transverse stability of the ship. What is resilience

The ability of a vessel to stay afloat, not to capsize or go to the bottom when flooded, is characterized by its seaworthiness. These include:

SHIP STABILITY

For ship stability big influence renders the presence fuel tank with a liquid fuel surface mirror from side to side, i.e. transverse arrangement of the elongated fuel tank. In this case, the fuel may overflow to one side of the tank and overhang the vessel on that side, which may cause the vessel to roll over.
To increase the stability of the vessel, such tanks are either equipped with internal baffles that do not prevent the fuel from flowing, but do not allow the fuel to move sharply through the tank when the boat is maneuvering, or the tanks must be narrowed at the top to reduce the liquid fuel surface mirror. In both cases, the volume of moving fuel decreases.

A floating vessel is acted upon by gravity forces vertically downwards, and hydrostatic forces proportional to the mass of displaced water act vertically upwards. The resulting force of gravity (P) is equal to the sum of the forces of gravity of the vessel itself and all the cargo on it, and is always directed vertically downwards. The resultant hydrostatic force (D) is always directed vertically upwards and is called sustaining force.
Center of buoyancy ship (Co) - the point of application of the resultant support forces (D) acting on the ship. In other words, the center of magnitude is the center of gravity of the volume of water displaced by the ship, that is, the center of gravity of the underwater volume of the ship.
Center of gravity ship (G) - the point of application of the resultant gravity (P) acting on the ship.
metacenter(M) - the point of intersection of the line of action of the support force with the diametrical plane.
metacentric height(h) - distance between the metacenter (M) and the center of gravity (G).
The initial metacentric height characterizes the stability at low inclinations of the vessel (5 - 10 °), is measured in meters and is a criterion for the initial stability of the vessel. As a rule, the initial metacentric height of motorboats and boats is considered good if it is more than 0.5 m. , for some vessels it is permissible less, but not less than 0.35 m .
Stability shoulder(L) - the distance between the line of action of the support force (D) and the line of action of the resultant gravity (P).

	If the metacenter M is located above the center of gravity G, then h is considered positive, in which case the ship has a positive initial stability and is safe for navigation.
	If the metacenter M coincides with the center of gravity G, i.e. h=0, then the vessel has zero stability, i.e. is in a state of indifferent equilibrium. Such a vessel does not have a restoring moment, and it may, under the influence of minor external forces tip over.
	If the metacenter M is located below the center of gravity G, then the initial stability of the vessel is negative (h

SHIP BUOYABILITY

SHIP UNSinkability

• 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 active forces distinguish between static and dynamic stability.

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 free surface for 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 Efremova. T. F. Efremova. 2000... Modern Dictionary Russian language Efremova

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

Stability called the ability of a vessel tilted by the action of external forces from a position of equilibrium, to return to a state of equilibrium after the termination 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 a vessel, which determines its seaworthiness and the degree of navigation safety. 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; zg- elevation of the ship's CG above the OL.

Meaning zg determined when calculating the load mass. Approximately possible

accept (for a ship with a full load) zg = (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 zg. 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

Stability sea ​​vessels must comply with the Stability Standards of the Register of the USSR, providing as the main criterion (called the "weather criterion") the condition: overturning 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 the maximum values ​​of the restoring moments on the chart be achieved at a heel angle of at least 30°, and the maximum stability arm should be at least 0.25 m for ships up to 80 m in length and not less than 0.20 m for ships with a length of over 105 m.

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 a free liquid surface, 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.

STABILITY

Stability is called - the ability of the vessel, deviated by an external moment in the vertical plane from the equilibrium position, to return to its original equilibrium position after the elimination of the moment that caused the deviation.

MAIN TASKS OF STATIC STABILITY

The problems of the balance of a banked ship, encountered in the practice of E1 operation, are reduced to three main types:

determination of the roll angle under the action of a given heeling moment;

determining the heeling moment from the known angle of heel, and

determination of the maximum heeling moment that the ship can withstand

without tipping over.

The lines of action of the original and new direction of the support force will intersect at the point m. This point of intersection of the line of action of the support force at an infinitely small equal-volume inclination of a floating vessel is called transverse metac centerabout m.

The metacenter of the ship (metacenter) is the point of intersection of the lines of action of the buoyancy forces when the ship is heeling at a small angle.

Initial lateral stability

All are connected by relations (elevation along the axis X)

m-metacenter

Zm - elevation of the metacenter

Zg- elevation CT

Zc-elevation CV

h-metacentric height

r-metacentric radius

a-elevation of CG rad CV

ℓ-shoulder of static stability

G is the resultant of gravity P

P is the resultant of the maintenance forces (the force of Archimedes, the center of magnitude.)

hypotenuse θ⁰

Leg(shoulderℓ)

You can see the dependence ℓ=hsinθ⁰ in radians, if in degrees, then divide by 57.3 to convert it to radian 10⁰:57.3=0.174, etc.

Then Mв=Dℓ=Dhsinθ⁰-metacentric stability formula.

h is the most important stability criterion h= Zm- Zg=r+ Zc- Zg

ℓst=ℓf-ℓv(Zg)

If the vessel, under the action of Mcr, gets a roll at an angle θ, then due to a change in the shape of the underwater part of the hull, the center of magnitude C will move to point C1, and this movement will occur

along an arc of a circle centered at the point M.

The support force D will be applied at point C and directed to the current waterline WL1 Point M is located at the intersection of the DP with the line of action of the support forces and

called transverse metacenter.

Vessel weight force P stay in the center of gravityG; along with strengthDit forms a pair of forces, which prevents the vessel from tilting due to the heeling moment

Mkr. The moment of this pair is called Mv, its value characterizes the degree of stability of the vessel

The perpendicular GK, lowered from the center of gravity of the ship to the line of action of the support forces, which is the shoulder of the restoring pair, is called stability shoulder ιst

The figure shows that the value of the shoulder of stability depends on the relative position points C, G and M. The distance between the metacenter M and the center of magnitude C is transverse

metacentric radiusr. Distance between metacenter M and center of gravity G

transverse metacentric heighth(in meters).

Metacentric formula for transverse stability. The value of MV is in a straight line

depending on the value of h; the more h, the more stable the ship.

Metacentric height h is a criterion for the ship's stability.

stable vessel

Unstable ship in unstable equilibrium

STABILITY AT HIGH INCLINES.

STATIC STABILITY DIAGRAM (READ DIAGRAM)

D:lst \u003d Mtm 2000: 0.35 \u003d 700tm

lst \u003d M: D \u003d 550: 2000 \u003d 0.275

The static stability diagram is built in the following axes: along the abscissa axis lay the roll angles E (in degrees), and along the ordinate axis - the shoulders of static stability /st (in meters). The diagram is built for a certain applicate of the ship's CG and a certain displacement.

Since the magnitude of the moment is proportional to the magnitude of the shoulder, the scale of moments in ton-force-meters per meters can also be built along the ordinate axis.

When the ship is tilted, the static stability arms gradually increase from zero (with the ship in a straight position) to maximum value(usually at a roll of 30-40°), and then decrease to zero and then become negative. This can be seen in the diagram below, where some typical cases of stability with ship inclinations are shown below.

Position 1(0 = 0°) corresponds to the position of static equilibrium: the static stability arm is equal to zero (/st = 0).

Position 2/(9 = 20°): static stability shoulder appeared ( l st = 0.2 m).

Position 3(0 = 37°): the static stability arm has reached the Maximum ( l Art. max = 0.35 m).

Regulation IV(8 = 60°): the static stability arm is reduced ( l st = 0.22 m).

Position V(6 = 82°): the static stability arm is zero ( l st = 0). The vessel is in a position of static unstable equilibrium, since even a small increase in heel will cause the vessel to capsize.

PositionVI (O=100°): the static stability arm has become negative ( l st = -0.18 m), the ship capsizes.

Thus, a vessel inclined to an angle of 9 = 82°, being left to itself, will return to a straight position, i.e., the vessel is stable within the range of heel angles from 0° to 82°. The point of intersection of the curve with the abscissa axis, corresponding to the angle of capsizing of the vessel (0 = 82 °), is called chart sunset point. The maximum heeling moment that the vessel can withstand without capsizing corresponds to the maximum static stability arm.

For a ship with a displacement D = 2000 tf, this moment is equal to
Mcr max =D/ ℓst = 2000-0.35 = 700 tf.m

Such a moment, acting on the ship, creates an angle of heel, called the maximum angle of heel. For the Vessel under consideration O max = 37°.

Using the diagram, you can determine the angle of heel from a known heeling moment or find the heeling moment from a known angle of heel. For example, it is known that the heeling moment Mi = 550 tf-m acted on the ship. It is necessary to determine the angle of heel that the ship will receive under the influence of this moment. On the y-axis we find the value of the moment M1 \u003d 550 ts-m 1, we draw a horizontal line until it intersects with the curve and from the intersection point we lower the perpendicular to the abscissa axis, from where we remove the desired value of O1 (in Fig. 152 O1 \u003d 26 °).

The reverse problem is solved in a similar way. Usually, there are several diagrams in the ship's documents, corresponding to the most typical cases of loading the ship. To solve problems of stability at large angles of heel, an approximately suitable diagram is selected. According to the static stability diagram, it is possible to determine the value of the initial transverse metacentric height of the vessel for a given loading case. To do this, from a point on the abscissa axis corresponding to a bank angle of 57.3 ° (i.e., 1 rad), you need to set up a perpendicular, and draw a tangent to the initial section of the curve from the origin of coordinates. The segment of the perpendicular enclosed between the abscissa axis and the tangent is equal (on the scale of the stability arms) to the metacentric height of the ship. For this vessel _ h = 0.47 m

1 If there is a scale on the y-axis only for the shoulders of static stability, then the stability corresponding to the heeling moment M1 can be determined for a given displacement D \u003d 2000 tf according to the formula "lst \u003d M1 / ​​D \u003d 550/2000 \u003d 0.275, which is plotted on the y-axis.

Stability diagram

The stability diagram is the dependence of the restoring force on the angle of inclination. Sometimes called a Reed diagram, after the engineer who introduced it. For lateral stability (for which it was originally compiled by Reed), the coordinates will be the angle of roll Θ and righting moment arm GZ. You can replace the shoulder at the very moment M, this does not change the appearance of the chart.

Typically, the diagram shows a roll to one side (starboard), at which the angles and moments are considered positive. If you continue it to the other side, the roll and the restoring (straightening) moment change sign. That is, the diagram is symmetrical about the starting point.

| DSO PROPERTIES

Types of stability diagram

The main elements of the stability diagram

Starting point O , which is usually the equilibrium point. At this moment roll Θ = 0, no straightening moment GZ= 0. If for some reason the initial stability is negative, the equilibrium point may not coincide with the origin. Then GZ= 0 at Θ = Θ 1 .

Maximum point . Represents the angle at which the straightening moment is maximum GZ max. Up to this angle, further inclination causes an increase in moment. After reaching the maximum, the inclination is accompanied by a drop in the moment, until the third characteristic point is reached:

Sunset point C . Represents the angle at which the straightening moment drops to zero GZ= 0. Corresponds to the capsizing point of the vessel, since there are no more directing forces. For ordinary displacement ships sunset angle (static) lies in the region of 65÷75°. For keel yachts- in the region of 120÷125°.

Curvature . Characterizes the rate of rise of the straightening moment. The first derivative is work. Tangent to the stability curve at a point O characterizes the initial metacentric height. Its ordinate, plotted at an angle

Θ = 1 rad is equal to the metacentric height h.

Area under the curve for the current angle B presents work A restoring moment and is a measure dynamic stability.

Types of stability diagram

Normal .

Typical for most displacement ships with a normal metacentric height, such as bulk carriers.

S-shaped (with an inflection).

It is typical for ships with a reduced metacentric height, for example, high-sided passenger ships.

with recess .

Not typical for most ships. Occurs when the initial stability is negative. At the same time, the ship floats in balance not on an even keel, but with a roll Θ 1 corresponding to the point of intersection of the curve and the axis Θ . For example, such a diagram occurs with timber carriers that are reloaded or ships that have free surfaces in tanks. Rules of all major world classification societies (for example, Lloyd's Register, Russian Maritime Register of Shipping, Russian River Register and etc.) forbidden operation of ships with a metacentric height of less than 0.2 m (including ships with negative initial stability). Thus, the initial stability of the ship can become negative either as a result of an accident or as a result of a misconduct on the part of the captain of the ship.

Factors affecting the change in stability

1. Movement of goods 2. Free surfaces 3. Acceptance and removal of goods

DYNAMIC STABILITY

With the dynamic action of the heeling moment, when it acts on the ship suddenly, with a jerk, with a blow (for example, during a squall), the ship rolls much faster than with a static action of a moment of the same magnitude. Gaining a significant angular velocity, the vessel will by inertia pass the position of static equilibrium and roll to a greater angle. The cessation of inclination will occur when the work of the heeling moment becomes equal to the work of the restoring moment.

Diagrams of static and dynamic stability

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. 9.5., 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

Vessel dynamic stability diagram

When constructing a diagram of dynamic stability according to the results of the above table, the dynamic heeling moment is assumed to be constant over the angles of heel. Therefore, its work is linearly dependent on the angle θ, and the graph of the product f(θ) = 1cr * 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 1kr on this vertical. The straight line connecting the point E with the origin O in this way will represent the desired graph f (θ) = 1kr * θ, i.e., the graph of the heeling moment, related to the ship's weight force 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 heeling and restoring moments is equal.

Point B has no practical significance.

If the graph of the product lcr * 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 lopr, and the moment itself is determined by multiplying the shoulder lopr by the weight of the vessel P. The touch point C will determine the limiting angle of the dynamic roll θdyn.prep.

DDO properties.

Controlling the correctness of the DDO construction, one should know its properties

1. At the origin, DDO is tangent to the x-axis

2. At θ order of the diagram of static stability - DDO has a maximum,

3. The angle θst.max of the static stability diagram corresponds to the inflection point on the DDO (up to the angle θst.max, the restoring moment Mv increases, and around the angle θst.max it decreases)
4. Tangent (ON) to DDO is the work schedule of the minimum overturning moment and cuts on the perpendicular to the angle θ = 1 rad a segment equal to the magnitude of the overturning moment on the scale of the vertical axis M With .

The dynamic bank angle θ DIN is determined by the ordinate of the intersection point (point M) schedules of restoring moment (RDO) and dynamic heeling moment (straight OK angle θ d = 35°.

Problems solved with the help of stability diagrams.

1.Vertical movement of cargo.

Parameters get worse:

Θzap.↓,ιst↓θst.max.↓

2.Horizontal movement of cargo.

Moving cargo to starboard y2 y1

Parameters are deteriorating: the vessel will float with a roll to starboard

Moving cargo to port side y2 ‹ y1

The parameters are getting better.

The DDO minimum is shifted towards the carrying of cargo with a heeling angle WHERE THE SHIP IS IN EQUILIBRIUM.

THE ACTION OF A SQUELE ON A SHIP WITH A ROLL

If the ship rolled to starboard, and a squall from the port side, then the ship will withstand

M is the largest, If the ship is listing to starboard, and the squall is from the starboard side, then it will be more dangerous, the squall acting in the direction where the ship is tilted.

If the ship is heeled by wind or waves. If on the windward side, then the balance is determined by θst max.

If from the lee side to the port side, and the ship has a left list and a squall hit the port side, then the ship is threatened great danger.

SHIP WITH NEGATIVE INITIAL STABILITY.

Of interest is the question of transshipment of the vessel from one side to another when the vessel is straightened. If you straighten the ship by moving cargo from side to side, the ship will straighten up and tilt to the other side, and will be established with a certain roll

And a restorative moment. With the increase negativeh ,negativeι , AΘzak.↓, dynamic roll when the vessel is transferred to the other side, and will lead to its capsizing.

DSO with moving loads.

DSO will behave like a vertical movement of cargo.

liquid cargo.

A liquid load is equivalent to a fixed load of the same mass, but with the CG positioned vertically. The presence of a liquid cargo on a ship with a free surface reduces stability.

When filling the tank, the influence of the free surface of the liquid should be taken into account during the following tank filling levels 12%, 50%, 70%

BULK CARGO.

DSO WITH A LOAD LOAD IS OBTAINED AS WITH A FIXED LOAD, BUT WITH THE SUBTRACTION OF THE MOMENTS FROM THE LOAD LOADING.

weather criterion.

Assesses the ability to withstand wind and waves at the same time. Stability is considered sufficient if K≥1

The calculation of Мcr(Мv) according to the Register is made:

Мv = 0.001pv Avz

Mv heeling moment

Pv - wind pressure in PA

Av- S windage sq.m.

z- shoulder of the sail from the center of the sail to the current.

ACCOUNTING FOR ICING.

The increase in ∆ is taken into account;

CT increase,

S windage

When sailing in areas north of the 66⁰30‘N parallel, the accepted ice mass per sq.m. S open decks 30kg, for the rest 15kg.

LONGITUDINAL STABILITY AND TRIM

1. Initial stability when the vessel is tilted in the longitudinal plane.

2. Vessel trim and trim angle.

3. Methods for determining longitudinal stability and trim calculation.

1) THE CONCEPT OF THE LONGITUDINAL STABILITY OF THE SHIP.

Stability, which manifests itself with the longitudinal inclinations of the vessel, those. when trimmed, is called the longitudinal stability of the vessel.

Despite the fact that the trim angles of the vessel rarely reach 10 degrees, and usually amount to 2-3 degrees, the longitudinal inclination leads to significant linear trims with a large length of the vessel. So, for a ship 150 m long, the angle of inclination is 1 degree, which corresponds to a linear trim equal to 2.67 m. In this regard, in the practice of operating ships, issues related to trim are more important than issues of longitudinal stability, since transport ships with normal ratios of the main dimensions, the longitudinal stability is always positive.

FORMULA FOR LONGITUDINAL STABILITY AND TRIM.

SHIP TRIM AND TRIM ANGLE. In the practice of calculating the ship's inclinations in the longitudinal plane, associated with the determination of the trim, instead of the angular trim, it is customary to use a linear trim, the value of which is determined as the difference between the ship's bow and stern draft, i.e. d \u003d Tn - Tk, and

To determine ψ in the radial myra, the formula has the form.

trim to the stern is considered negative. In most cases, ships sail with a trim to the stern.

The formula is the metacentric formula for longitudinal stability.

Мψ= D Н sinψ

Since the value of the longitudinal metacentric radius R is many times greater than the transverse r, the longitudinal metacentric height H of any vessel is many times greater than the transverse h, therefore, if the vessel has transverse stability, then longitudinal stability is certainly ensured.

Xg=xс - the vessel does not have ψ; Мψ=∆(Xg- xс)-vessel has ψ

1. LOGICAL METHOD.

Determination of the CV abscissa for a ship without ψ

2.TABLE METHOD

3. INSTRUMENT METHOD

Settling change scale using the “wavemeter” device

LONGITUDINAL CARGO MOVEMENT. We put the load on the midship, then move it to the bow, stern - while ∆z= ∆weight, ∆volume, dav.

Тн= Тн+∆р +∆Тн; Тк=Тк+∆р-∆Тк

§ 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.