By the relative position of the cargo on the ship, the navigator can always find the most favorable value of the metacentric height, at which the ship will be sufficiently stable and less subject to pitching.

The heeling moment is the product of the weight of the cargo moved across the vessel by a shoulder equal to the distance of movement. If a person weighs 75 kg, sitting on a bank will move across the ship by 0.5 m, then the heeling moment will be equal to 75 * 0.5 = 37.5 kg/m.

Figure 91. Static stability diagram

To change the moment that heels the ship by 10°, it is necessary to load the ship to full displacement completely symmetrically relative to the center plane.

The vessel's loading should be checked by drafts measured on both sides. The inclinometer is installed strictly perpendicular to the center plane so that it shows 0°.

After this, you need to move loads (for example, people) at pre-marked distances until the inclinometer shows 10°. The test experiment should be carried out as follows: tilt the ship on one side and then on the other side.

Knowing the fastening moments of a ship heeling at various (up to the greatest possible) angles, it is possible to construct a static stability diagram (Fig. 91), which will evaluate the stability of the ship.

Stability can be increased by increasing the width of the vessel, lowering the center of gravity, and installing stern buoys.

If the center of gravity of the vessel is located below the center of magnitude, then the vessel is considered very stable, since the supporting force during a roll does not change in magnitude and direction, but the point of its application shifts towards the tilt of the vessel (Fig. 92, a).

Therefore, when heeling, a pair of forces is formed with a positive restoring moment, tending to return the ship to its normal vertical position on a straight keel. It is easy to verify that h>0, with the metacentric height equal to 0. This is typical for yachts with a heavy keel and is not typical for larger vessels with a conventional hull structure.

If the center of gravity is located above the center of magnitude, then three cases of stability are possible, which the navigator should be well aware of.

The first case of stability.

Metacentric height h>0. If the center of gravity is located above the center of magnitude, then when the vessel is in an inclined position, the line of action of the supporting force intersects the center plane above the center of gravity (Fig. 92, b).

Rice. 92. The case of a stable ship

In this case, a couple of forces with a positive restoring moment is also formed. This is typical for most conventionally shaped boats. Stability in this case depends on the hull and the position of the center of gravity in height.

When heeling, the heeling side enters the water and creates additional buoyancy, tending to level the ship. However, when a ship rolls with liquid and bulk cargo that can move towards the roll, the center of gravity will also shift towards the roll. If the center of gravity during a roll moves beyond the plumb line connecting the center of magnitude with the metacenter, then the ship will capsize.

The second case of an unstable vessel in indifferent equilibrium.

Metacentric height h = 0. If the center of gravity lies above the center of magnitude, then during a roll the line of action of the supporting force passes through the center of gravity MG = 0 (Fig. 93).

In this case, the center of magnitude is always located on the same vertical as the center of gravity, so there is no recovering pair of forces. Without the influence of external forces, the ship cannot return to an upright position.

In this case, it is especially dangerous and completely unacceptable to transport liquid and bulk cargo on a ship: with the slightest rocking, the ship will capsize. This is typical for boats with a round frame.

The third case of an unstable vessel in unstable equilibrium.

Metacentric height h<0. Центр тяжести расположен выше центра величины, а в наклонном положении судна линия действия силы поддержания пересекает след диаметральной плоскости ниже центра тяжести (рис. 94).

The main characteristic of stability is righting moment, which must be sufficient for the vessel to withstand the static or dynamic (sudden) action of heeling and trim moments arising from the displacement of cargo, under the influence of wind, waves and other reasons.

The heeling (trimming) and righting moments act in opposite directions and are equal in the equilibrium position of the vessel.

Distinguish lateral stability, corresponding to the inclination of the vessel in the transverse plane (vessel roll), and longitudinal stability(ship trim).

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

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

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

Metacenter - the center of curvature of the trajectory along which the center of magnitude C moves during the process of tilting the ship. If the inclination occurs in the transverse plane (roll), the metacenter is called transverse, or small, while the inclination in the longitudinal plane (trim) is called longitudinal, or large.

Accordingly, transverse (small) r and longitudinal (large) R metacentric radii are distinguished, representing the radii of curvature of the trajectory C during roll and trim.

The distance between the initial metacenter t and the center of gravity of the vessel G is called initial metacentric height(or simply metacentric height) and are designated by the letter h. The initial metacentric height is a measure of the ship's stability.

h = zc + r - zg; h = zm ~ zc; h = r - a,

where a is the elevation of the center of gravity (CG) above the CV.

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

OG – elevation of the center of gravity above the keel; OM – elevation of the metacenter above the carina;

GM - metacentric height; CM – metacentric radius;

m – metacenter; G – center of gravity; C – center of magnitude

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

the metacenter m is located above the center of gravity of the ship G (h > 0). With a low inclination, gravity and buoyancy forces create a pair of forces, the moment of which tends to return the ship to its original equilibrium position;

The ship's CG G is located above the metacenter m (h< 0). В этом случае момент пары сил веса и плавучести будет стремиться увеличить крен судна, что ведет к его опрокидыванию;

The ship's center of gravity G and the metacenter m coincide (h = 0). The ship will behave unstable, since the shoulder of the couple of forces is missing.

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

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 vessel at any particular angle of heel, the more stable the vessel.

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-, double-seater rowing and collapsible boats, for example, 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.

Internal ballast made from metal castings placed in the ship's hold is less effective. 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, great importance has the width of the boat along the waterline and its coefficient of completeness α. 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 α coefficient 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 small vessels, 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°) - sunset angle 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. The moment 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 center of gravity of such a vessel turns out to be located much higher than the center of gravity - a position of unstable equilibrium is reached, from which the boat can be removed 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 go into position A. Consequently, the position of the vessel corresponding to the point B, is unstable.

Dynamic stability. Above, we considered the static effect of a heeling moment on a 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°.

§ 12. Seaworthiness of ships. Part 1

Both civilian vessels and military ships must have seaworthiness.

A special scientific discipline deals with the study of these qualities using mathematical analysis - ship theory.

If a mathematical solution to the problem is impossible, then they resort to experiment to find the necessary dependence and test the conclusions of the theory in practice. Only after a comprehensive study and experience testing of all the seaworthiness of the vessel do they begin to create it.

Seaworthiness in the subject “Ship Theory” is studied in two sections: statics and dynamics of the vessel. Statics studies the laws of equilibrium of a floating vessel and the associated qualities: buoyancy, stability and unsinkability. Dynamics studies a ship in motion and considers its qualities such as controllability, pitching and propulsion.

Let's get acquainted with the seaworthiness of the vessel.

Buoyancy of the vessel is called its ability to float on water at a certain draft, carrying intended loads in accordance with the purpose of the vessel.

A floating ship is always acted upon by two forces: a) on the one hand, weight force, equal to the sum of the weight of the vessel itself and all cargo on it (calculated in tons); the resultant of the weight forces is applied to ship's center of gravity(CG) at point G and is always directed vertically downwards; b) on the other hand, maintaining forces, or buoyancy forces(expressed in tons), i.e., the water pressure on the submerged part of the hull, determined by the product of the volume of the submerged part of the hull by the volumetric weight of the water in which the ship floats. If these forces are expressed by the resultant applied at the center of gravity of the underwater volume of the vessel at point C, called center of magnitude(CV), then this resultant will always be directed vertically upward in all positions of the floating vessel (Fig. 10).

Volumetric displacement is the volume of the immersed part of the hull, expressed in cubic meters. Volumetric displacement serves as a measure of buoyancy, and the weight of water displaced by it is called weight displacement D) and is expressed in tons.

According to Archimedes' law, the weight of a floating body is equal to the weight of the volume of liquid displaced by this body,

Where y is the volumetric weight of sea water, t/m 3, taken in calculations to be equal to 1.000 for fresh water and 1.025 for sea water.

Rice. 10. Forces acting on a floating ship and the points of application of the resultant forces.

Since the weight of a floating vessel P is always equal to its weight displacement D, and their resultants are directed opposite to each other along the same vertical, and if we designate the coordinates of points G and C along the length of the vessel, respectively x g and x c, along the width y g and y c and along height z g and z c , then the equilibrium conditions of a floating vessel can be formulated by the following equations:

P = D; x g = x c .

Due to the symmetry of the ship relative to the DP, it is obvious that points G and C must lie in this plane, then

Y g = y c = 0.

Typically, the center of gravity of surface vessels G lies above the center of magnitude C, in which case

Sometimes it is more convenient to express the volume of the underwater part of the hull through the main dimensions of the vessel and the coefficient of overall completeness, i.e.

Then the weight displacement can be represented as

If we denote by V n the total volume of the hull up to the upper deck, provided that all side openings are closed watertight, we obtain

The difference V n - V, representing a certain volume of the waterproof hull above the load waterline, is called reserve buoyancy. In the event of an emergency ingress of water into the ship's hull, its draft will increase, but the ship will remain afloat, thanks to its reserve of buoyancy. Thus, the buoyancy reserve will be greater, the more more height watertight freeboard. Consequently, buoyancy reserve is an important characteristic of a vessel, ensuring its unsinkability. It is expressed as a percentage of normal displacement and has the following minimum values: for river boats 10-15%, for tankers 10-25%, for dry cargo ships 30-50%, for icebreakers 80-90%, and for passenger ships 80-100%.

Rice. 11. Construction along frames

The weight of the vessel P (weight load) And the coordinates of the center of gravity are determined by a calculation that takes into account the weight of each part of the hull, mechanisms, pieces of equipment, supplies, supplies, cargo, people, their luggage and everything on the ship. To simplify calculations, it is planned to combine individual specialty titles into articles, subgroups, groups and workload sections. For each of them, the weight and static moment are calculated.

Considering that the moment of the resultant force is equal to the sum of the moments of the component forces relative to the same plane, after summing up the weights and static moments over the entire vessel, the coordinates of the vessel’s center of gravity G are determined. Volumetric displacement, as well as the coordinates of the center of the value C along the length from the midsection x c and along height from the main line z c is determined from a theoretical drawing using the trapezoidal method in tabular form.

For the same purpose, they use auxiliary curves, the so-called construction curves, also drawn according to the data of the theoretical drawing.

There are two curves: formation along the frames and formation along the waterlines.

Construction on frames(Fig. 11) characterizes the distribution of the volume of the underwater part of the hull along the length of the vessel. It is built in the following way. Using the method of approximate calculations, the area of ​​the immersed part of each frame (w) is determined from a theoretical drawing. The length of the vessel is plotted along the abscissa axis on the selected scale and the position of the frames of the theoretical drawing is plotted on it. On the ordinates reconstructed from these points, the corresponding areas of the calculated frames are plotted on a certain scale.

The ends of the ordinates are connected by a smooth curve, which is the line along the frames.

Rice. 12. Drilling along the waterline.

Drilling along the waterline(Fig. 12) characterizes the distribution of the volume of the underwater part of the hull along the height of the vessel. To construct it, using a theoretical drawing, calculate the areas of all waterlines (5). These areas on a selected scale are laid out along the corresponding horizontal lines located along the draft of the vessel, in accordance with the position of a given waterline. The resulting points are connected by a smooth curve, which is the line along the waterlines.

Rice. 13. Cargo size curve.

These curves serve as the following characteristics:

1) the areas of each of the combat units express the volumetric displacement of the vessel on the appropriate scale;

2) the abscissa of the center of gravity of the combat area along the frames, measured on the scale of the length of the vessel, is equal to the abscissa of the center of magnitude of the vessel x c;

3) the ordinate of the center of gravity of the building area along the waterlines, measured on the draft scale, is equal to the ordinate of the center of the vessel's size z c. Cargo size is a curve (Fig. 13) characterizing the volumetric displacement of the vessel V depending on its draft T. Using this curve, you can determine the displacement of the vessel depending on its draft or solve the inverse problem.

This curve is constructed in a system of rectangular coordinates based on pre-calculated volumetric displacements along each waterline of the theoretical drawing. On the ordinate axis, on a selected scale, the draft of the vessel is plotted along each of the waterlines and horizontal lines are drawn through them, on which, also on a certain scale, the displacement value obtained for the corresponding waterlines is plotted. The ends of the resulting segments are connected by a smooth curve, which is called the load size.

Using the cargo size, it is possible to determine the change in the average draft due to the receipt or discharge of cargo or, based on a given displacement, to determine the draft of the vessel, etc.

Stability called the ability of a ship to resist the forces that caused it to tilt, and after the cessation of these forces, return to its original position.

The tilting of the vessel is possible for various reasons: from 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, etc.

The inclination of the ship in the transverse plane is called roll, and in the longitudinal plane - d ifferent; the angles formed in this case are denoted by O and y, respectively,

There are initial stability, i.e. stability at small angles of heel at which the edge of the upper deck begins to enter the water (but not more than 15° for high-sided surface vessels), and stability at high inclinations .

Let's imagine that, under the influence of external forces, the ship tilted at an angle of 9 (Fig. 14). As a result, the volume of the underwater part of the vessel retained its size, but changed its shape; On the starboard side, an additional volume entered the water, and on the left side, an equal volume came out of the water. The center of magnitude moved from the original position C towards the ship's roll, to the center of gravity of the new volume - point C 1. When the vessel is in an inclined position, the gravity force P applied at point G and the support force D applied at point C, remaining perpendicular to the new waterline B 1 L 1 form a pair of forces with the arm GK, which is a perpendicular lowered from point G to the direction of the support forces .

If we continue the direction of the support force from point C 1 until it intersects with its original direction from point C, then at small roll angles corresponding to the conditions of initial stability, these two directions will intersect at point M, called transverse metacenter .

The distance between the metacenter and the center of magnitude MC is called transverse metacentric radius, denoted by p, and the distance between point M and the center of gravity of the vessel G is transverse metacentric height h 0. Based on the data in Fig. 14 we can form an identity

H 0 = p + z c - z g .

In a right triangle GMR, the angle at the vertex M will be equal to angle 0. From its hypotenuse and the opposite angle, one can determine the leg GK, which is shoulder m of a couple restoring a vessel GK=h 0 sin 8, and the restoring moment will be equal to Mvost = DGK. Substituting the leverage values, we get the expression

Mvost = Dh 0 * sin 0,

Rice. 14. Forces acting when the ship rolls.

The relative position of points M and G allows us to establish the following feature characterizing lateral stability: if the metacenter is located above the center of gravity, then the restoring moment is positive and tends to return the vessel to its original position, i.e., when heeling, the vessel will be stable, vice versa, if point M is located below point G, then with a negative value of h 0 the moment is negative and will tend to increase the roll, i.e. in this case the ship is unstable. A case is possible when points M and G coincide, forces P and D act along the same vertical line, a pair of forces does not arise, and the restoring moment is zero: then the ship should be considered unstable, since it does not strive to return to its original equilibrium position (Fig. 15).

The metacentric height for representative load cases is calculated during the design process of the vessel and serves as a measure of stability. The value of the transverse metacentric height for the main types of ships lies in the range of 0.5-1.2 m and only for icebreakers it reaches 4.0 m.

To increase the lateral stability of a vessel, it is necessary to reduce its center of gravity. This is an extremely important factor that must always be remembered, especially when operating a vessel, and strict records must be kept of the consumption of fuel and water stored in double-bottom tanks.

Longitudinal metacentric height H 0 is calculated similarly to the transverse one, but since its value, expressed in tens or even hundreds of meters, is always very large - from one to one and a half lengths of the vessel, then after the verification calculation the longitudinal stability of the vessel is practically not calculated; its value is interesting only in the case of determining the draft of the vessel bow or stern during longitudinal movements of cargo or when compartments are flooded along the length of the vessel.

Rice. 15. Transverse stability of the vessel depending on the location of the cargo: a - positive stability; b - equilibrium position - the ship is unstable; c - negative stability.

The issues of vessel stability are given exceptional importance, and therefore usually, in addition to all theoretical calculations, after the construction of the vessel, the true position of its center of gravity is checked by experimental inclination, i.e., lateral inclination of the vessel by moving a load of a certain weight, called incline ballast .

All previously obtained conclusions, as already mentioned, are practically valid at initial stability, i.e., at small angles of roll.

When calculating lateral stability at large angles of roll (longitudinal inclinations in practice are not large), the variable positions of the center of magnitude, metacenter, transverse metacentric radius and the arm of the righting moment GK are determined for various angles of roll of the vessel. This calculation is made starting from the straight position through 5-10° to the angle of roll when the righting arm turns to zero and the ship acquires negative stability.

According to the data of this calculation, for a visual representation of the stability of the vessel at large angles of heel, a static stability diagram(it is also called the Reed diagram), showing the dependence of the static stability arm (GK) or the righting moment Mvost on the roll angle 8 (Fig. 16). In this diagram, the roll angles are plotted along the abscissa axis, and the value of the righting moments or the arms of the righting pair are plotted along the ordinate axis, since in equal-volume inclinations, at which the displacement of the vessel D remains constant, the righting moments are proportional to the stability arms.

Rice. 16. Diagram of static stability.

A static stability diagram is constructed for each characteristic case of ship loading, and it characterizes the stability of the ship as follows:

1) at all angles at which the curve is located above the x-axis, the restoring arms and moments have a positive value, and the ship has positive stability. At those heel angles when the curve is located below the abscissa axis, the ship will be unstable;

2) the maximum of the diagram determines the maximum heel angle of 0 max and the maximum heeling moment when the vessel is statically tilted;

3) the angle 8 at which the descending branch of the curve intersects the abscissa axis is called sunset angle diagram. At this roll angle, the righting arm becomes zero;

4) if on the abscissa axis we plot an angle equal to 1 radian (57.3°), and from this point we construct a perpendicular to the intersection with the tangent drawn to the curve from the origin, then this perpendicular on the scale of the diagram will be equal to the initial metacentric height h 0 .

Stability is greatly influenced by moving, i.e., unsecured, as well as liquid and bulk cargoes that have a free (open) surface. When the vessel tilts, these loads begin to move in the direction of the roll and, as a result, the center of gravity of the entire vessel will no longer be at a fixed point G, but will also begin to move in the same direction, causing a decrease in the lateral stability arm, which is equivalent to a decrease in the metacentric height with all consequences arising from this. To prevent such cases, all cargo on ships must be secured, and liquid or bulk cargo must be loaded into containers that prevent any transfer or spilling of cargo.

With the slow action of forces that create a heeling moment, the ship, tilting, will stop when the heeling and righting moments are equal. Under the sudden action of external forces, such as a gust of wind, the pull of a tug on board, pitching, a broadside salvo from guns, etc., the ship, tilting, acquires angular speed and even with the cessation of the action of these forces will continue to roll by inertia for an additional angle until all its kinetic energy (living force) of the rotational motion of the vessel is used up and its angular velocity becomes zero. This tilting of the ship under the influence of suddenly applied forces is called dynamic tilt. If during a static heeling moment the ship floats, having only a certain roll of 0 ST, then in the case of dynamic action of the same heeling moment it can capsize.

When analyzing dynamic stability, for each displacement of the vessel, a dynamic stability diagrams, the ordinates of which represent, on a certain scale, the areas formed by the curve of the moments of static stability for the corresponding roll angles, i.e., they express the work of the righting pair when the vessel is tilted at an angle of 0, expressed in radians. In rotational motion, as is known, the work is equal to the product of the moment and the angle of rotation, expressed in radians,

T 1 = M kp 0.

Using this diagram, all issues related to the determination of dynamic stability can be resolved as follows (Fig. 17).

The roll angle with a dynamically applied heeling moment can be found by plotting the operation of the heeling pair on a diagram on the same scale; The abscissa of the intersection point of these two graphs gives the desired angle 0 DIN.

If in a particular case the fastening moment has a constant value, i.e. M cr = const, then the work will be expressed

T 2 = M kp 0.

And the graph will look like a straight line passing through the origin.

In order to construct this straight line on the dynamic stability diagram, it is necessary to plot an angle equal to a radian along the abscissa axis and draw an ordinate from the resulting point. Having plotted the value M cr on it on an ordinate scale in the form of a segment Nn (Fig. 17), it is necessary to draw a straight line ON, which is the desired graph of the operation of the heeling pair.

Rice. 17. Determination of the roll angle and maximum dynamic inclination using the dynamic stability diagram.

The same diagram shows the dynamic inclination angle 0 DIN, defined as the abscissa of the point of intersection of both graphs.

With an increase in the moment M cr, the secant ON can take a limiting position, turning into an external tangent OT drawn from the origin to the dynamic stability diagram. Thus, the abscissa of the tangent point will be the maximum limiting angle of the dynamic inclinations 0. The ordinate of this tangent, corresponding to the radian, expresses the maximum heeling moment at the dynamic inclinations M crmax.

When sailing, a ship is often exposed to dynamic external forces. Therefore, the ability to determine the dynamic heeling moment when deciding on the stability of a vessel is of great practical importance.

A study of the causes of ship deaths leads to the conclusion that ships mainly die due to loss of stability. To limit loss of stability in accordance with different conditions navigation, the Register of the USSR has developed Stability Standards for transport and fishing fleet vessels. In these standards, the main indicator is the ship’s ability to maintain positive stability under the combined action of roll and wind. The vessel meets the basic requirement of the Stability Standards if, when worst case scenario loading it M KR remains less than M OPR.

In this case, the minimum capsizing moment of the vessel is determined from static or dynamic stability diagrams, taking into account the influence of the free surface of liquid cargo, roll and elements of the calculation of the vessel's windage for various cases of vessel loading.

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

the metacentric height must have a positive value, the sunset angle of the static stability diagram must be at least 60°, and taking into account icing - at least 55°, etc. Mandatory compliance with these requirements in all cases of loading gives the right to consider the vessel stable.

Unsinkability of the ship called its ability to maintain buoyancy and stability after flooding of a part interior spaces water coming from overboard.

The unsinkability of the vessel is ensured by the reserve of buoyancy and the preservation of positive stability in partially flooded rooms.

If the ship has a hole in the outer hull, then the amount of water Q flowing through it is characterized by the expression

where S is the area of ​​the hole, m²;

G - 9.81 m/s²

N - distance of the center of the hole from the waterline, m.

Even with a minor hole, the amount of water entering the body will be so large that the sump pumps will not be able to cope with it. Therefore, drainage equipment is installed on the ship based on the calculation of only removing water entering after the hole has been repaired or through leaks in the joints.

To prevent the spread of water flowing into the hole throughout the ship, constructive measures are provided: the hull is divided into separate compartments watertight bulkheads and decks. With this division, in the event of a hole, one or more limited compartments will flood, which will increase the vessel's draft and, accordingly, reduce the freeboard and the vessel's buoyancy reserve.

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Stability is one of the most important seaworthiness of a vessel, which is associated with extremely important issues regarding navigation safety. Loss of stability almost always means the death of the ship and, very often, the crew. Unlike changes in other seaworthiness, the decrease in stability is not visible, and the crew of the ship, as a rule, is unaware of the impending danger until the last seconds before capsizing. Therefore, the greatest attention must be paid to the study of this section of the theory of the ship.

In order for a ship to float in a given equilibrium position relative to the water surface, it must not only satisfy the conditions of equilibrium, but also be able to resist external forces tending to take it out of the equilibrium position, and after the cessation of the action of these forces, return to its original position. 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, brought out of a state of equilibrium by external forces, to return to its original equilibrium position again after the action of these forces ceases.

The stability of the vessel is associated with its balance, which serves as a characteristic of the latter. If the ship's balance 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 Captain Shiryaev
Source: fleetphoto.ru

This chapter will examine the lateral inclinations of the ship in the midship frame plane.

Stability during transverse inclinations, i.e. when a roll occurs, is called transverse. Depending on the angle of inclination of the vessel, lateral 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 tilting of the ship occurs under the influence of a pair of forces; the moment of this pair of forces, causing the vessel to rotate around the longitudinal axis, will be called heeling Mkr.

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

The heeling moment acting on the ship instantly leads to the emergence of angular acceleration and inertial forces. The stability that appears with such an inclination is called dynamic.

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

Let us consider the uniform transverse inclination of the vessel. We will assume that in the initial position the ship has a straight landing. In this case, the supporting force D' acts in the DP and is applied at point C - the center of the vessel’s size (Center of buoyancy-B).

Rice. 1

Let us assume that the vessel, under the influence of a heeling moment, has received a transverse inclination at a small angle θ. Then the center of the magnitude will move from point C to point C 1 and the supporting force, perpendicular to the new existing waterline B 1 L 1, will be directed at an angle θ to the center plane. The action lines 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 supporting force at an infinitesimal equal-volume inclination of a floating vessel is called the transverse metacentre.

We can give another definition to 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 curve of displacement of the center of a quantity in the transverse plane is called the transverse metacentric radius (or small metacentric radius). 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 area of ​​the waterline relative to the longitudinal axis passing through the center of gravity of this area, divided by the volumetric displacement V corresponding to this waterline.

Stability conditions

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

The supporting force D', remaining unchanged, will be directed vertically upward perpendicular to the new effective waterline, and its line of action will intersect the DP at 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 the arm GK, where point K is the base of the perpendicular lowered from point G to the direction of action of the supporting force.

The pair of forces formed by the weight of the vessel and the supporting force, tending to return the vessel to its original equilibrium position, is called a restoring pair, and the moment of this pair is called the restoring moment Mθ.

The issue of stability of a heeled ship is decided by the direction of action of the righting 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. In Fig. Figure 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 occurs if the CG lies below the metacenter.

Rice. 2 Rice. 3

In Fig. Figure 3 shows the opposite case, when the restoring moment is negative (the center of gravity lies above the metacenter). It tends to further deflect the ship from its equilibrium position, 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 vessel tilts is equal to zero, i.e. the force of the weight of the vessel and the supporting force are located on the same vertical, as shown in Fig. 4.

Rice. 4

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

Thus, according to the relative position of the transverse metacenter m and C.T. G can be judged on the sign of the righting moment or, in other words, on the stability of the vessel. 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.

This gives rise to the concept of metacentric height: transverse metacentric height is the elevation of the transverse metacenter above the center of gravity of the vessel in the initial equilibrium position.

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

If the transverse metacenter is located above the center of gravity of the vessel, then the transverse metacentric height is considered positive. Then the condition for the stability of the vessel can be given in the following formulation: the vessel is stable if its transverse metacentric height is positive. This definition is convenient in that it allows one to judge the stability of the vessel without considering its inclination, i.e., at a roll angle of zero, when there is no righting moment at all. To establish what data is necessary 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 a vessel having positive initial lateral stability.

Rice. 5

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 a vessel arise when determining the applicate of the center of gravity ZG, which is determined using a summary table of the vessel's mass load (the issue was discussed 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 metacentre;
• KV - applicate of the center of magnitude;
• KG - applicate of the center of gravity;
• KM - 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.

The static stability arm, denoted in our literature as GK, is denoted in foreign literature as GZ.

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