (multi-support) (Figure 4.2, a, 6);

Semi-suspended (single-support - suspended on a stock and supported on the body at one point) (Figure 4.2, c);

Suspended (unsupported, suspended on a stock) (Figure 4.2, d).

By axis position baller relative to the pen are distinguished:

The rudders are unbalanced (ordinary), in which the axis of the stock passes near the leading edge of the pen;

Balancing, the axis of the baller in which is located at some distance from the leading edge of the rudder. Semi-suspended balancing rudders are also called semi-balancing.

Unbalanced rudders are installed on single-rotor ships, semi-balanced and balanced - on all ships. The use of outboard (balanced) rudders makes it possible to reduce the power of the steering machine by reducing the torque required to shift the rudder.

Figure 4.1 - Steering device with a semi-suspended balanced streamlined steering wheel: 1 - rudder blade; 2 - ruderpis; 3 - lower thrust bearing of the baller; 4 - helmport pipe; 5 - upper support-thrust bearing of stock; 6 - steering machine; 7 - spare roller steering gear; 8 - stock; 9 - lower pin of the rudder blade; 10 - ruderpost

Rudder stock- this is a massive shaft with which the rudder blade is rotated. The lower end of the stock usually has a curved shape and ends with a paw - a flange that serves to connect the stock with the rudder blade with bolts, which makes it easier to remove the rudder during repairs. Sometimes instead of a flange (or a cone connection is used. The attachment of the rudder blade to the stock and the hull on many types of ships has much in common and differs slightly.

The rudder stock enters the aft clearance of the hull through a helm port tube, which ensures the tightness of the hull, and has at least two supports (bearings) in height. The lower support is located above the helm port pipe and, as a rule, has a stuffing box seal that prevents water from entering the ship's hull; the upper support is placed directly at the place where the sector or tiller is fixed. Usually, the upper support (thrust bearing) takes the mass of the stock and rudder blade, for which an annular protrusion is made on the stock.

In addition to rudders, thrusters are used on ships. By means of a propeller installed in the transverse channel of the ship's hull, they create a traction force in the direction perpendicular to its DP, provide controllability when the ship is not moving or when it is moving at extremely low speeds, when conventional steering devices are ineffective. Fixed or variable pitch propellers, vane propellers or pumps are used as propellers. Thrusters are located at the bow or stern ends, and on some ships two such devices are installed at both the bow and stern ends. In this case, it is possible not only to turn the vessel on the spot, but also to move it sideways without using the main propellers. To improve handling, there are also rotary nozzles fixed on the stock and special balancing rudders.

Control post

Part control schemes steering gear includes:

Control post with servo electrical system;

Electrical transmission from the control station to the electric motor.

For remote control of electro-hydraulic steering machines on ships, the Aist control system is widely used. Together with a gyrocompass and a steering machine, it provides four types of control: "Automatic", "Tracking", "Simple", "Manual".

Types of control "Automatic", "Tracking" are the main ones. In the event of a malfunction of these types of control of the steering machine, they are transferred to "Simple". In case of failure in the operation of the remote electrical transmission system, they switch to the “Manual” view.

The components of the "Aist" system are the control panel (PU) - the autopilot "Aist", the actuator (IM-1) and the steering sensor (RD).

The main control post is located in the wheelhouse near the steering compass and gyrocompass repeater. The steering wheel or steering control panel is usually mounted on the same column with the autopilot unit. The main element of the electrical transmission is a system of controllers placed in the steering column and connected by electrical wiring to the main drive electric motor in the tiller compartment.

steering machines

Steering machines. Currently, two types of steering machines are widely used - electric and hydraulic. The operation of the steering machines is controlled remotely from the wheelhouse, using a cable, roller, electric or hydraulic transmission. On modern ships, the last two are most common.

Steering gears

A variety of steering gears are used on ships of the navy, among which steering gears with electrical and hydraulic drives of domestic and foreign production. They provide the transmission of the forces of the steering motor to the stock.

Among them, two main types of drives are widely known.

Mechanical sector-tiller drive from an electric motor (Figure 4.3) is used on ships of small and medium displacement.

In this drive, the tiller is rigidly fastened to the rudder stock. The sector, freely mounted on the stock, is connected to the tiller with the help of a spring shock absorber, and with the steering motor - by a gear.

The rudder is shifted by an electric motor through the sector and tiller, and dynamic loads from wave shocks are damped by shock absorbers.

Figure 4.3 - Steering device with a mechanical sector tiller drive

from electric motor:

1 - manual (emergency) wheel drive; 2 - tiller; 3 - reducer; 4 - steering sector; 5- electric motor; 6 - spring, 7 - rudder stock; 8-profile figured steering wheel; 9 - segment of the worm wheel and brake; 10 - worm.

The control scheme of the sector-steering machine with electric transmission is shown on

figure 4.4

Figure 4.5 - Hydraulic steering control scheme

two-plunger steering machine:

1 - steering wheel position sensor; 2 - cable network; 3 - drive electric motor of the oil pump; 4 - oil pump; 5 - steering column; 6 - rudder position repeater; 7- telemotor receiver; 8- hydraulic cylinders of the steering machine; 9- rudder stock; 10 - oil pipeline; 11 - adjusting rod feedback of the servo system; 12 - telemotor sensor; 13 - oil pipeline.

Power plunger drive from hydraulic cylinders is used on modern ships (Figure 4.5). It consists of two hydraulic cylinders, an oil pump, a telemotor and a hydraulic system.

The operation of the device is as follows. When the steering wheel located in the wheelhouse is rotated, the teledynamic sensor of the control station generates a command signal in the form of oil pressure, which is pumped into the telemotor cylinder by the hydraulic system. Under the action of this signal, the telemotor drives

lever feedback system, which opens the access of power oil to one of the hydraulic cylinders. In this case, the oil under the pressure of the pump is transferred from one cylinder to another, moving the piston and turning the tiller, stock and rudder in the right direction. After that, the adjusting rod returns to the zero position, and the sensor and repeater fix the new position of the steering wheel.

So that the oil pressure in the hydraulic cylinders does not increase when a strong wave or a large ice floe strikes the rudder, the hydraulic system is equipped with safety valves and shock-absorbing springs.

In the event of a failure of the telemotor, the steering machine can be controlled manually from the tiller compartment.

When both oil pumps fail, they switch to manual rudder shifting, for which the hydraulic system pipes are directly connected to the hydraulic cylinders, creating pressure in them by rotating the steering wheel in the control station.

The layout of the units of a two-plunger steering machine with a similar principle of operation is shown in Figure 4.6. These machines are most widely used on modern ships, as they provide the highest efficiency of the entire steering gear. In them, the pressure of the working oil in the hydraulic cylinders is directly converted first into the translational movement of the plunger, and then through a mechanical transmission into the rotational movement of the rudder stock, which is rigidly connected to the tiller. The required oil pressure and power of the steering gear are formed by radial piston pumps of variable capacity, and it is distributed over the cylinders by a telemotor, which receives a command from the steering wheel from the wheelhouse.

The utilization factor of the vessel's net carrying capacity (formula, its explanation and limits for changing this indicator).

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

The equilibrium conditions of the ship obtained in Chapter 4 "Buoyancy" are not sufficient for it to constantly float in a given position relative to the water surface. It is also necessary that the balance of the vessel is stable. The property, which in mechanics is called the stability of equilibrium, in the theory of the ship is usually called stability. Thus, buoyancy provides the conditions for the equilibrium position of the vessel with a given landing, and stability ensures the preservation of this position.

The stability of the vessel changes with an increase in the angle of inclination and at a certain value it is completely lost. Therefore, it seems appropriate to study the stability of the vessel at small (theoretically infinitesimal) deviations from the equilibrium position with Θ = 0, Ψ = 0, and then determine the characteristics of its stability, their permissible limits at large inclinations.

It is customary to distinguish vessel stability at low inclination angles (initial stability) and stability at high inclination angles.

When considering small inclinations, it is possible to make a number of assumptions that make it possible to study the initial stability of the vessel within the framework of the linear theory and obtain simple mathematical dependences of its characteristics. Vessel stability at large angles of inclination is studied using a refined non-linear theory. Naturally, the stability property of the ship is unified and the accepted division is purely methodological.

When studying the stability of a vessel, its inclinations are considered in two mutually perpendicular planes - transverse and longitudinal. When the vessel is tilted in the transverse plane, determined by the angles of heel, it is studied lateral stability; with inclinations in the longitudinal plane, determined by the trim angles, study it longitudinal stability.

If the inclination of the ship occurs without significant angular accelerations (pumping liquid cargo, slow water flow into the compartment), then stability is called static.

In some cases, the forces tilting the vessel act suddenly, causing significant angular accelerations (wind squall, wave surge, etc.). In such cases, consider dynamic stability.

Stability is a very important nautical property of a vessel; together with buoyancy, it ensures the navigation of the vessel in a given position relative to the surface of the water, which is necessary to ensure propulsion and maneuver. A decrease in the ship's stability can cause an emergency roll and trim, and a complete loss of stability can cause it to capsize.

In order to prevent a dangerous decrease in the ship's stability, all crew members must:

always have a clear idea of ​​the ship's stability;

know the reasons that reduce stability;

know and be able to apply all means and measures to maintain and restore stability.

By the relative position of the cargo on the ship, the navigator can always find the most favorable value of the metacentric height, at which the ship will be sufficiently stable and less subject to rolling.

The heeling moment is the product of the weight of the cargo moved across the vessel by a shoulder equal to the distance of movement. If a person weighing 75 kg, sitting on the bank will move across the ship by 0.5 m, then the heeling moment will be equal to 75 * 0.5 = 37.5 kg/m.

Figure 91. Static stability diagram

To change the moment that heels the ship by 10 °, it is necessary to load the ship to full displacement, completely symmetrical about the diametrical plane.

The loading of the ship should be checked by drafts measured from both sides. The inclinometer is set strictly perpendicular to the diametral plane so that it shows 0°.

After that, it is necessary to move loads (for example, people) at pre-marked distances until the inclinometer shows 10 °. An experiment for verification should be carried out as follows: heel the ship on one side, and then on the other side.

Knowing the fixing moments of the heeling ship at various (up to the largest possible) angles, it is possible to build a static stability diagram (Fig. 91), which will evaluate the stability of the ship.

Stability can be increased by increasing the width of the vessel, lowering the CG, and installing stern boules.

If the center of gravity of the vessel is located below the center of magnitude, then the vessel is considered to be very stable, since the support force during a roll does not change in magnitude and direction, but the point of its application shifts towards the inclination of the vessel (Fig. 92, a).

Therefore, when heeling, a pair of forces is formed with a positive restoring moment, tending to return the ship to a normal vertical position on a straight keel. It is easy to see that h>0, while the metacentric height is 0. This is typical for yachts with a heavy keel and atypical for larger ships with a conventional hull.

If the center of gravity is located above the center of magnitude, then three cases of stability are possible, which the navigator should be well aware of.

The first case of stability.

Metacentric height h>0. If the center of gravity is located above the center of gravity, then with the inclined position of the vessel, the line of action of the support force crosses the diametrical plane above the center of gravity (Fig. 92, b).

Rice. 92. The Case of a Steady Vessel

In this case, a pair of forces with a positive restoring moment is also formed. This is typical of most conventionally shaped ships. Stability in this case depends on the body and the position of the center of gravity in height.

When heeling, the heeling side enters the water and creates additional buoyancy, tending to level the ship. However, when a vessel rolls with liquid and bulk cargoes capable of moving in the roll direction, the center of gravity will also shift in the roll direction. If the center of gravity during a roll moves beyond the plumb line connecting the center of magnitude with the metacenter, then the ship will capsize.

The second case of unstable sudok with indifferent equilibrium.

Metacentric height h \u003d 0. If the center of gravity lies above the center of magnitude, then with a roll, the line of action of the support force passes through the center of gravity MG \u003d 0 (Fig. 93).

In this case, the center of magnitude is always located on the same vertical with the center of gravity, so there is no restoring pair of forces. Without the influence of external forces, the ship cannot return to a straight position.

In this case, it is especially dangerous and completely unacceptable to transport liquid and bulk cargoes on a ship: with the slightest rocking, the ship will capsize. This is typical for boats with a round frame.

The third case of an unstable ship in unstable equilibrium.

Metacentric height h<0. Центр тяжести расположен выше центра величины, а в наклонном положении судна линия действия силы поддержания пересекает след диаметральной плоскости ниже центра тяжести (рис. 94).