Fundamentals of the theory of the ship. Operational, seaworthy and maneuvering qualities. The concept of vessel stability

Stability is the ability of a vessel, brought out of equilibrium by an external influence, to return to it after the termination of this influence.

The main characteristic of stability is the restoring moment, which must be sufficient for the ship to withstand the static or dynamic (sudden) action of heeling and trimming moments arising from the displacement of goods, under the influence of wind, waves, and for other reasons. The heeling (trim) and restoring moments act in opposite directions and are equal in the equilibrium position of the vessel.

There are transverse stability, corresponding to the inclination of the vessel in the transverse plane (roll of the vessel), and longitudinal stability (trim of the vessel).

Longitudinal stability sea ​​vessels is obviously provided and its violation is practically impossible, while the placement and movement of goods leads to changes in lateral stability.

When the vessel is tilted, its center of magnitude (CV) will move along a certain curve, called the CV trajectory. With a small inclination of the ship (no more than 12°), it is assumed that the CV trajectory coincides with a flat curve, which can be considered an arc of radius r centered at point m (Fig. 1).

The radius r is called the transverse metacentric radius of the vessel, and its center m is the initial metacenter of the vessel.

The metacenter is the center of curvature of the trajectory along which the center of the value C moves in the process of inclining the ship. If the inclination occurs in the transverse plane (roll), the metacenter is called transverse, or small, while inclination in the longitudinal plane (trim) is called longitudinal, or large. Accordingly, transverse (small) r and longitudinal (large) R metacentric radii are distinguished, representing the radii of curvature of the trajectory C during roll and trim.

The distance between the initial metacenter m and the ship's center of gravity G is called the initial metacentric height (or simply the metacentric height) and is denoted by the letter h. The initial metacentric height is a measure of the ship's stability.

h \u003d z c + r - z g; h z m ~ z c ; h \u003d r - a,

• where α is the elevation of the center of gravity (CG) above the CG.

Metacentric height (m.h.) - the distance between the metacenter and the ship's center of gravity. M.v. is a measure of the initial stability of the vessel, which determines the restoring moments at small angles of heel or trim. With increasing m.v. the ship's stability is improved. For positive stability of the vessel, it is necessary that the metacenter be above the vessel's CG. If m.v. is negative, i.e. the metacenter is located below the ship’s CG, the forces acting on the ship form a heeling moment, not a restoring one, and the ship floats with an initial roll (negative stability), which is not allowed.

Rice. 1 Elements of initial lateral stability: OG - elevation of the center of gravity above the keel; OM is the elevation of the metacenter above the keel; GM, metacentric height; CM is the metacentric radius; m is the metacenter; G is the center of gravity; C - center of magnitude

There are three possible cases of the location of the metacenter m relative to the ship's center of gravity G:

• the metacenter m is located above the CG of the vessel G (h > 0). With a small inclination, gravity and buoyancy forces create a pair of forces, the moment of which tends to return the ship to its original equilibrium position;
• The CG of the vessel G is located above the metacenter m (h< 0). В этом случае момент пары сил веса и плавучести будет стремиться увеличить крен судна, что ведет к его опрокидыванию;
• The CG of the ship G and the metacenter m coincide (h = 0). The vessel will behave unstably, as there is no arm of the pair of forces.

The physical meaning of the metacenter is that this point serves as the limit to which the ship's center of gravity can be raised without depriving the ship of positive initial stability.

Static stability diagram

The stability of the vessel at small angles of inclination (θ less than 12 0) is called initial, in this case the restoring moment depends linearly on the angle of heel.

Consider the equal volume inclinations of the vessel in the transverse plane. In doing so, we will assume that:

• the angle of inclination θ is small (up to 12°);
• the section of the curve SS 1 of the CV trajectory is an arc of a circle lying in the plane of inclination;
• the line of action of the buoyancy force in the inclined position of the vessel passes through the initial metacenter m.

Under such assumptions, the total moment of a pair of forces (forces of weight and buoyancy) acts in the plane of inclination on the shoulder GK, which is called the shoulder of static stability, and the moment itself is the restoring moment and is denoted M c.

This formula is called the metacentric lateral stability formula.

With transverse inclinations of the vessel at an angle exceeding 12 °, it is not possible to use the above expression, since the center of gravity of the inclined waterline area is shifted from the diametrical plane, and the center of magnitude does not move along an arc of a circle, but along a curve of variable curvature, i.e. metacentric the radius changes its value.

To solve stability issues at large angles of heel, a static stability diagram (DSD) is used, which is a graph expressing the dependence of the static stability shoulders on the angle of heel (Fig. 2).

The diagram of static stability is built using pantocarens - graphs of the dependence of the stability shoulders of the form lφ on the volumetric displacement of the ship and the angle of heel. Pantocarenes of a specific ship are built in design office for heeling angles from 0 to 90 0 for displacements from an empty ship to a ship's displacement in full load (there are tables of curved elements of the theoretical drawing on the ship).

To build a DSO, you need:

• on the abscissa axis of the pantocaren, set aside a point corresponding to the volumetric displacement of the vessel at the time of completion of loading;
• restore the perpendicular from the obtained point and read off the values ​​of 1f from the curves for roll angles of 10, 20 0, etc.;
• calculate the shoulders of static stability according to the formula:

l \u003d l f - a * sin θ \u003d l f - (Z g - Z c) * sin θ,

• where a \u003d Z g - Z c (in this case, the applicate of the ship's CG Zg is found from the calculation of the load corresponding to a given displacement - they fill in a special table, and the applicate of the CV Z c - from the tables of curved elements of the theoretical drawing);
• construct a curve l 1 f and a sinusoid α∗sinθ, the differences in the ordinates of which are the shoulders of static stability l.

To plot the static stability diagram, on the abscissa axis lay the roll angles 0 in degrees, and along the ordinate axis, the static stability shoulders in meters (Fig. 3). The diagram is built for a certain displacement.

On fig. 9.3 shows certain states of the ship at various inclinations:

• position I (θ = 0 0) - corresponds to the position of static equilibrium (l= 0);
• position II (θ = 20 0) - a shoulder of static stability appeared (1 = 0.2 m);
• position III (θ = 37 0) - the static stability arm has reached its maximum (I = 0.35 m);
• position IV (θ = 60 0) - the static stability arm decreases (I = 0.22 m);
• position V (θ = 83 0) — the static stability arm is equal to zero. The ship is in a position of static unstable equilibrium, since even a slight increase in heel will cause the ship to capsize;
• position VI (θ = 100°) - the static stability arm becomes negative and the ship capsizes.

Starting from positions greater than position III, the vessel will not be able to independently return to the equilibrium position without applying an external force to it.

Thus, the vessel is stable within the angle of heel from zero to 83°. The point of intersection of the curve with the abscissa axis, corresponding to the angle of capsizing of the vessel (0 = 83 0) is called the chart sunset point, and this angle is the chart sunset angle.

The maximum heeling moment M kr max that the vessel can withstand without capsizing corresponds to the maximum static stability arm.

Using the diagram of static stability, you can determine the angle of roll from the known heeling moment M 1 that arose under the action of wind, waves, cargo displacement, etc. To determine it, a horizontal line is drawn from the point M 1 until it intersects with the curve of the diagram, and from the obtained point, a perpendicular is lowered to the abscissa axis (θ = 26 0). The reverse problem is solved in the same way.

According to the static stability diagram, one can determine the value of the initial metacentric height (Fig. 3), to find which it is necessary:

• from a point on the x-axis corresponding to a bank angle of 57.3° (one radian), restore the perpendicular;
• from the origin, draw a tangent to the initial section of the curve;
• measure the segment of the perpendicular enclosed between the abscissa axis and the tangent, which is equal to the ship's metacentric height on the scale of the stability arms.

Dynamic stability diagram

In practice, a ship is often affected by a sudden dynamic moment (wind squall, wave blow, broken tug, etc.). In this case, the vessel receives a dynamic heel angle, although short-term, but significantly exceeding the heel that could occur under the static action of the same moment.

Imagine that a heeling moment M cr is suddenly applied to a ship in a normal (straight) position, under the influence of which the ship begins to roll at a constantly increasing speed (with acceleration), since in the initial period the restoring moment M in will increase much more slowly M cr. After the ship reaches the angle of static equilibrium θ ST, i.e. when M cr = M in, the angular velocity is maximum. By inertia, the ship continues to roll, but with a decreasing angular velocity (deceleration). This is explained by the fact that M in becomes more than M cr.

At some point, the angular velocity becomes equal to 0, the ship's heeling stops (the ship "freezes" at the bottom of the roll) and the roll angle reaches its maximum. This angle is called the dynamic roll angle θdyn. The ship will then begin to return to its original position.

Under the dynamic heeling moment, which is usually called the overturning moment, is understood the value of the maximum moment applied to the vessel, which it can withstand without capsizing.

Dynamic stability refers to the ability of a vessel to withstand the dynamic effects of a heeling moment.

A relative measure of dynamic stability is the shoulder of dynamic stability ldyn.

The curve expressing the dependence of the work of the restoring moment or the dynamic stability arm on the roll angle is called the dynamic stability diagram (DDO).

A graphic representation of the diagram of dynamic stability in relation to the diagram of static stability is given in fig. 4, which shows that:

• the intersection points of the diagram of static stability with the abscissa axis correspond to the points O and D of the extremum of the diagram of dynamic stability;
• point A of the maximum of the static stability diagram corresponds to the inflection point C of the dynamic stability diagram;
• any ordinate of the dynamic stability diagram corresponding to a certain heel angle θ represents on a scale the area of ​​the static stability diagram corresponding to this heel angle (shaded in the figure).

Usually, in ship conditions, a dynamic stability diagram is built according to a known static stability diagram; the scheme for calculating the dynamic stability shoulders is shown in Fig. 5:

When constructing a dynamic stability diagram (Fig. 6), according to the results of the above table, the dynamic heeling moment is assumed to be constant over the roll angles. Therefore, its work is linearly dependent on the angle θ, and the graph of the product ƒ(θ) = 1 cr *θ will be displayed on the dynamic stability diagram as a straight inclined line passing through the origin. To build it, it is enough to draw a vertical through a point corresponding to a roll of 1 radian and set aside a given shoulder of 1 cr on this vertical. The straight line thus connecting the point E with the origin O will represent the desired graph ƒ (θ) \u003d 1 kr * θ, i.e., the graph of the heeling moment, related to the weight of the ship P. This straight line will cross the diagram of dynamic stability at points A and B. The abscissa of point A determines the angle of dynamic roll θ, at which the work of the heeling and restoring moments is equal. Point B has no practical significance.

If the graph of the product l cr *θ constructed in this way does not cross the dynamic stability diagram at all, then this means that the ship is capsizing.

To find the overturning moment that the vessel can still withstand without capsizing, one should draw a tangent to the dynamic stability diagram from the origin of coordinates until it intersects at point D with the vertical corresponding to a roll of 1 radian. The segment of this vertical from the abscissa axis to its intersection with the tangent gives the shoulder of the overturning moment 1 def, and the moment itself is determined by multiplying the shoulder 1 def by the weight of the vessel P. The touch point C will determine the limiting angle of the dynamic roll θ dyn.prep.

Stability criteria

The Register Rules have introduced the following stability criteria for all transport ships of 20 m and more in length:

• Criterion strong wind and rolling (weather) K must be greater than or equal to one, i.e. the ratio of the overturning moment M opr to the moment of heeling M cr is greater than or equal to 1;
• the maximum arm of the static stability diagram must be at least 0.25 m for vessels of length L< 80 м и не менее 0,20 м для судов длиной L>105 m at bank angle 0 > 30°. For intermediate ship lengths, l max is determined by linear interpolation;
• the angle of heel at which the stability arm reaches its maximum must be at least 30°;
• the slope angle of the static stability diagram must be at least 60°;
• the corrected initial metacentric height h must be at least 0.15 m;
• acceleration criterion K* must be at least one. The acceleration criterion is calculated for variants of complex loading of the ship, or for partial or full loading of holds with cargoes with a small specific loading volume (lead, etc.).

All transport ships have computer program to calculate the landing, strength and stability of a particular vessel. This program is subject to survey by the Register and only after its approval can it be used as a cargo instrument.

For ships sailing in winter time in winter seasonal zones, in addition to the main load options, stability should be checked taking into account icing. When calculating icing, changes in displacement, elevation of the center of gravity and wind area due to icing should be taken into account. The calculation in relation to stability in icing shall be carried out for the worst case, in relation to the stability of the design load case. The mass of ice when checking the stability for the case of icing is included in the overload and is not included in the ship's deadweight. The mass of ice per square meter of the area of ​​the general horizontal projection of open decks should be taken, in accordance with the Register requirements, to be 30 kg. The total horizontal projection of the decks should include the sum of the horizontal projections of all open decks and passages, regardless of the presence of canopies above them. The moment in height from this load is determined by the elevation of the center of gravity of the corresponding sections of the deck and transitions. The mass of ice per square meter of sail area should be taken equal to 15 kg.

Recommended for reading.

§ 12. Seaworthiness of ships. Part 1

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 of 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 related qualities: 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.

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, provided that all side openings are closed watertight, 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

Given that the moment of the resultant force is equal to the sum of the moments of the constituent 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 vessel. 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.

Rice. 13. Cargo dimension curve.

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 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 upper deck begins to enter the water (but not more than 15° for high-sided surface vessels), and stability at high inclinations .

Imagine that under the action external forces the vessel 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 a 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 angles of heel, 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 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 account 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 vessel, depending on the location of the cargo: a - positive stability; b - equilibrium position - the vessel is unstable; c - negative stability.

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), the 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 vessel 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.

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 ship;

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 .

Big influence stability is affected 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 immersed in 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. With a sudden action of external forces, such as a gust of wind, pulling the tug on board, pitching, a broadside 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 ship 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.

With an increase in the moment M cr, the secant ON can take the limiting position, turning into an external tangent OT drawn from the origin to the diagram of dynamic stability. Thus, the abscissa of the point of contact will be the 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 conditions swimming, register USSR Standards for stability of ships of the transport and fishing fleet have been developed. 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.

At the same time, the minimum capsizing 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 cargoes, rolling, and ship sail calculation elements for various ship load cases.

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

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

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 draft of the vessel and, accordingly, the freeboard and buoyancy of the vessel will decrease.

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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 vessel 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.

There are concepts of stability of the following types: static and dynamic, with small inclinations of the vessel and with large inclinations.

Static stability - the stability of the vessel with a gradual, smooth inclination of the vessel, when the forces of inertia and water resistance can be neglected.

The laws of initial stability retain their validity only up to a certain angle of heel. The value of this angle depends on the type of vessel and the state of its loading. For ships with low initial stability (passenger and timber carriers), the maximum heel angle is 10-12 degrees, for tankers and dry cargo ships up to 25-30 degrees. The location of the CG (center of gravity) and CG (center of magnitude) are the main factors affecting the stability when the ship rolls.

Basic elements of stability: displacement ∆ , shoulder of the restoring moment (shoulder of static stability) - lct, initial metacentric radius - r,

transverse metacentric height - h, roll angle - Ơ, restoring moment - MV

Heeling moment - Mkr, stability coefficient -K, elevation of the center of gravity Zg,

center of magnitude elevation -Zc, Weather criterion-K, DSO (static stability diagram), DDO (dynamic stability diagram).

DSO - gives complete description vessel stability : transverse metacentric height, shoulder of static stability, limit angle of DSO, sunset angle of DSO.

DSO allows you to solve the following tasks:

• the magnitude of the heeling moment from the displacement of the load and the overturning moment;
• creation of the necessary exposure of the side for the repair of the hull, outboard fittings;
• definition largest statically applied heeling moment that the ship can withstand without capsizing, and the roll that it will receive in this case;
• determination of the ship's roll angle from the instantaneously applied heeling moment in the absence of an initial roll;
• determination of the roll angle from a suddenly applied heeling moment in the presence of an initial roll in the direction of the heeling moment;
• determination of the angle of roll from a suddenly applied heeling moment in the presence of an initial roll in the direction opposite to the action of the heeling moment.
• Determining the roll angle when moving cargo along the deck;
• Determination of static overturning moment and static overturning angle;
• Determination of dynamic overturning moment and dynamic overturning angle;
• Determining the required heeling moment to straighten the vessel;
• Determination of the weight of the cargo during the movement of which the ship will lose stability;
• What can be done to improve the stability of the vessel.

Standardization of stability at the request of the Register of Shipping of Russia and Ukraine:

1. the maximum arm of the static stability of the DSO is more than or = 0.25 m with a maximum length of the vessel less than or = 80 m and more or = 0.20 m with a vessel length of more than or = 105 m;
2. diagram maximum angle more than or = 30 degrees;
3. sunset angle DSO more or = 60 degrees. and 55 degrees, taking into account icing

4. weather criterion - K more than or \u003d 1, and when sailing in the North Atlantic - 1.5

5. corrected transverse metacentric height for all loading options

should always be positive, and for fishing vessels not less than -0.05 m.

The roll characteristics of a vessel depend on the metacentric height. The greater the metacentric height, the sharper and more intense the pitching, which negatively affects the securing of the cargo and its integrity, and, in general, the safety of the entire vessel.

Approximate value of the optimal metacentric height for various vessels in meters:

• cargo-passenger large tonnage 0.0-1.2 m, medium tonnage 0.6-0.8 m.
• dry cargo of large tonnage 0.3-1.5 m., medium tonnage 0.3-1.0 m.
• big tankers 1.5-2.5 m.

For dry cargo ships average tonnage, based on field observations, four stability zones have been identified:

A - roll zone or insufficient stability-h|B =0.0-0.02 - when such vessels turn at full speed, a list of up to 15-18 degrees occurs.

B - zone of optimal stability h|B=).02-0.05 – in rough seas, ships experience smooth rolling, crew habitability is good, lateral inertial forces do not exceed 10% of deck cargo gravity.

B - zone of discomfort or increased stability h|B=0.05-0.10 - sharp pitching, working and rest conditions for the crew are poor, lateral inertial forces reach 15-20% of the gravity of the deck cargo.

G-zone of excessive stability or destruction h|B more than 0.10 - transverse inertial forces on rolling can reach 50% of the gravity of the deck cargo, while the cargo is broken, deck rigging parts (rings, shells), the ship's bulwark are destroyed, which leads to loss of cargo and death of the ship.

The Ship's Stability Information usually gives complete stability calculations without icing:

• 100% ship's stores without cargo
• 50% ship's stores and 50% cargo, of which may be deck cargo
• 50% inventory and 100% cargo
• 25% ship's stores, no cargo, cargo on deck
• 10% ship stores, 95% cargo.

Taking into account icing, the same + with ballast in tanks.

In addition to calculating stability for typical loading cases with and without icing, information on stability allows you to conduct a complete calculation of the vessel's stability for non-standard loading cases. In this case, it is necessary:

• Have an accurate picture of the location of cargo in cargo spaces in tons;
• Data in tons for ship stock tanks: heavy fuel oil, diesel fuel, oil, water;
• Compile a table of weights for a given vessel load, calculate the ship's CG moments

relative to the vertical and horizontal axes and applicates vertically and horizontally -

• Calculate the sums of the weights (total displacement of the ship), the value of the longitudinal moment of the ship's CG (taking into account the signs + and -), the vertical static moment
• Determine the applicate and abscissa of the ship's CG as the corresponding moments divided by the present gross displacement of the ship in tons
• According to the amount of reserves in % and cargo in % according to the reference tables (limiting curve), it is rough to estimate whether the vessel is stable or not and whether there is a need to take additional sea water ballast into the ship's double-bottom tanks.
• Determine boat's trim curves (see tables in Stability Information)
• Determine the initial transverse metacentric height, as the difference between the applicate of the center of magnitude - and the applicate of the center of gravity, select from the tables (Appendix of Stability Information - hereinafter referred to as "Information") the correction for free surface to the transverse metacentric value - determine the corrected transverse metacentric value.
• With the calculated values ​​of the displacement of the vessel for this flight and with the corrected metacentric height, enter the diagram of the shoulders of the static stability curves (attached in the "Information") and after 10 degrees construct the DSS of the static stability shoulders from the angle of heel at a given displacement (Reed's diagram)
• From the DSO diagram remove all the main data according to the requirements of the Register of Shipping of Ukraine, Russia.
• Determine the value of the conditional calculated roll amplitude for this loading case, using the recommendations in the reference data. Increase this amplitude by 2-5 degrees due to wind pressure (wind pressure of 6-7 points is taken into account). Taking into account all the acting factors simultaneously, this amplitude can reach values ​​of -15-50 degrees.
• Continue DSO in the direction of negative values ​​of the abscissa and set aside the value of the calculated pitching amplitude to the left of the zero coordinates, then restore the perpendicular from the point on the negative value of the abscissa axis. By eye, draw a horizontal line parallel to the abscissa axis like this. So that the area to the left of the x-axis and to the right of the DSO are equal. (see example) - determine the shoulder of the overturning moment.
• At the same time, remove the overturning moment arm from the DSO and calculate the overturning moment as the product of the displacement and the overturning moment arm.
• According to the value of the average draft (calculated earlier), select the value of the heeling moment from additional tables (Information)
• Calculate the weather criterion -K, if it meets the requirements of the Register of Shipping of Ukraine, including all the other 4 criteria, then the stability calculation ends here, but according to the requirements of the IMO Code of Stability for Vessels of All Types of -1999, it is required to additionally have two more stability criteria, which can only be determined from the DDO (Dynamic Stability Diagram). When the ship is sailing in icing conditions, calculate the weather criterion for these conditions.
• The construction of DDO - dynamic stability diagrams is easier to perform on the basis of the DSO diagram, using the scheme of Table. 8 (p. 61 - L.R. Aksyutin "Cargo plan of the vessel" - Odessa-1999 or p. 22-24 "Stability control of sea vessels" - Odessa-2003) - to calculate the shoulders of dynamic stability. If, according to the diagram of limiting moments in the Information on Stability, the ship is stable according to our calculations, then it is not necessary to calculate DDO-.

According to the requirements of the IMO-1999 Stability Code (IMO Resolution A.749 (18) of June 1999)

the minimum transverse metacentric height GM o -0.15 m. for passenger ships, and for fishing - more than or equal to 0.35;

· shoulder of static stability not less than 0.20 m;

· maximum DSO with maximum static stability arm - more than or equal to 25 degrees;

· shoulder of dynamic stability at a roll angle of more than or plus 30 degrees - not less than -0.055 m-rad .; (meter)

shoulder of dynamic stability at 40 degrees (or flooding angle) not less than - 0.09 m-rad.; (meter)

Difference of dynamic stability shoulders at 30 and 40 degrees - not less than 0.03 m-rad. (meter)

· weather criterion more than or = one (1) - for ships more than or = 24 m.

· additional angle of heel due to constant wind for passenger ships not more than 10 degrees, for all other ships not more than 16 degrees or 80% of the angle at which the edge of the deck enters the water, depending on which angle is minimal.

On June 15, 1999, the IMO Navigational Safety Committee issued circular 920 - Model loading and stability Manual, which recommends that all states with a fleet provide all ships with a special Manual for calculating the loading and stability of the ship, in which to give the types of optimal load and stability calculations of the vessel, give all the symbols and abbreviations given at the same time, how to control the stability, landing of the vessel and its longitudinal strength. This manual contains all abbreviations and units for the above calculations, tables for calculating stability and bending moments.

In the sea verification of the transverse metacentric height of the vessel is carried out according to an approximate formula that takes into account the width of the vessel - B (m), the pitching period - To (sec) and C - coefficient from 0.6 - to 0.88, depending on the type of vessel and its load - h = (CB / To) 2 with an accuracy of 85-90% .(h-m).

To fulfill the RGZ on the subject "Transportation of special regime and dangerous goods", you can use the author's manual "Calculation of the ship's cargo plan" published by SevNTU.

Get a specific task for calculating the cargo plan from the teacher. Original

Information about the stability of the vessel is with the teacher. To perform calculations

for this vessel, the student needs to make copies of the calculation tables and graphs from the "Information". The use of other "Information on the stability of the vessel" during the marine production practice for one's own, specific vessel and transported cargo is allowed to be protected by the RGZ.

§ 41. Stability.

Stability is the ability of a vessel, brought out of a position of normal equilibrium by any external forces, to return to its original position after the termination of these forces. External forces that can take the ship out of normal equilibrium include wind, waves, the movement of goods and people, as well as centrifugal forces and moments that occur when the ship turns. The navigator is obliged to know the features of his vessel and correctly assess the factors affecting its stability. Distinguish between transverse and longitudinal stability.

Figure 89 Static forces acting on the ship at low heels

The transverse stability of the vessel is characterized by the relative position of the center of gravity G and the center of magnitude C.

If the ship is tilted on one side at a small angle (5-10 °) (Fig. 89), the CV will move from point C to point C 1. Accordingly, the support force acting perpendicular to the surface will cross the diametrical plane (DP) at point M.

The point of intersection of the ship's DP with the continuation of the direction of the support force at the crepe is called the initial metacenter M. The distance from the point of application of the support force C to the initial metacenter is called the metacentric radius.

The distance from the initial metacenter M to the center of gravity G is called the initial metacentric height h 0.

The initial metacentric height characterizes the stability at low inclinations of the vessel, is measured in meters and is a criterion for the initial stability of the vessel. As a rule, the initial metacentric height of motor boats and boats is considered good if it is more than 0.5 m, for some ships it is permissible less, but not less than 0.35 m.

Rice. 90. Dependence of the initial metacentric height on the length of the vessel

A sharp inclination causes the ship to roll, and the period of free roll is measured with a stopwatch, i.e., the time of full swing from one extreme position to another and back. The transverse metacentric height of the vessel is determined by the formula:

h 0 \u003d 0.525 () 2 m,

Where IN- ship's width, m;

T- pitching period, sec.

The curve in Fig. 1 serves to evaluate the obtained results. 90, built according to well-designed boats. If the initial metacentric height h o, determined by the above formula, is below the shaded strip, it means that the ship will have smooth rolling, but insufficient initial stability, and navigation on it can be dangerous. If the metacenter is located above the shaded strip, the ship will be distinguished by rapid (sharp) rolling, but increased stability, and therefore such a ship is more seaworthy, but habitability on it is unsatisfactory. Optimal values ​​will fall within the zone of the shaded band.

Stability motorboats and boats must withstand the following conditions: the angle of heel of a fully equipped vessel with a motor from placing on board a load equal to 60% of the established carrying capacity must be less than the angle of flooding.

The established carrying capacity of the vessel includes the weight of passengers and the weight of additional cargo (equipment, provisions).

The list of the vessel on one of the sides is measured by the angle between the new inclined position of the centreline and the vertical line. When heeling through an angle q, the resultant of the ship's weight forms the same angle q with the plane of the DP.

The heeled side will displace more water than the opposite side, and the CV will shift in the direction of the roll.

Then the resultant forces of support and weight will be unbalanced, forming a pair of forces with a shoulder equal to

l = h 0sin q .

The repeated action of the weight and support forces is measured by the restoring moment

M = Dl = Dh 0sin q .

Where D is the buoyancy force equal to the ship's weight force;

l - stability shoulder.

This formula is called the metacentric stability formula and is valid only for small heeling angles, at which the metacenter can be considered constant. At large angles of heel, the metacenter is not constant, as a result of which the linear relationship between the restoring moment and the angles of heel is violated.

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 more large ships with a conventional body structure.

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 magnitude, 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).

The force of gravity and the force of support at the slightest heel form a pair of forces with a negative restoring moment and the ship capsizes.

Rice. 93. The Case of an Unstable Vessel in Indifferent Equilibrium

Rice. 94. The case of an unstable ship in unstable equilibrium

The analyzed cases show that the ship is stable if the metacenter is located above the center of gravity of the ship. The lower the center of gravity falls, the more stable the ship. In practice, this is achieved by placing cargo not on the deck, but in the lower rooms and holds.