initial stability. The equal volume inclinations of the ship. Euler's theorem. Landing a ship straight and on an even keel

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:

• The criterion of 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 heeling moment M kr 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.

Stability called the ability of a vessel tilted by the action external forces from a position of equilibrium, to return to a state of equilibrium after the termination of the action of these forces.

The inclination of the vessel can occur under the influence of such external forces as the movement, acceptance or expenditure of cargo, wind pressure, the action of waves, the tension of the towline, etc.

The stability that a ship has with longitudinal inclinations, measured by trim angles, is called longitudinal. It is usually quite large, so the danger of capsizing the vessel through the bow or stern never arises. But studying it is necessary to determine the trim of the vessel under the influence of external forces. The stability that the ship has with transverse inclinations, measured by roll angles 6, is called transverse.

Lateral stability is the most important characteristic of the vessel, which determines its seaworthiness and the degree of safety of navigation. When studying transverse stability, a distinction is made between initial stability (at small inclinations of the vessel) and stability at large angles of heel. initial stability. When the ship rolls at a small angle, under the action of any of the named external forces, the CV moves due to the movement of the underwater volume (Fig. 149). The value of the restoring moment formed in this case depends on the value of the shoulder l= GK between forces

weight and support of the tilted vessel. As can be seen from the figure, the restoring moment MV= Dl = Dh sinθ, where h- point elevation M above the ship's CG G called ship's transverse metacentric height. Dot M is called the transverse metacenter of the vessel.

Rice. 149. The action of forces when the ship rolls

Metacentric height is the most important characteristic of stability. It is defined by the expression

h = z c + r - 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 OL.

Meaning z g determined when calculating the load mass. Approximately possible

accept (for a ship with a full load) z g = (0,654-0,68) H, Where H- height amidships.

Meaning z c And r determined according to a theoretical drawing or (for estimated calculations) according to approximate formulas, for example:

Where IN- width of the vessel, m; T- draft, m; α is the coefficient of completeness of the waterline; δ - coefficient of overall completeness; TO- coefficient depending on the shape of the waterline and its completeness and varying within 0.086 - 0.089.

From the above formulas it can be seen that the transverse stability of the vessel increases with an increase in B and α; with decreasing T and δ; with CV elevation z c; With

decrease in CG z g. Thus, wide ships are more stable, as well as ships with low location CT. When lowering the central heating, i.e., when placing heavier loads - mechanisms and equipment - as low as possible and with

facilitation of high-lying structures (superstructures, masts, pipes, which are sometimes made of light alloys for this purpose), the metacentric height increases. And vice versa, when receiving heavy loads on the deck, icing over the surface of the hull, superstructures, masts, etc., while the vessel is navigating in winter conditions, the stability of the vessel decreases.

Inclining experience. On the built vessel, the initial metacentric height is determined (using the metacentric stability formula) empirically - by inclining the vessel, which is carried out at an angle of 1.5-2 by transferring a pre-weighed load from side to side. The scheme of the inclining experience is shown in fig. 150.

Rice. 150. Scheme of inclining experience.

1 - rail with divisions; 2 - weight and lionfish; 3 - bath with water or oil; 4 - weight thread; 5 - portable securing weight

heeling moment M cr caused by the transfer of cargo R at a distance at: M cr = Ru. According to the metacentric stability formula h = M KP /Dθ (sin θ is replaced by θ due to the smallness of the bank angle θ). But θ = d/l, That's why h = Pyl/Dd.

The values ​​of all quantities included in this formula are determined during the inclining test. The displacement is found by calculation from the drafts measured by the marks of the deepening.

On small ships, the transfer of cargo (cast iron ingots, sandbags, etc.) is sometimes replaced by rushes of people with a total mass of about 0.2-0.5% of the empty ship's displacement. The roll angle θ is measured with weights dipped in oil baths. IN Lately weights are replaced with special devices that allow you to accurately measure the angle of heel during the inclining test (taking into account the rocking of the vessel during the transfer of cargo), the so-called inclinographs.

Based on the initial metacentric height found using the inclining experience, the position of the CG of the constructed vessel is calculated using the above formulas.

The following are approximate transverse metacentric heights for different types vessels with a full load:

Large passenger ships …………………………… 0.3-1.5

Medium and small passenger ships. . . ……………… 0.6-0.8

Large dry cargo ships …………………………….. 0.7-1.0

Medium ………………………………………………….. 0.5-0.8

Large tankers ………………………………… 2.0-4.0

Medium …………………………………………………... 0.7-1.6

River passenger ships …………………………….... 3.0-5.0

Barges ……………………………………………………… 2.0-10.0

Icebreakers ……… ………………………………………… 1.5-4.0

Tugs …………………………………………………… 0.5-0.8

Fishing vessels …………………………………. 0.7-1.0

Stability at high angles of heel. As the ship's roll angle increases, the restoring moment first increases (Fig. 151, a-c), then decreases, becomes equal to zero and no longer prevents, but, on the contrary, contributes to the further inclination of the vessel (Fig. 151, d).

Rice. 151. The action of forces when the vessel rolls at large angles

Since the displacement D for a given load state remains constant, then the restoring moment M in changes in proportion to the change in the shoulder l transverse stability. This change in the shoulder of stability depending on the angle of heel 8 can be calculated and displayed graphically, in the form static stability diagrams(Fig. 152), which is built for the most typical and dangerous cases of ship loading in relation to stability.

The static stability diagram is important document characterizing the ship's stability. With its help, it is possible, knowing the value of the heeling moment acting on the ship, for example, from wind pressure, determined on the Beaufort scale (Table 8), or from the transfer of cargo on board, from ballast water or fuel reserves received asymmetrically by the DP, etc. , - find the value of the resulting roll angle in the event that this angle is large (more than 10 °). The small bank angle is calculated without plotting the chart using the above metacentric formula.

Rice. 152. Diagram of static stability

From the static stability diagram, it is possible to determine the initial metacentric height of the ship, which is equal to the segment between the horizontal axis and the point of intersection of the tangent to the curve of the stability arms at the origin of coordinates with the vertical, drawn at a heel angle equal to one radian (57.3 °). Naturally, the steeper the curve at the origin, the greater the initial metacentric height.

The static stability diagram is especially useful when it is necessary to know the angle of the ship's heel from the action of a suddenly applied force - with the so-called dynamic action of the force.

If any statically, i.e. smoothly, without jerks, applied force acts on the ship, then the heeling moment formed by it creates a heel angle, which is determined from the static stability diagram (built in the form of a curve for changing restoring moments D(from the roll angle) at the point of intersection with the curve of a horizontal straight line drawn parallel to the horizontal axis at a distance equal to the value of the heeling moment (Fig. 153, a). At this point (point A) heeling moment from the action of static

Characteristics of wind and sea waves

force is equal to the restoring moment that occurs when the ship rolls and tends to return the rolled ship to its original, straight position. The angle of roll at which the heeling and restoring moments are equal is the desired angle of roll from a statically applied force.

If the heeling force acts on the ship dynamically, i.e. suddenly (a gust of wind, a jerk of a towing cable, etc.), then the angle of heel caused by it is determined from the static stability diagram in a different way.

Rice. 153. Determination of the angle of roll from the action of static ( A) and dynamically ( b) applied force

The horizontal line of the heeling moment, for example, from the action of wind during a squall, is continued to the right of point A (Fig. 153, b) until the area ABC cut off by it inside the diagram becomes equal to the area AOD outside of it; while the angle of roll (point E) corresponding to the position of the straight line sun, is the desired roll angle from the action of a dynamically applied force. Physically, this corresponds to the angle of heel at which the work of the heeling moment (graphically represented by the area of ​​the rectangle ODCE) turns out to be equal to the work of the restoring moment (the area of ​​the figure BOTH).

If the area bounded by the restoring moment curve is insufficient to equal the area of ​​the figure bounded by the heeling moment outside it, then the ship will capsize. Therefore, one of the main characteristics of the diagram, indicating the stability of the vessel, is its area, limited by the curve and the horizontal axis. On fig. 154 shows the curves of the shoulders of static stability of two vessels: with a large initial stability, but with a small diagram area ( 1 ) and with a smaller initial metacentric height, but with larger area diagrams (2). The last vessel is capable of withstanding more than strong wind, it is more stable. Typically, the chart area is larger for a vessel with a high freeboard and less for a vessel with a low freeboard.

Rice. 154. Static stability curves of a vessel with high (1) and low (2) freeboard

The stability of sea-going vessels must comply with the Stability Standards of the Register of the USSR, which provide for the following condition as the main criterion (called the “weather criterion”): capsizing moment M def, i.e. the minimum dynamically applied moment, which, with the simultaneous action of rolling and the worst load, causes the ship to capsize, should not be less than the heeling moment dynamically applied to the ship M cr on wind pressure, i.e. K = M def/M cr≥ l.00.

In this case, the value of the overturning moment is found from the static stability diagram according to a special scheme, and the value (in kN∙m) of the heeling moment (Fig. 155) compared with it is found using the formula M cr = 0.001P in S p z n, Where R in- wind pressure, MPa or kgf / m 2 (determined according to the Beaufort scale in the column "during a squall" or according to the table of the Register of the USSR); S n- sail area (area of ​​the lateral projection of the surface part of the vessel), m 2; z n- elevation of the center of sail above the waterline, m

When studying the static stability diagram, the angle at which the curve intersects the horizontal axis is of interest - the so-called sunset angle. According to the Register Rules, for marine vessels this angle should not be less than 60°. The same rules require that maximum values restoring moments on the diagram were achieved at a heel angle of at least 30°, and the maximum stability arm would be at least 0.25 m for ships up to 80 m long and at least 0.20 m for ships over 105 m long.

Rice. 155. To the determination of the heeling moment from the action of wind force

in a squall (sail area is shaded)

Influence of liquid cargoes on stability. The liquid cargoes in the tanks, when the tanks are not completely filled, move in the direction of inclination in case of inclination of the vessel. Because of this, the ship's CG moves in the same direction (from the point G0 exactly g), which leads to a decrease in the lever of the restoring moment. On fig. 156 shows how the shoulder of stability l 0 when taking into account the displacement of the liquid cargo, it decreases to l. At the same time, the wider the tank or compartment having free surface liquid, the greater the displacement of the CG and, consequently, the greater the decrease in lateral stability. Therefore, in order to reduce the effect of liquid cargo, they seek to reduce the width of the tank, and during operation - to limit the number of tanks in which free levels are formed, i.e., not to spend stocks from several tanks at once, but alternately.

Influence of bulk cargoes on stability. Bulk cargo includes grain of all kinds, coal, cement, ore, ore concentrates, etc.

The free surface of liquid cargoes always remains horizontal.

In contrast, bulk cargoes are characterized by the angle of repose, i.e., the largest angle between the surface of the cargo and the horizontal plane, at which the cargo is still at rest and above which spillage begins. For most bulk cargoes, this angle is in the range of 25-35°.

Bulk cargo loaded onto a ship is also characterized by porosity, or porosity, that is, the ratio of the volumes directly occupied by the cargo particles and the voids between them. This characteristic, which depends both on the properties of the cargo itself and on the method of its loading into the hold, determines the degree of its shrinkage (compaction) during transportation.

Rice. 156. To determine the influence of the free surface of a liquid cargo

for stability

When transporting bulk cargo (especially grain), as a result of the formation of voids as they shrink from shaking and vibration of the hull during the voyage, with sharp or large inclinations of the vessel under the action of a squall (exceeding the angle of repose), they are poured onto one side and no longer return completely to the original position after the vessel is straightened.

The amount of cargo (grain) poured in this way gradually increases and causes a roll, which can lead to the capsizing of the vessel. To avoid this, special measures are taken - they place bags of grain on top of the grain poured into the hold (bagging of cargo) or install additional temporary longitudinal bulkheads in the holds - shifting boards (see Fig. 154). If these measures are not taken, serious accidents and even the death of ships occur. Statistics show that more than half of the ships lost due to capsizing were carrying bulk cargo.

A particular danger arises during the transportation of ore concentrates, which, when their humidity changes during the voyage, for example, when thawing or sweating, acquire high mobility and easily shift to the side. This still little-studied property of ore concentrates has caused a number of severe ship accidents.

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 ship.

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 (applicate Information on Stability - hereinafter referred to as "Information") the free surface correction 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.

• Depending on the plane of inclination, there are lateral stability when heeling and longitudinal stability at trim. With regard to surface ships (vessels), due to the elongation of the shape of the ship's hull, its longitudinal stability is much higher than the transverse one, therefore, for the safety of navigation, it is most important to ensure proper transverse stability.

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

• Depending on the nature of the acting forces, static and dynamic stability are distinguished.

Initial lateral stability

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

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

Free surfaces

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

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

Influence of free surface on stability

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

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

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

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

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

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

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

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

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

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

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

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

   ,

   on the interval from 0 to θ dyn.

   Reaching dynamic bank angle θ dyn, the ship does not come into equilibrium, but under the influence of an excess restoring moment, it begins to straighten rapidly. In the absence of water resistance, the ship would enter into undamped oscillations around the equilibrium position when heeling θ st / ed. Physical Encyclopedia

Vessel, the ability of the vessel to resist external forces that cause it to heel or trim, and return to its original equilibrium position after the termination of their action; one of the most important seaworthiness of a vessel. O. when heeling ... ... Great Soviet Encyclopedia

The quality of the ship is to be in balance in a straight position and, being taken out of it by the action of some kind of force, return to it again after the termination of its action. This quality is one of the most important for the safety of navigation; there were many… … Encyclopedic Dictionary F.A. Brockhaus and I.A. Efron

G. The ability of the vessel to float upright and to straighten up after tilting. Explanatory Dictionary of Ephraim. T. F. Efremova. 2000... Modern explanatory dictionary of the Russian language Efremova

Stability, stability, stability, stability, stability, stability, stability, stability, stability, stability, stability, stability (