The stability of the ship on the water. Elements of initial transverse stability

The ability of a vessel to resist the action of external forces tending to tilt it in the transverse and longitudinal directions, and to return to a straight position after the termination of their action is called stability. The most important thing for any ship is its lateral stability, since the point of application of the forces opposing 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 a roll, then gravity D and buoyancy γ V, applied respectively in the CT and CV, act along the same vertical. If the crew or other components of the weight load do not move during a roll at an angle θ, then at any inclination 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 . Due to this, a moment of a pair of forces arises D and γ V 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 a straight position and therefore is called regenerating.

Rice. 7. Scheme for determining the shoulders of transverse stability when tilted at an angle θ.

With a roll, the CV moves along a curved trajectory 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 with a 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 the ship's stability and is called transverse metacentric height. The more h, the greater the heeling force required to roll the ship at any particular heel angle, the more stable the ship.

From a 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 to

M in = D · h· sin θ kgm.

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

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

From a triangle C 0 GK can be found that

l in = GK = C 0 G sin θ m,

where C 0 G = a- the elevation of the CG over the CG in the forward position of the vessel.

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

An effect similar to the reduction of the CG is given by the heeling - the movement of the crew on board, opposite to the inclination. This method is widely used on light sailing dinghies, where the crew, hung overboard on a special device - a trapezoid, manages to move the general CG 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 is positive (see Fig. 197).

Since the mass of the crew on small vessels makes up the bulk 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 the motorboat to stand up so that the center of gravity becomes 250-300 mm higher, and one person who sits 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 much less than the mass of a person. Therefore, the designers, and the persons 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 the floorboard is 150 mm, and the seats on planing motor boats are 250 mm. On single, double rowing and collapsible boats, for example, kayaks, rowers can be located on a very low seat (no more than 70 mm) or directly on the bottom of the boat. On lightweight boats, payolas are often replaced with wooden planks glued from the inside to the bottom.

When upgrading serial boats or building home-made large fuel reserves (40-150 l), it is desirable to concentrate under the floorboards 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 to lighten the structure of the superstructure as much as possible and reduce its height, lower the level of the cockpit platform and the helmsman's station. The stationary engine on the boat should also be mounted as low as possible.

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

Less effective is the internal ballast of metal castings, laid in the hold of the vessel. 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, you need to take care that the ingots do not break through the thin skin of the bottom when sailing in waves.

When developing a project for a new ship, the designer has the ability to change the value of stability by setting one or another form of the hull. For example, the width of the boat along the waterline and the coefficient of its completeness α are of great importance. Approximate value of the metacentric radius r can be determined by the formula

Therefore, most significantly by the value 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 possible for reasons of propulsion.

The following average ratios can be named 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-, four-seater boats (fofans, 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; planing boats of open type - 3.2÷3.5; displacement boats 6-8 m long - 3.5 ÷ 4.5.

The coefficient α is also of great importance, especially for slow-moving rowboats and displacement boats, the waterlines of which are often made too narrow to reduce water resistance. On small boats - tuziks, it is advisable to carry out the contours of the waterline with maximum completeness - α \u003d 0.75 ÷ 0.85. On tourist kayaks, it is desirable to have a coefficient α of more 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 such as "sea sleigh", 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 the center of magnitude shifts to the side during a roll and the greater the shoulder of the restoring moment. The extreme poles are double-hulled vessels - catamarans and a boat with a midship bypass close to a circle (Fig. 8), in which the stability arm during roll changes very slightly. The more pronounced the cheekbone in the cross sections of the hull, the more stable the boat. For small boats, a hull with bulges near the cheekbones and a hull outline close to a rectangle is optimal.

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

Stability at high angles of heel. As shown above, the restoring shoulder changes with the roll increase in proportion to the sine of the roll angle. In addition, the transverse metacentric height does not remain constant either. h, the value of which depends on the change in the metacentric radius r. Obviously, the complete characteristic of the stability of the vessel can be a graph of the change in the restoring shoulder or moment depending on the angle of heel, 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 limit angle of heel at which the vessel capsizes (θ s - the angle of sunset 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 CV; therefore, the stability arm is zero.

Rice. 9. Diagram of static stability

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

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

However, the dangerous moment can come even earlier if the vessel has an open cockpit, side windows or deck hatches through which water can enter the vessel at a lower angle of heel. This corner is called pouring angle.

The shape of the static stability diagram and the position of its characteristic points depend on the contours of the hull and the position of the ship's CG. Usually, the maximum restoring lever occurs at the angle of heel corresponding to the beginning of the deck edge submersion 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 leaves the water, the width of the heeling waterline begins to decrease; accordingly, the value of the metacentric radius also decreases r. At the same time, the weight stability arm also increases with a list of 50-60 ° on most small vessels, the restoring arm l becomes zero.

The exception is sailing yachts with a heavy false keel, in which the maximum stability occurs at a roll of 90 °, i.e. when the mast is already on the water. If, in addition, all openings in the deck are sealed, then the moment of loss of stability ( l= 0) occurs approximately at a roll of 130°, when the mast is directed downward at an angle of 40° to the water surface. There are many cases when yachts that capsized with the keel up (heel angle 180 °) again returned to a straight position.

The same self-straightening property from the capsized position can be achieved on boats with large volume superstructures fitted with airtight closures. When the keel is positioned upwards, 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 outboard water at one of the sides.

In 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 hull DPs. This position is achieved in most catamarans with a list of 8-15 °. With a further increase in the roll, the stability arm rapidly 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 the captain can evaluate the ability of the vessel to withstand certain heeling forces that arise, for example, when moving part of the cargo to one of the sides, the effect of wind on the sails, etc. Heeling moment M kr (or its shoulder equal to M cr / D) is plotted on the diagram as a curve (or straight line) depending on the bank angle. The point of intersection of this curve with the restoring moment diagram corresponds to the angle of heel that the ship will receive. If the curve M cr passes above the maximum of the static stability diagram, the ship will capsize. If the curve M kr crosses the restoring moment 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 termination of this additional moment, it returns to its previous position A. On the downward branch of the diagram at the point B a small increase in the heeling moment will cause a significant increase in the roll, since the restoring moment will be less than the heeling moment; the ship may capsize. With a decrease in the heeling moment, the vessel from the position B will move into position A. Therefore, 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 or wave strikes a windward cheekbone, a person jumps on board a boat from a high embankment, etc. In these cases, not only the value of the heeling moment is important, but also the kinetic energy imparted to the ship and absorbed by the work of the restoring moment . An important role is played by the height of the freeboard and the angle of heel at which it is possible to flood the boat 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 the heeling forces is absorbed by the work of the restoring moment when the vessel is tilted.

When operating small craft, 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 of the crew, which, with its mass, tilts the boat even before water enters it.

You can increase the stability of the vessel with the help of side fittings - booley(see fig. 172), an inflatable chamber or a foam plastic fender encircling the sides of the boat near their upper edge, floats of a sufficiently large volume fixed 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 motorized ships, where an increase in displacement is associated with additional power and fuel costs. On planing boats and dinghies, outboard water 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 support forces are insignificant. Water from the tank will be removed through the aft cut of the transom as soon as it breaks away from 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 assumed to be 20-25% of the ship's displacement.

Rice. 10. Ballast tank on a planing boat.

1 - the cavity of the tank; 2 - ventilation pipe; 3 - water inlet to the tank; 4 - the second bottom.

In passing, mention should be made of the effect of water in the hold of a vessel (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

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

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

Rationing and checking the stability of pleasure-tourist vessels. A dangerous roll of a small vessel can be caused by the movement of the crew to one side, as well as the influence of various external forces. As a rule, pleasure-tourist vessels are operated in shallow coastal areas of the seas and in reservoirs with limited depth. In these areas, the wave is characterized by a dangerous steepness and a breaking crest. In the side to the wave position, the swing of the boat can fall into undesirable resonance with the wave period; if the ship is not stable enough, it can capsize.

Small vessels also have to withstand such loads that are dangerous for lateral stability, such as jerks in the towing cable when the boat is towed by another vessel; dynamic action of the outboard motor propeller stop when the rudder is sharply shifted; climbing into the boat through the board of a person; a squall when sailing, etc. All this makes it necessary to impose very stringent requirements on the stability of small vessels.

The minimum value of the transverse metacentric height, which ensures the 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 becomes critical when it comes to very light rowing boats. After all, it is always possible that one or two passengers stand up to their full height and the center of gravity of the boat will increase by 0.2-0.3 m. For ships that go to open water, it is recommended to ensure a metacentric height of at least 0.5 m; if the boat is designed to sail with a wave of up to 3 points, the metacentric height must be at least 0.7 m.

Accurate measurements of the metacentric height are associated with a rather laborious experience of the ship's heeling, which for boats 4-5 m long does not always give accurate results and cannot characterize the stability sufficiently fully. In the practice of control and testing of small craft, a more visual and simple experiment is carried out, provided for by GOST 19356-74 ¹. 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 nameplate 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 placed in the centreline of the ship. With such a load, the gunwale from the side of the heeled side should not enter the water.

¹ GOST 19356-74 “Recreational propeller motor boats. Test Methods»

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

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.

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 (that is, dynamic) forces, for example, wind, sea waves, cargo movement, etc.

Initial lateral stability

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

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

Free surfaces

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

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

Influence of free surface on stability

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

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

δm θ = − γ x i x θ,

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:

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

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:

Dynamic stability of the ship

Unlike static, the dynamic effect of forces and moments imparts significant angular velocities and accelerations to the ship. Therefore, their influence is considered in energies, more precisely in the form of the work of forces and moments, and not in the efforts themselves. In this case, the kinetic energy theorem is used, according to which the increment in the kinetic energy of the ship's inclination is equal to the work of the forces acting on it.

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 moment. 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 ship. O. when heeling ... ... Great Soviet Encyclopedia

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

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

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

The stability of a vessel is its property, due to which the vessel, when exposed to external factors (wind, waves, etc.) and internal processes (displacement of cargo, movement of liquid reserves, the presence of free liquid surfaces in compartments, etc.) does not roll over. The most capacious definition of ship stability can be the following: the ability of a ship not to capsize when exposed to natural marine factors (wind, waves, icing) in the navigation area assigned to it, as well as in combination with “internal” reasons caused by the actions of the crew

This feature is based on the natural property of an object floating on the surface of the water - it tends to return to its original position after the termination of this impact. Thus, stability, on the one hand, is natural, and, on the other hand, requires regulated control by the person involved in its design and operation.

Stability depends on the shape of the hull and the position of the ship's CG, so by right choice the design of the hull shape and the correct placement of cargo on the vessel during operation can provide sufficient stability to ensure that the vessel does not capsize under any sailing conditions.

Vessel inclinations are possible for various reasons: from the action of incoming waves, due to asymmetric flooding of compartments during a hole, from the movement of goods, wind pressure, due to the acceptance or expenditure of goods, etc. There are two types of stability: transverse and longitudinal. From the point of view of navigation safety (especially in stormy weather), the most dangerous are transverse inclinations. Lateral stability manifests itself when the vessel rolls, i.e. when tilting it on board. If the forces that cause the vessel to tilt act slowly, then the stability is called static, and if it is fast, then dynamic. 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 respectively by O and y. Stability at small angles of inclination (10 - 12 °) is called initial stability.

(fig.2)

Imagine that under the action of external forces, the ship received a roll at an angle of 9 (Fig. 2). As a result, the volume of the underwater part of the vessel retained its value, but changed its shape; on the starboard side, an additional volume entered the water, and on the port side, an equal volume came out of the water. The center of magnitude has moved from the initial position C towards the roll of the vessel, to the center of gravity of the new volume - point C1. When the vessel is inclined, the gravity P applied at point G and the support force D applied at point C, remaining perpendicular to the new waterline V1L1, form a pair of forces with a shoulder GK, which is a perpendicular lowered from point G to the direction of the support forces.

If we continue the direction of the support force from point C1 to the intersection with its original direction from point C, then at small angles of heel, corresponding to the conditions of initial stability, these two directions will intersect at point M, called the transverse metacenter.

The mutual position of points M and G allows you to establish the following sign characterizing the lateral stability: (Fig. 3)

A) If the metacenter is located above the center of gravity, then the restoring moment is positive and tends to return the ship to its original position, i.e., when heeling, the ship will be stable.
B) If point M is below point G, then with a negative value of h0, the moment is negative and will tend to increase the roll, i.e., in this case, the vessel is unstable.
C) When the points M and G coincide, the forces P and D act along one vertical line, no pair of forces arise, and the restoring moment is zero: then the ship must be considered unstable, since it does not tend to return to its original equilibrium position (Fig. 3 ).

Fig.3

External signs of negative initial stability of the ship are:

-- sailing of the ship with a roll in the absence of heeling moments;
- the desire of the ship to roll over to the opposite side when straightening;
- transfer from side to side during circulation, while the roll remains even when the ship enters a direct course;
-- a large amount of water in the holds, on platforms and decks.

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

With the longitudinal inclination of the vessel at an angle w around the transverse axis Ts.V. will move from point C to point C1 and the support force, the direction of which is normal to the current waterline, will act at an angle w to the original direction. The lines of action of the original and new direction of the support forces intersect at a point. The point of intersection, the line of action of the forces of support at an infinitely small inclination in the longitudinal plane is called the longitudinal metacenter M. seaworthy stability propulsion ship

The longitudinal moment of inertia of the waterline area IF is much greater than the transverse moment of inertia IX. Therefore, the longitudinal metacentric radius R is always much larger than the transverse r. It is tentatively considered that the longitudinal metacentric radius R is approximately equal to the length of the vessel. Since the value of the longitudinal metacentric radius R is many times greater than the transverse r, the longitudinal metacentric height H of any ship is many times greater than the transverse one h. therefore, if the ship has transverse stability, then longitudinal stability is certainly ensured.

Factors affecting ship stability that have a strong influence on ship stability.

Factors to be taken into account when operating a small boat include:

1. The stability of the vessel is most significantly affected by its width: the greater it is in relation to its length, height and draft, the higher the stability. A wider vessel has more righting moment.
2. The stability of a small vessel increases if the shape of the submerged part of the hull is changed at large angles of heel. On this statement, for example, the action of side bollards and foam fenders is based, which, when immersed in water, create an additional restoring moment.
3. Stability deteriorates if there are fuel tanks on the ship with a surface mirror from side to side, so these tanks must have partitions installed parallel to the center plane of the ship, or be narrowed in their upper part.
4. Stability is most strongly affected by the placement of passengers and cargo on the ship, they should be placed as low as possible. It is impossible to allow people on board and their arbitrary movement to sit on a small vessel during its movement. Loads must be securely fastened to prevent their unexpected displacement from their regular places.
5. In strong winds and waves, the action of the heeling moment (especially dynamic) is very dangerous for the vessel, therefore, with deterioration weather conditions it is necessary to take the ship to shelter and wait out the bad weather. If this is not possible due to the considerable distance to the shore, then in stormy conditions you should try to keep the ship "bow to the wind", throwing out the floating anchor and running the engine at low speed.

Excessive stability causes rapid pitching and increases the risk of resonance. Therefore, the register set limits not only for the lower, but also for the upper limit of stability.

To increase the stability of the vessel (increase in the restoring moment per unit of heel angle), it is necessary to increase the metacentric height h by appropriate placement of cargo and stores on the ship (heavier cargo at the bottom, and lighter cargo at the top). For the same purpose (especially when sailing in ballast - without cargo), they resort to filling ballast tanks with water.

Stability (stability) is one of the most important seaworthiness of the ship, which is associated with extremely important issues related to the safety of navigation. Loss of stability almost always means the death of the ship and very often the crew. Unlike the change in other seaworthiness, the decrease in stability does not manifest itself in a visible way, and the crew of the vessel, as a rule, is unaware of the imminent danger until the last seconds before capsizing. Therefore, the study of this section of the theory of the ship must be given the greatest attention.

In order for the vessel to float in a given equilibrium position relative to the water surface, it must not only satisfy the equilibrium conditions, but also be able to resist external forces seeking to take it out of the equilibrium position, and after the termination of these forces, return to its original position. Therefore, the balance of the ship must be stable, or, in other words, the ship must have positive stability.

Thus, stability is the ability of a vessel, taken out of equilibrium by external forces, to return to its original equilibrium position after the termination of these forces.

The stability of the vessel is associated with its balance, which serves as a characteristic of the latter. If the balance of the ship is stable, then the ship has positive stability; if its equilibrium is indifferent, then the ship has zero stability, and, finally, if the ship's equilibrium is unstable, then it has negative stability.

Tanker Kapitan Shiryaev
Source: fleetphoto.ru

This chapter will consider the transverse inclinations of the ship in the plane of the midship frame.

Stability during transverse inclinations, i.e., when a roll occurs, is called transverse. Depending on the angle of inclination of the vessel, transverse stability is divided into stability at small angles of inclination (up to 10-15 degrees), or the so-called initial stability, and stability at large angles of inclination.

The inclinations of the vessel occur under the action of a pair of forces; the moment of this pair of forces, which causes the ship to rotate around the longitudinal axis, will be called the heeling Mcr.

If Mcr, applied to the vessel, increases gradually from zero to a final value and does not cause angular accelerations, and, consequently, inertia forces, then stability with such an inclination is called static.

The heeling moment acting on the vessel instantly leads to the occurrence of angular acceleration and inertial forces. The stability that manifests itself with such an inclination is called dynamic.

Static stability is characterized by the occurrence of a restoring moment, which tends to return the ship to its original equilibrium position. Dynamic stability is characterized by the work of this moment from the beginning to the end of its action.

Consider the equal-volume transverse inclination of the vessel. We will assume that in the initial position the ship has a direct landing. In this case, the support force D' acts in the DP and is applied at point C - the center of the ship's size (Center of buoyancy-B).

Rice. 1

Let us assume that the ship under the action of the heeling moment received a transverse inclination at a small angle θ. Then the center of magnitude will move from point C to point C 1 and the support force, perpendicular to the new effective waterline B 1 L 1, will be directed at an angle θ to the diametrical plane. The lines of action of the original and new direction of the support force will intersect at 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 the transverse metacenter (metacentre).

You can give another definition of the metacenter: the center of curvature of the curve of displacement of the center of magnitude in the transverse plane is called the transverse metacenter.

The radius of curvature of the displacement curve of the center of magnitude in the transverse plane is called the transverse metacentric radius (or small metacentric radius) (Radius of metacentre). It is determined by the distance from the transverse metacenter m to the center of magnitude C and is denoted by the letter r.

The transverse metacentric radius can be calculated using the formula:

i.e., the transverse metacentric radius is equal to the moment of inertia Ix of the waterline area relative to the longitudinal axis passing through the center of gravity of this area, divided by the volume displacement V corresponding to this waterline.

Stability conditions

Let us assume that the vessel, which is in a direct position of equilibrium and floating along the waterline of the overhead line, as a result of the action of the external heeling moment Mkr, has tilted so that the initial waterline of the overhead line with the new effective waterline B 1 L 1 forms a small angle θ. Due to the change in the shape of the part of the hull submerged in water, the distribution of hydrostatic pressure forces acting on this part of the hull will also change. The ship's center of magnitude will move in the direction of the roll and move from point C to point C 1 .

The support force D', remaining unchanged, will be directed vertically upwards perpendicular to the new effective waterline, and its line of action will cross the DP in the original transverse metacenter m.

The position of the ship's center of gravity remains unchanged, and the weight force P will be perpendicular to the new waterline B 1 L 1 . Thus, the forces P and D', parallel to each other, do not lie on the same vertical and, therefore, form a pair of forces with a shoulder GK, where point K is the base of the perpendicular dropped from point G to the direction of action of the support force.

The pair of forces formed by the ship's weight and the support force, which tends to return the ship to its original equilibrium position, is called the restoring pair, and the moment of this pair is called the restoring moment Мθ.

The question of the stability of a heeled ship is decided by the direction of action of the restoring moment. If the restoring moment tends to return the ship to its original equilibrium position, then the restoring moment is positive, the stability of the ship is also positive - the ship is stable. On fig. 2 shows the location of the forces acting on the ship, which corresponds to a positive restoring moment. It is easy to verify that such a moment arises if the CG lies below the metacenter.

Rice. 2

Rice. 3

On fig. 3 shows the opposite case, when the restoring moment is negative (the CG lies above the metacenter). He tends to deflect the ship from the equilibrium position even more, since the direction of its action coincides with the direction of action of the external heeling moment Mkr. In this case, the ship is not stable.

Theoretically, it can be assumed that the restoring moment when the ship is tilted is zero, i.e., the weight force of the ship and the support force are located on the same vertical, as shown in fig. four.

Rice. four

The absence of a restoring moment leads to the fact that after the end of the heeling moment, the ship remains in an inclined position, i.e., the ship is in indifferent equilibrium.

Thus, according to the mutual position of the transverse metacenter m and C.T. G can be judged on the sign of the restoring moment or, in other words, on the stability of the ship. So, if the transverse metacenter is above the center of gravity (Fig. 2), then the ship is stable.

If the transverse metacenter is located below the center of gravity or coincides with it (Fig. 3, 4), the ship is not stable.

Hence the concept of metacentric height (Metacentric height) arises: the transverse metacentric height is the elevation of the transverse metacenter above the center of gravity of the vessel in the initial position of equilibrium.

The transverse metacentric height (Fig. 2) is determined by the distance from the center of gravity (point G) to the transverse metacenter (point m), i.e., the segment mG. This segment is a constant value, because and C.T. , and the transverse metacenter do not change their position at low inclinations. In this regard, it is convenient to take it as a criterion for the initial stability of the vessel.

If the transverse metacenter is above the ship's center of gravity, then the transverse metacentric height is considered positive. Then the ship stability condition can be given in the following formulation: the ship is stable if its transverse metacentric height is positive. Such a definition is convenient in that it allows one to judge the ship's stability without considering its inclination, i.e., at a heel angle equal to zero, when there is no restoring moment at all. To establish what data must be available to obtain the value of the transverse metacentric height, let us turn to Fig. 5, which shows the relative location of the center of magnitude C, the center of gravity G and the transverse metacenter m of the vessel, which has a positive initial transverse stability.

Rice. five

The figure shows that the transverse metacentric height h can be determined by one of the following formulas:

h = Z C ± r - Z G ;

The transverse metacentric height is often determined using the last equality. The applicate of the transverse metacenter Zm can be found from the metacentric diagram. The main difficulties in determining the transverse metacentric height of the vessel arise when determining the applicate of the center of gravity ZG, which is determined using the summary table of the ship's mass load (the issue was considered in the lecture -).

In foreign literature, the designation of the corresponding points and stability parameters may look as shown below in Fig. 6.

Rice. 6

where K is the keel point;
B - center of buoyancy;
G - center of gravity;
M - transverse metacenter (metacentre);
KV - applicate of the center of magnitude;
KG - applicate center of gravity;
CM — applicate of the transverse metacenter;
VM - transverse metacentric radius (Radius of metacentre);
BG - elevation of the center of gravity above the center of magnitude;
GM - transverse metacentric height (Metacentric height).

The shoulder of static stability, designated in our literature as GK, is designated in foreign literature as GZ.