Negative stability of the vessel. Lateral stability of the vessel. Free surface influence

Stability is the ability of a ship to resist forces that deviate it from its equilibrium position, and to return to its original equilibrium position after the action of these forces ceases.

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

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

It is customary to distinguish stability of the vessel at small angles of inclination (initial stability) and stability at large angles of inclination.

When considering small inclinations, it is possible to make a number of assumptions that allow one to study the initial stability of the vessel within the framework of linear theory and obtain simple mathematical dependencies of its characteristics. The stability of the vessel at large angles of inclination is studied using a refined nonlinear theory. Naturally, the stability property of a vessel is uniform and the accepted division is purely methodological in nature.

When studying the stability of a vessel, its inclinations in two mutually perpendicular planes – transverse and longitudinal – are considered. When the ship tilts in the transverse plane, determined by the roll angles, it is studied lateral stability; when inclinations in the longitudinal plane are determined by the trim angles, study it longitudinal stability.

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

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

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

In order to prevent a dangerous decrease in the stability of the vessel, all crew members are obliged to:

always have a clear understanding of the vessel’s stability;

know the reasons that reduce stability;

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

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

Static stability is the stability of a vessel during 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 roll angle. The magnitude of this angle depends on the type of vessel and its loading condition. For ships with low initial stability (passenger ships 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 CV (center of magnitude) are the main factors affecting the stability when the vessel rolls.

Basic elements of stability: displacement ∆, righting moment arm (static stability arm) - 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,

elevation of the center of the value -Zc, Weather Criterion-K, DSO (static stability diagram), DSO (dynamic stability diagram).

DSO – gives full description ship 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 repair of the hull and outboard fittings;
determining the maximum value of the statically applied heeling moment that the ship can withstand without capsizing, and the roll that it will receive;
determination of the ship's roll angle from an instantly applied heeling moment in the absence of an initial roll;
determining 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 roll angle from a suddenly applied heeling moment in the presence of an initial roll in the direction opposite to the action of the heeling moment.
Determination of the heel angle when moving cargo along the deck;
Determination of static tipping moment and static tipping angle;
Determination of dynamic overturning moment and dynamic overturning angle;
Determination of the required heeling moment to straighten the vessel;
Determining the weight of the cargo, when moving which the ship will lose stability;
What to do to improve ship stability.

Standardization of stability as required by the Register of Shipping of Russia and Ukraine:

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

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

5. corrected transverse metacentric height for all loading options

must always be positive, and for fishing vessels no less than 0.05 m.

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

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

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

For dry cargo ships of medium tonnage, based on field observations, four stability zones have been determined:

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

B - zone of optimal stability h|B=).02-0.05 – in rough seas the ships experience a smooth roll, the habitability conditions for the crew are good, the transverse inertial forces do not exceed 10% of the gravity force of the deck cargo.

B - discomfort zone or increased stability h|B=0.05-0.10 - sharp rolling, working and resting conditions for the crew are poor, transverse 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 force of the deck cargo, while the fastening of the cargo is broken, deck rigging parts (eyes, linings), the bulwark of the ship are destroyed, which leads to the loss of cargo and the death of the ship.

The Vessel Stability Information usually gives full calculations of stability without icing:

100% of ship's stores without cargo
50% ship's stores and 50% cargo, of which may be deck cargo
50% inventory and 100% cargo
25% of ship's stores, without cargo, cargo on deck
10% of ship's stores, 95% of cargo.

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

In addition to calculating stability for typical load cases with and without icing, Stability Information allows for a complete calculation of the vessel's stability for non-typical load 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 storage tanks: heavy fuel, diesel fuel, oil, water;
Compile a table of weights for a given vessel load, calculate the vessel’s CG moments

relative to the vertical and horizontal axis and applicates vertically and horizontally

Calculate the sum of the weights (total displacement of the vessel), the value of the longitudinal moment of the vessel’s CG (taking into account the + and - signs), and the vertical static moment
Determine the applicate and abscissa of the ship's CG as the corresponding moments divided by the present total displacement of the ship in tons
Based on the amount of reserves in % and cargo in % using the reference tables (limit curve), you can roughly estimate whether the ship is stable or not and whether there is a need to take additional seawater ballast into the ship's double-bottom tanks.
Determine the landing of the vessel using the trim curves (see tables in Stability Information)
Determine the initial transverse metacentric height as the difference between the applicate of the center of magnitude - and the applicate of the center of gravity, select from the tables (Appendix Information on Stability - hereinafter “Information”) the free surface correction to the transverse metacentric value - determine the corrected transverse metacentric value.
With the calculated values of the vessel's displacement for a given voyage and the corrected metacentric height, enter into the diagram of the arms of the static stability curves (attached in the “Information”) and after 10 degrees construct the DSO of the arms of static stability from the heel angle at a given displacement (Reed diagram)
From the DSO diagram, remove all the basic data according to the requirements of the Shipping Register of Ukraine and Russia.
Determine the value of the conditional calculated amplitude of roll for a given 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 operating factors at the same time, this amplitude can reach values of 15-50 degrees.
Continue the DSO in the direction of negative abscissa values and move the value of the calculated pitching amplitude to the left of the zero coordinates, then restore the perpendicular from the point on the negative abscissa value. By eye, draw a horizontal line parallel to the x-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) - we determine the arm of the overturning moment.
Remove the overturning moment arm from the DSO and calculate the overturning moment as the product of the displacement and the overturning moment arm.
By size average draft(calculated earlier) select the heeling moment value 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 calculation of stability ends here, but according to the requirements of the IMO Stability Code for all types of ships from 1999, it is required to additionally have two more stability criteria, which can only be determined from the DST (dynamic stability diagram). When the ship is sailing in icing conditions, calculate the weather criterion for these conditions.
It is easier to construct DDO - dynamic stability diagrams based on the DSO diagram, using the diagram in Table. 8 (p. 61- L.R. Aksyutin “Cargo plan of the vessel” - Odessa-1999 or p. 22-24 “Stability control sea vessels"-Odessa-2003) - for calculating the dynamic stability shoulders. If, according to the diagram of the limiting moments in the Stability Information, the vessel is stable according to our calculations, then it is not necessary to calculate the DDO.

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

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

· static stability shoulder of at least 0.20 m;

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

· dynamic stability shoulder at a roll angle of more than or plus 30 degrees – no less than -0.055 m-rad.; (meters)

dynamic stability shoulder at 40 degrees (or flood angle) no less than 0.09 m-rad.; (meter)

· difference in dynamic stability arms at 30 and 40 degrees – not less than 0.03 m-rad. (meters)

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

· the additional angle of heel due to the action of constant wind for passenger ships is no more than 10 degrees, for all other ships no more than 16 degrees or 80% of the angle at which the edge of the deck enters the water, depending on which angle is the minimum.

On June 15, 1999, the IMO Maritime 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 loading and stability of a ship, which gives the types of optimal loading and calculations of the stability of the vessel, give all the symbols and abbreviations given in this case., how to control the stability, landing of the vessel and its longitudinal strength. This Manual provides all abbreviations and units of measurement for the above calculations, tables for calculating stability and bending moments.

In the sea the transverse metacentric height of the vessel is checked using an approximate formula taking into account the width of the vessel - B (m), the rolling period - To (sec) and the 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 carry out the RGZ on the subject “Transportation of special-duty and dangerous goods”, you can use the author’s manual “Calculation of a vessel’s cargo plan” published by SevNTU.

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

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

for this vessel, the student must make copies of the calculation tables and graphs from the “Information”. The use of other “Information on vessel stability” during maritime production practice for one’s own, specific vessel and transported cargo is allowed for the protection of the RGZ.

ship it longitudinal stability significantly higher than the transverse one, therefore it is most important for safe navigation to ensure proper lateral stability.

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

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

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

Initial lateral stability

Initial lateral stability. System of forces acting on the ship

During roll, stability is considered as initial at angles up to 10-15°. Within these limits, the righting force is proportional to the roll angle 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 size, but changes in shape. Equal-volume inclinations correspond to equal-volume waterlines, cutting off immersed volumes of the hull of equal magnitude. The line of intersection of the waterline planes is called the inclination axis, which, with equal volume inclinations, passes through the center of gravity of the waterline area. With transverse inclinations, it lies in the center plane.

Free surfaces

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

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

Effect of free surface on stability

If the liquid does not completely fill the tank, i.e. has a free surface that always occupies a horizontal position, then when the ship tilts at an angle θ the liquid flows towards the inclination. The free surface will take the same angle relative to the KVL.

Levels of liquid cargo cut off equal volumes of tanks, i.e. they are similar to equal volume waterlines. Therefore, the moment caused by the overflow of liquid cargo during a roll δm θ, can be represented similarly to the moment of shape stability m f, only δm θ opposite m f by sign:

δm θ = - γ f i x θ,

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

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

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

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

The effect of the iridescent weight gives a correction to the transverse metacentric height δ h = - γ f i x /γV

The densities of water and liquid cargo are relatively stable, that is, the main influence on the correction is exerted by 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 correction value is that the presence of free surfaces is always reduces stability. Therefore, organizational and constructive measures are being taken to reduce them:

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 you tilt, the restoring moment increases, but at first, up to the angle θ st, at which m cr = m θ, it will be less heeling. Upon reaching the static equilibrium angle θ st, the kinetic energy of rotational motion will be maximum. Therefore, the ship will not remain in the equilibrium position, but due to kinetic energy it will roll further, but slowly, since the righting moment is greater than the heeling moment. The previously accumulated kinetic energy is extinguished by the excess work of the restoring torque. As soon as the magnitude of this work is sufficient to completely extinguish the kinetic energy, the angular velocity will become zero and the ship will stop heeling.

The greatest angle of inclination that a ship receives from a dynamic moment is called the dynamic angle of heel θ din. In contrast, the angle of roll with which the ship will float under the influence of the same moment (according to the condition m cr = m θ), is called the static roll angle θ st.

If we refer to the static stability diagram, the work is expressed by the area under the righting moment curve m in. Accordingly, the dynamic roll angle θ din can be determined from the equality of areas OAB And BCD, corresponding to the excess work of the restoring torque. Analytically the same work is calculated as:

in the range from 0 to θ din.

Having reached the dynamic bank angle θ din, the ship does not come into equilibrium, but under the influence of an excess righting moment begins to accelerate to straighten. In the absence of water resistance, the ship would enter into undamped oscillations around the equilibrium position when heeling θ st Marine Dictionary - Refrigerated vessel Ivory Tirupati initial stability is negative Stability is the ability of a floating craft to withstand external forces causing it to roll or trim and return to a state of equilibrium after the end of the disturbance... ... Wikipedia

A vessel whose hull rises above the water when moving under the influence of lift created by wings submerged in the water. The patent for the vessel was issued in Russia in 1891, but these vessels began to be used in the 2nd half of the 20th century... ... Great Soviet Encyclopedia

An all-terrain vehicle capable of moving both on land and on water. An amphibious vehicle has an increased volume of a sealed body, which is sometimes supplemented with mounted floats for better buoyancy. Moving on water... ... Encyclopedia of technology

- (Malay) type of sailing vessel, lateral stability to the horn is provided by an outrigger float, attached. to the main body with transverse beams. The vessel is similar to a sailing catamaran. In ancient times, P. served as a means of communicating about the Pacific Ocean... ... Big Encyclopedic Polytechnic Dictionary

amphibian Encyclopedia "Aviation"

amphibian- (from the Greek amphíbios leading a dual lifestyle) seaplane equipped with a land landing gear and capable of being based both on the water surface and at land airfields. The most common are A. boats. Taking off from the water... ... Encyclopedia "Aviation"

The ability of a ship to resist the action of external forces tending to tilt it in the transverse and longitudinal directions, and to return to an upright position after the cessation of their action is called stability. The most important thing for any ship is its lateral stability, since the point of application of forces counteracting the roll is located within the width of the hull, which is 2.5-5 times less than its length.

Initial stability (at small roll angles). When a ship floats without heeling, then gravity D and buoyancy γ V, applied respectively to the CG and CV, act along the same vertical. If, during a roll at an angle θ, the crew or other components of the weight load do not move, then for any tilt the CG retains its original position in the DP (point G in Fig. 7), rotating with the ship. At the same time, due to the changed shape of the underwater part of the hull, the CV moves from the point C 0 towards the heeled side to the position C 1 . Thanks to this, a moment of a couple of forces arises D and γ V with shoulder l, equal to the horizontal distance between the CG and the new CG of the vessel. This moment tends to return the ship to an upright position and is therefore called restorative.

Rice. 7. Scheme for determining the lateral stability arms when tilted at an angle θ.

During a roll, the CV moves along a curved path C 0 C 1, the radius of curvature of which is called transverse metacentric radius, and the corresponding center of curvature M - transverse metacenter.

Obviously, the restoring moment arm depends on the distance GM- elevation of the metacenter above the center of gravity: the smaller it is, the less it turns out during roll and shoulder l. At the very initial stage of the ship’s inclination (up to 10-15°), the value GM or h is considered by shipbuilders as a measure of ship stability and is called transverse metacentric height. The more h, the greater the heeling force required to heel the ship at any particular angle of heel, the more stable the ship.

From the triangle GMN it is easy to establish that the restoring shoulder

l = GN = h· sin θ m.

The restoring moment, taking into account the equality γ V And D, is equal

M in = D · h· sin θ kgm.

Consequently, the stability of the vessel - the magnitude of its righting moment - is proportional to the displacement: a heavier vessel is able to withstand a heeling moment of greater magnitude than a lighter one, even at equal metacentric heights.

The righting arm can be represented as the difference between two distances (see Fig. 7): l f - shape stability arm and l c - weight stability arms. It is not difficult to establish the physical meaning of these quantities, since the first of them is determined by the displacement of the center of the quantity towards the roll, and the second by the deviation of the line of action of the weight force during roll D from the initial position exactly above the CV. Considering the action of forces D and γ V relatively C 0 , you can see that the force D tends to tilt the ship even more, and the force γ· V, on the contrary, straighten it.

From the triangle C 0 GK one can find that

l in = GK = C 0 G sin θ m,

Where C 0 G = a- elevation of the CG above the CV in the upright position of the vessel.

From here it is clear that in order to reduce the negative effect of the weight force, it is necessary to lower the ship’s CG as much as possible. In the ideal case - sometimes on racing yachts with a ballast keel, the mass of which reaches 45-60% of the vessel's displacement, the CG is located below the CV. In such yachts, weight stability becomes positive and helps straighten the vessel.

An effect similar to a decrease in CG is produced by heeling - moving the crew on board opposite to the inclination. This method is widely used on light sailing dinghies, where the crew, hanging overboard on a special device - a trapezoid, manages to move the general center of gravity of the boat so much that the line of action of the force D intersects with the DP significantly below the CV and the weight stability arm turns out to be positive (see Fig. 197).

Since the mass of the crew on small ships makes up the majority of the displacement, the movement of people in the boat significantly affects both the change in the position of the center of gravity and the magnitude of the heeling moment. It is enough, for example, for all four passengers of a motorboat to stand up so that the center of gravity becomes 250-300 mm higher, and one person sitting on board causes a roll of more than 10°. An even more significant role is played by the mass of the crew on light rowing boats and kayaks, where the width of the hull is small and its mass is significantly less than the mass of a person. Therefore, designers, and those responsible for the operation of the vessel, strive to place the center of gravity of the crew as low as possible.

First of all, high seats should be avoided - the height of rowing cans from a floorboard of 150 mm is quite sufficient, and the height of seats on planing motorboats is 250 mm. On single- and double-seater rowing and collapsible boats, such as kayaks, rowers can sit on a very low seat (no more than 70 mm) or directly on the bottom of the boat. On lightweight boats, floorboards are often replaced with wooden strips glued to the bottom from the inside.

When modernizing serial boats or building homemade ones, it is advisable to concentrate large reserves of fuel (40-150 l) under the floors in the form of a tank with a cross-section corresponding to the deadrise of the bottom. If the ship is equipped with a cabin, then it is necessary, if possible, to lighten the design of the superstructure and reduce its height, lower the level of the cockpit platform and the helmsman's post. The inboard engine on a boat should also be mounted as low as possible.

It is necessary to remember about the stability of the boat when packing equipment for a long trip; the heaviest things should be placed as low and compact as possible. In cases where it is necessary to ensure particularly high stability, necessary for sailing or to compensate for the influence of bulky superstructures, it is necessary to load the vessel ballast. Its optimal location is outside the hull in the form of a false keel - a lead or cast iron casting attached to the keel and reinforced floors with bolts. The deeper the false keel is secured below the waterline, the more the overall center of gravity of the vessel is lowered.

Less effective is internal ballast made from metal castings placed in the ship's hold. It must be securely fastened to prevent movement towards the heeled side, because in this case the ballast will contribute to the capsizing of the vessel. In addition, care must be taken to ensure that the pigs do not pierce the thin lining of the bottom when sailing in rough seas.

When developing a project for a new vessel, the designer has the opportunity to change the value of stability, specifying one or another shape for the hull. For example, the width of the boat along the waterline and its coefficient of fullness α are of great importance. Approximately the value of the metacentric radius r can be determined by the formula

Therefore, most significantly by the amount r and transverse metacentric height h = r − A affects the width of the hull at the waterline B, which should be chosen as large as can be tolerated for reasons of maneuverability.

The following average ratios can be given as approximate figures for choosing the width of the boat: L/B: tourist kayaks and canoes - 5.5÷8.5; rowing and motor boats up to 2.5 m long - 1.8÷2; rowing three- and four-seater boats (fofanas, flat-bottomed shuttles, etc.) - about 3.5, small motor boats up to 3 m long - 2.4; large planing motor boats 4-5.5 m long - 3÷3.4; open type planing boats - 3.2÷3.5; displacement boats 6-8 m long - 3.5÷4.5.

The coefficient α is also of great importance, especially for low-speed rowing vessels and displacement boats, the waterlines of which are often made too narrow to reduce water resistance. On small tug boats, it is advisable to carry out the waterline contours with maximum completeness - α = 0.75÷0.85. On tourist kayaks, it is desirable to have a coefficient α greater than 0.70; on large rowing boats and displacement boats α = 0.65÷0.72.

It is clear that the most favorable shape of the waterline for stability is a rectangle, therefore, if particularly high stability is needed, hulls with contours of the “sea sleigh” type, catamaran or trimaran, in which the sides are almost parallel along the entire length, are advisable. The greater the proportion of the volume of the underwater part of the hull is concentrated near the sides, the more during a roll the center of magnitude shifts toward the side and the greater the righting moment arm. The extreme poles are double-hulled vessels - catamarans and a boat with a midsection contour close to a circle (Fig. 8), in which the stability arm changes very slightly when heeling. The more clearly defined the chine is in the cross sections of the hull, the more stable the boat is. For small boats, the optimal hull is one with convexities near the cheekbones and a hull outline close to a rectangle in plan.

Rice. 8. Cross sections of small ships, arranged in order of decreasing initial stability (from top to bottom).

Stability at high roll angles. As shown above, the righting arm changes with increasing roll in proportion to the sine of the roll angle. In addition, the transverse metacentric height does not remain constant h, the value of which depends on the change in the metacentric radius r. Obviously, a complete characteristic of the stability of a vessel can be a graph of changes in the righting arm or moment depending on the angle of roll, which is called static stability diagram(Fig. 9). The characteristic points of the diagram are the moment of maximum stability of the vessel and the maximum angle of heel at which the ship capsizes (θ z - the angle of decline of the static stability diagram). With such a roll, the center of gravity again turns out to be located on the same vertical with the center of gravity; therefore, the stability arm is equal to zero.

Rice. 9. Static stability diagram

1 - high-sided boat with a cabin; 2 - open type boat; 3 - seaworthy motor yacht with ballast; 4 - heeling moment arm M cr.

A(roll angle θ = 16°) - stable position of the vessel under the influence of moment M cr; and (θ = 60°) - unstable position; C(θ = 33°) - flooding angle of the boat; D(θ = 38°) - maximum restoring moment; E(θ = 82°) - angle of decline of the stability diagram 1 .

However, the dangerous moment may occur even earlier if the ship has an open cockpit, side windows or deck hatches through which water can penetrate into the ship at a lower angle of heel. This angle is called flood angle.

The shape of the static stability diagram and the position of its characteristic points depend on the hull contours and the position of the ship's CG. Typically, the maximum righting arm occurs at the heel angle corresponding to the beginning of the deck edge immersion in the water, when the width of the heeling waterline is greatest. Therefore, the higher the freeboard, the greater the angle of heel the ship retains its stability. At the moment when the keel emerges from the water, the width of the heeling waterline begins to decrease; the value of the metacentric radius decreases accordingly r. At the same time, the weight stability arm increases and at a list of 50-60° on most small ships the righting arm l becomes equal to zero.

The exception is sailing yachts with a heavy false keel, in which maximum stability occurs at a heel of 90°, that is, when the mast is already lying on the water. If all the holes in the deck are sealed, then the moment of loss of stability ( l= 0) occurs at approximately 130° heel, when the mast is pointing down at an angle of 40° to the water surface. There are many known cases when yachts that capsized upward with their keels (a heel angle of 180°) returned to an upright position again.

The same property of self-righting from an overturned position can be achieved on boats with large superstructures equipped with hermetically sealed closures. When the keel is positioned upward, the CG of such a vessel turns out to be located much higher than the CG - a position of unstable equilibrium is reached, from which the boat can be brought out by the action of a small wave or by filling a special tank with sea water at one of the sides.

For catamarans, the stability arm reaches its maximum value when one of the hulls is completely out of the water - it is slightly less than half the distance between the hulls' hulls. This position is achieved in most catamarans at a list of 8-15°. With a further increase in roll, the stability arm quickly decreases and at a roll of 50-60°, a moment of unstable equilibrium occurs, after which the stability of the catamaran becomes negative.

Using the static stability diagram, the designer and captain can evaluate the ship’s ability to withstand certain heeling forces that arise, for example, when moving part of the cargo to one of the sides, the action of wind on the sails, etc. Heeling moment M kr (or its shoulder equal to M kr/ D) is plotted on the diagram as a curve (or straight line) depending on the roll angle. The point of intersection of this curve with the righting moment diagram corresponds to the angle of heel that the ship will receive. If the curve M kr passes above the maximum of the static stability diagram, the ship will capsize. If the curve M cr intersects the restoring torque curve, then on the ascending branch of the diagram (point A) its position will be stable - if, under the action of a small additional heeling moment, the roll of the vessel increases, then with the cessation of the action of this additional moment it returns to its previous position A. On the descending branch of the diagram at the point B a small increase in heeling moment will cause a significant increase in roll, since the righting moment will be less than the heeling moment; the boat may capsize. When the heeling moment decreases, the ship from the position B will move to position A. Consequently, the position of the vessel corresponding to the point B, is unstable.

Dynamic stability. Above, we considered the static effect of the heeling moment on the ship, when the forces gradually increase in magnitude. In practice, however, one often has to deal with dynamic by the action of external forces, in which the heeling moment reaches its final value in a short period of time - instantly. This happens, for example, when a squall hits or a wave hits a windward chine, a person jumps on board a boat from a high embankment, etc. In these cases, not only the magnitude of the heeling moment is important, but also the kinetic energy imparted to the vessel and absorbed by the work of the righting moment . An important role is played by the height of the freeboard and the angle of heel at which the boat can be flooded with water. These parameters, like the width, determine stability under the dynamic action of external forces: the higher the freeboard and the later the water begins to enter the hull, the greater the energy of heeling forces is absorbed by the work of the righting moment when the vessel tilts.

When operating small vessels, in particular when sailing, performing rescue operations, etc., it is recommended to provide at least a narrow side formwork (120-250 mm). With a sudden roll, the deck enters the water, which is followed by a quick reaction from the crew, who, with their mass, tilts the boat even before water enters it.

You can increase the stability of the vessel with the help of side fittings - boules(see Fig. 172), an inflatable chamber or a foam fender, encircling the sides of the boat near their upper edge, floats of a sufficiently large volume, mounted on brackets to the sides, or by connecting two boats into a catamaran.

Increasing stability with the help of solid ballast is not always justified, especially on motor ships, where an increase in displacement is associated with additional power and fuel costs. On planing boats and dinghies, seawater can be used as temporary ballast, filling special bottom tanks by gravity (Fig. 10). On a boat it is needed only when stationary and at low speed, when the dynamic supporting forces are insignificant. Water from the tank will be removed through the aft section of the transom as soon as it comes off the water. On a dinghy, on the contrary, ballast is necessary to increase stability under sail; When sailing under a motor or when climbing ashore, water can be removed from the tank using a pump. The volume of such ballast tanks is usually taken to be 20-25% of the vessel's displacement.

Rice. 10. Ballast tank on a planing boat.

1 - tank cavity; 2 - ventilation pipe; 3 - water entry into the tank; 4 - second bottom.

In passing, mention should be made of the effect of water in the ship’s hold (or other liquids in tanks) on stability. The effect consists not so much in the movement of masses of liquids towards the heeled side, but in the presence of a free surface of the overflowing liquid - its moment of inertia relative to the longitudinal axis. If, for example, the surface of the water in the hold has a length l, and the width b, then the metacentric height decreases by the amount

Water is especially dangerous in the holds of flat-bottomed dinghies and motorboats, where the free surface is large. Therefore, when sailing in stormy conditions, water must be removed from the hull.

The free surface of liquids in fuel tanks is divided into several narrow parts by longitudinal fenders. Holes are made in the bulkheads for the flow of liquid.

Rating and checking the stability of pleasure and tourist vessels. A dangerous list of a small vessel can be caused by the crew moving to one side, as well as by the influence of various external forces. As a rule, pleasure and tourist vessels operate in shallow coastal areas of the seas and in reservoirs with limited depth. In these areas the wave is dangerously steep and has a breaking crest. In a position with the side facing the wave, the swing of the boat may come into undesirable resonance with the period of the wave; if the stability is insufficient, the vessel may capsize.

Small vessels also have to withstand loads that are dangerous for lateral stability, such as jerks of the tow rope when towing the boat by another vessel; dynamic action of the outboard motor propeller stop when the steering wheel is sharply shifted; lifting a person into the boat over the side; squall when sailing, etc. All this makes it necessary to impose very stringent requirements on the stability of small ships.

The minimum value of the transverse metacentric height, ensuring safe navigation of a boat or boat in the lightest conditions - in an internal closed water area, is considered to be 0.25 m. However, this figure also becomes critical when it comes to very light rowing boats. After all, it is always possible that one or two passengers will stand up to their full height and the center of gravity of the boat will increase by 0.2-0.3 m. For ships going out on open water, it is recommended to ensure a metacentric height of at least 0.5 m; if the boat is designed to sail in waves up to force 3, the metacentric height must be at least 0.7 m.

Accurate measurements of the metacentric height are associated with a rather labor-intensive experiment of inclining the vessel, which for boats 4-5 m long does not always give accurate results and cannot sufficiently characterize stability. In the practice of monitoring and testing small vessels, a more visual and simple experiment is carried out, provided for by GOST 19356-74¹. For testing, an outboard motor and a gas tank filled with fuel are installed on the boat, ballast is loaded onto the seats, equal in weight to the rated carrying capacity, and in such a way that 60% of it is located at the side with the center of gravity at a distance of 0.2 m from the gunwale in width and 0. 3 m above the seat in height. The remaining 40% of the payload capacity must be located in the centerline of the vessel. With such a load, the gunwale on the heeled side should not enter the water.

¹ GOST 19356-74 “Pleasure rowing motor boats. Test methods"

According to the rules of Det Norske Veritas, similar tests are carried out, but at the same time they additionally check the stability of the boat empty, that is, without an outboard motor and removable equipment that is not usually fixed in the boat. At gunwale height and at a distance of 0.5 B NB from the DP secure the heeling load with the mass n· 20 kg, where n- total passenger capacity of the vessel. In this case, the boat should not be filled with water over the side and the roll should not exceed 30°.

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

The tilting of the ship can occur due to the action of oncoming waves, due to asymmetrical flooding of compartments during a hole, from the movement of cargo, wind pressure, due to the receipt or consumption of cargo.

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

The stability that a ship has during longitudinal inclinations is called longitudinal. It is usually quite large, and there is never any danger of the vessel capsizing through the bow or stern.

The stability of the vessel during transverse inclinations is called transverse. It is the most important characteristic of a vessel, determining its seaworthiness.

A distinction is made between initial lateral stability at small roll angles (up to 10 - 15°) and stability at large inclinations, since the righting moment at small and large roll angles is determined in different ways.

Initial stability. If the ship, under the influence of the external heeling moment of the MKR (for example, wind pressure), receives a roll by an angle θ (the angle between the original WL0 and the current WL1 waterlines), then, due to a change in the shape of the underwater part of the vessel, the center of value C will move to point C1 (Fig. 5 ). The supporting force yV will be applied at point C1 and directed perpendicular to the effective waterline WL1. Point M is located at the intersection of the diametrical plane with the line of action of the supporting forces and is called the transverse metacenter. The weight force of the vessel P remains at the center of gravity G. Together with the force yV, it forms a pair of forces that prevents the vessel from tilting by the heeling moment of the MKR. The moment of this pair of forces is called the restoring moment of the MV. Its value depends on the arm l=GK between the forces of weight and support of an inclined vessel: MВ = Pl =Ph sin θ, where h is the elevation of point M above the center of gravity of the vessel G, called the transverse metacentric height of the vessel.

From the formula it is clear that the greater the h value, the greater the restoring torque. Therefore, the metacentric height can serve as a measure of stability for a given vessel.

The value h of a given vessel at a certain draft depends on the position of the vessel’s center of gravity. If the loads are positioned so that the center of gravity of the vessel takes a higher position, then the metacentric height will decrease, and with it the static stability arm and the righting moment, i.e. the stability of the vessel will decrease. As the position of the center of gravity decreases, the metacentric height will increase and the stability of the vessel will increase.

Since for small angles their sines are approximately equal to the magnitude of the angles measured in radians, we can write MV = Рhθ.

The metacentric height can be determined from the expression h = r + zc - zg, where zc is the elevation of the CV above the OL; r is the transverse metacentric radius, i.e. the elevation of the metacenter above the central point; zg is the elevation of the ship's CG above the main one.

On a constructed ship, the initial metacentric height is determined experimentally - by inclination, i.e., the transverse inclination of the vessel by moving a load of a certain weight, called heel ballast.

Stability at high roll angles. As the ship's roll increases, the righting moment first increases, then decreases, becomes equal to zero, and then not only does not prevent the tilt, but, on the contrary, contributes to it

Since the displacement for a given load state is constant, the restoring moment changes only due to a change in the lateral stability arm lst. Based on calculations of lateral stability at large roll angles, a static stability diagram is constructed, which is a graph expressing the dependence of lst on the roll angle. The static stability diagram is constructed for the most typical and dangerous cases of ship loading.

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

With a slow (static) action of the heeling moment, the state of equilibrium during the roll occurs if the condition of equality of moments is met, i.e. MKR = MV

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

The magnitude of the roll angle under the dynamic action of the heeling moment can be determined from the static stability diagram. The horizontal line of the heeling moment is continued to the right until the area ODSE (work of the heeling moment) becomes equal to the area of the figure OBE (work of the righting moment). In this case, the area of OACE is general, so we can limit ourselves to comparing the areas of OACE and ABC.

If the area limited by the curve of restoring moments is insufficient, the ship will capsize.

The stability of seagoing vessels must meet the requirements of the Register, in accordance with which it is necessary to fulfill the condition (the so-called weather criterion): K = Moprmin / Mdnmax ≥ 1 "where Moprmin is the minimum capsizing moment (the minimum dynamically applied heeling moment taking into account pitching), under the influence of which the ship will not lose stability yet; Mdnmax is the dynamically applied heeling moment from wind pressure under the worst loading option in terms of stability.

In accordance with the Register's requirements, the maximum arm of the static stability diagram lmax must be at least 0.25 m for ships with a length of 85 m and at least 0.20 m for ships over 105 m with a heel angle θ over 30°. The slope angle of the diagram (the angle at which the stability arm curve intersects the horizontal axis) for all ships must be at least 60°.

The influence of liquid cargo on stability. If the tank is not filled to the top, that is, there is a free surface of liquid in it, then when tilted, the liquid will flow in the direction of the list and the center of gravity of the vessel will shift in the same direction. This will lead to a decrease in the stability arm, and consequently to a decrease in the righting moment. Moreover, the wider the tank in which there is a free surface of the liquid, the more significant the reduction in lateral stability will be. To reduce the influence of the free surface, it is advisable to reduce the width of the tanks and strive to ensure that during operation there is a minimum number of tanks with a free liquid surface.

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

To prevent grain from spilling in the holds, suspended longitudinal semi-bulks - shifting boards - are installed, or bags of grain are placed on top of the grain poured in the hold (cargo bagging).

The influence of a suspended load on stability. If the cargo is in the hold, then when it is lifted, for example by a crane, it is as if the cargo is instantly transferred to the suspension point. As a result, the ship's CG will shift vertically upward, which will lead to a decrease in the righting moment arm when the ship rolls, i.e., to a decrease in stability. In this case, the decrease in stability will be greater, the greater the mass of the load and the height of its suspension.

It might be useful to read: