What is the name of the cargo for the stability of the vessel. Influence of the free surface. Comparing the expressions, we find that the transverse metacentric radius

Stability called the ability of the ship to resist the forces that deviate it from the equilibrium position, and return to its original equilibrium position after the termination of these forces.

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

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

It is customary to distinguish vessel stability at low inclination angles (initial stability) and stability at high inclination angles.

When considering small inclinations, it is possible to make a number of assumptions that make it possible to study the initial stability of the vessel within the framework of the linear theory and obtain simple mathematical dependences of its characteristics. Vessel stability at large angles of inclination is studied using a refined non-linear theory. Naturally, the stability property of the ship is unified and the accepted division is purely methodological.

When studying the stability of a vessel, its inclinations are considered in two mutually perpendicular planes - transverse and longitudinal. When the vessel is tilted in the transverse plane, determined by the angles of heel, it is studied lateral stability; with inclinations in the longitudinal plane, determined by the trim angles, study it longitudinal stability.

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

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

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

In order to prevent a dangerous decrease in the ship's stability, all crew members must:

Always have a clear idea of the ship's stability;

Know the reasons that reduce stability;

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

Let us find the condition under which a ship floating in equilibrium without heel and trim will have initial stability. We assume that the loads do not shift when the ship is tilted and the ship's CG remains at the point corresponding to the initial position.

When the vessel is tilted, the force of gravity P and the buoyancy forces γV form a pair, the moment of which acts on the vessel in a certain way. The nature of this impact depends on the relative position of the CG and the metacenter.

Figure 3.9 - First case of vessel stability

There are three typical cases of the state of the vessel for which the influence of the moment of forces P and γV on it is qualitatively different. Consider them on the example of transverse inclinations.

1st case(Figure 3.9) - the metacenter is located above the CG, i.e. z m > z g . In this case it is possible different arrangement center of magnitude relative to the center of gravity.

1) In the initial position, the center of magnitude (point C 0) is located below the center of gravity (point G) (Figure 3.9, a), but when tilted, the center of magnitude shifts in the direction of inclination so much that the metacenter (point m) is located above the center of gravity ship. The moment of forces P and γV tends to return the ship to its original equilibrium position, and therefore it is stable. A similar arrangement of points m, G and C 0 is found on most ships.

2) In the initial position, the center of magnitude (point C 0) is located above the center of gravity (point G) (Figure 3.9, b). When the ship is tilted, the resulting moment of forces P and γV straightens the ship, and therefore it is stable. In this case, regardless of the size of the displacement of the center of magnitude when tilted, a pair of forces always tends to straighten the ship. This is because the point G lies below the point C 0 . Such a low position of the center of gravity, which provides unconditional stability on ships, is difficult to implement constructively. Such an arrangement of the center of gravity can be found in particular on sailing yachts.

Figure 3.10 - Second and third case of vessel stability

2nd case(Figure 3.10, a) - the metacenter is located below the CG, i.e. z m< z g . В этом случае при наклонении судна момент сил Р и γV стремится еще больше отклонить судно от исходного положения равновесия, которое, следовательно, является неустойчивым. В этом случае наклонения судно имеет отрицательный восстанавливающий момент, т.е. оно не остойчиво.

3rd case(Figure 3.10, b) - the metacenter coincides with the CG, i.e. z m = z g . In this case, when the ship is tilted, the forces P and γV continue to act along the same vertical, their moment is equal to zero - the ship will be in a state of equilibrium in the new position. In mechanics, this is a case of indifferent equilibrium.

From the point of view of the theory of the ship, in accordance with the definition of ship stability, the ship is stable in the 1st case, and not stable in the 2nd and 3rd.

So, the condition for the initial stability of the vessel is the location of the metacenter above the CG. The ship has transverse stability if z m > z g , (3.7)

and longitudinal stability if z m > z g . (3.8)

Hence the physical meaning of the metacenter becomes clear. This point is the limit to which the center of gravity can be raised without depriving the vessel of positive initial stability.

The distance between the metacenter and the ship's CG at Ψ = Θ = 0 is called initial metacentric height or simply metacentric height. The transverse and longitudinal planes of inclination of the vessel correspond respectively to the transverse h and longitudinal H metacentric heights. It's obvious that

h = z m – z g and H = z m – z g , (3.9)

or h = z c + r – z g and H = z c + R – z g , (3.10)

h = r – α and H = R – α, 3.11)

where α = z g – z c is the elevation of the CT above the CV.

As you can see, h and H differ only in metacentric radii, because α is the same quantity.

, so H is much larger than h.

α \u003d (1%) R, therefore, in practice, it is believed that H \u003d R.

Ship unsinkability

unsinkability called the ability of the vessel after the flooding of part of the premises to maintain sufficient buoyancy and stability. Unsinkability, unlike buoyancy and stability, is not an independent seaworthiness of a vessel. Unsinkability can be called a property of a ship maintain their seaworthiness when a part of the watertight volume of the hull is flooded, and the theory of unsinkability can be characterized as the theory of buoyancy and stability of a damaged ship.

A ship with good unsinkability, when one or more compartments are flooded, must, first of all, remain afloat and have sufficient stability to prevent it from capsizing. In addition, the ship should not lose propulsion, which depends on draft, roll and trim. An increase in draft, a significant list and trim increase the resistance of water to the movement of the vessel and impair the efficiency of the propellers and ship mechanisms. The vessel must also maintain controllability, which, with a good steering gear, depends on roll and trim.

Unsinkability is one of the elements of the ship's survivability, since the loss of unsinkability is associated with severe consequences - the death of the ship and people, so its provision is one of the most important tasks for both shipbuilders and the crew. In practice, unsinkability is ensured at all stages of the ship's life: by shipbuilders at the stages of design, construction and repair of the ship; by the crew during the operation of an undamaged ship; crew directly to emergency. From such a division it follows that unsinkability is ensured by three sets of measures:

Structural measures that are carried out during the design, construction and repair of the ship;

Organizational and technical measures that are preventive and are carried out during the operation of the ship;

Measures to combat the unsinkability after the accident, aimed at combating the ingress of water, restoring stability and straightening the damaged ship.

constructive activities. These measures are carried out at the stages of design and construction of the vessel and are reduced to the appointment of such buoyancy and stability margins so that when a given number of compartments are flooded, the change in the landing and stability of the emergency vessel does not go beyond the minimum allowable limits. The most effective means for using the reserve buoyancy in case of damage to the hull is the division of the vessel into compartments by watertight bulkheads and decks. Indeed, if the ship does not have an internal subdivision into compartments, then in the presence of an underwater hole, the hull will fill with water and the ship will not be able to use the buoyancy reserve. The division of ships into compartments is carried out in accordance with Part V of the Rules for the Classification and Construction sea vessels” Maritime Register of Shipping. The waterline of an undamaged ship, used when dividing into compartments, the position of which is recorded in the ship's documentation, is called cargo waterline subdivision. The waterline of a damaged ship after flooding of one or more edema is called emergency waterline. The vessel loses its buoyancy if the damage waterline coincides with limit line of immersion- the line of intersection of the outer surface of the bulkhead deck plating with the outer surface of the side plating at the side. The greatest length of the part of the ship below the margin line is length of division of the vessel into compartments. Under bulkhead deck understand the most upper deck, to which transverse watertight bulkheads are brought along the entire width of the ship.

The amount of water poured into the damaged compartment of the ship is determined using room permeability coefficientμ is the ratio of the volume that can be filled with water when the compartment is flooded to the total theoretical volume of the room. The following permeability coefficients are regulated:

For premises occupied by mechanisms - 0.85;

For premises occupied by goods or stocks - 0.6;

For residential premises and premises occupied by cargoes with high permeability (empty containers, etc.) - 0.95;

For empty and ballast tanks - 0.98.

An important characteristic of the ship's unsinkability is maximum flood length, which is understood as the maximum length of the conditional compartment after flooding of which, with a permeability coefficient equal to 0.80, with the draft of the corresponding cargo waterline of dividing the ship into compartments and in the absence of an initial trim, the emergency waterline will touch the limit line of immersion.

An important constructive measure to ensure unsinkability is the creation of durable and watertight closures (doors, hatches, necks) installed along the contour of the watertight compartment, which should work well when heeling, trimming and sea waves. For all sliding and hinged doors in watertight bulkheads, indicators shall be provided on the navigation bridge to indicate their position. The watertightness and strength of the vessel must be ensured not only in the underwater part, but also in the surface part of the hull, since the latter determines the buoyancy margin consumed in case of damage.

For the active struggle of the crew for unsinkability, the ship also provides for:

Creation of ship systems (heeling, trim, drainage, drainage, pumping liquid cargo, flooding, descent and bypass, ballasting);

Supply of emergency equipment and materials.

Such closures, systems and mechanisms must be appropriately marked to ensure their correct use with maximum efficiency. Places of concentration emergency facilities called emergency posts. These can be special rooms or pantries, boxes and shields on the deck. Devices for remote start-up of ship systems can be brought to such posts.

Organizational and technical measures. Organizational and technical measures to ensure floodability are carried out by the ship's crew during operation in order to prevent water from entering the compartments, as well as to maintain the landing and stability of the ship, preventing it from flooding or capsizing. These activities include:

Proper organization and systematic training of the crew for the struggle for unsinkability;

Maintenance of all technical means of struggle for unsinkability, emergency supply in a condition that guarantees the possibility of their immediate use;

Systematic monitoring of the condition of all hull structures in order to check their wear (corrosion), replacement of individual structural elements during current or medium repairs in case of exceeding the established wear standards;

Planned painting of hull structures;

Elimination of distortions and sagging of watertight doors, hatches and windows, their systematic pacing and maintenance of all battening devices in good condition;

Control of outboard openings, especially when docking a ship;

Strict observance of the instructions for the reception and consumption of liquid fuels;

Fastening cargo in a stowed manner and preventing their movement during pitching (especially across the vessel);

Compensation for stability losses caused by icing of the ship by receiving liquid ballast and taking measures to remove ice (chipping, washing off hot water);

Fight for invincibility. The struggle for unsinkability is understood as a set of actions of the crew aimed at maintaining and possibly restoring the reserves of buoyancy and stability of the vessel, as well as bringing it into a position that provides propulsion and controllability.

The struggle for unsinkability is carried out immediately after the ship receives damage and consists of combating incoming water, assessing its condition and measures to restore stability and straighten the ship.

Fighting incoming water consists in detecting the ingress of water into the ship, taking possible measures to prevent or limit the ingress and further spread of outboard water through the ship, as well as to remove it. At the same time, measures are being taken to restore the impermeability of the sides, bulkheads, platforms, and ensure the tightness of emergency compartments. Small holes, open seams, cracks are sealed with wooden wedges and plugs (chops) (Figure 3.11). On holes bigger size put a hard metal patch or mat pressed down with a shield

Figure 3.11 - Wooden wedges and plugs: Figure 3.12 - Clamping bolts:

a, b, c - wedges; d, e - plugs a - with a folding bracket; b, c - hook.

For their fastening, the emergency equipment kit includes special bolts and clamps, spacer bars and wedges (Figure 3.12 3.15). Sealing the hole in the described ways is a temporary measure. After pumping out the water, the final restoration of the tightness is carried out by concreting the hole - placing a cement box. The success of sealing small holes depends on their location (surface or underwater), on the accessibility of the hole from inside the vessel, on its shape and the location of the edges of the torn metal (inside the hull or out).

Figure 3.13 - Metal patches:

a - valve; b - with clamping bolt; 1 - box-shaped body; 2 - stiffeners; 3 - socket for sliding stop; 4 - branch pipes with plugs for rods of hook bolts; 5 - valve; 6 - eyelets for fastening the tail ends; 7.8 - clamping bolt with a folding bracket; 9 - nut with handles; 10 - pressure disk.

Figure 3.14 - Metal sliding stop:

1.8 - thrust bearings; 2,3 - nuts with handles; 4 - pin; 5 - outer tube; 6 - inner tube; 7 - hinge

In the premises adjacent to the emergency compartment, water can enter as a result of its filtration through various leaks (violation of the tightness of the bulkhead glands of pipelines, cables, etc.). In such cases, the tightness is restored with caulking, wedges or plugs, and the bulkheads themselves are reinforced with emergency bars to prevent them from buckling or destruction.

Figure 3.15 - Emergency clamp: a - with grips for channel-type frames; b - grip for bulb type frames; 1 - clamp; 2 - clamping screw; 3 - clamping screw handles; 4 - nut-slider; 5 - locking screws; 6 - bolts fastening two

channel bars; 7- capture

Figure 3.16 - Soft patches

a - educational; 1 - canvas; 2 - firmware; 3 - lyktros; 4 - corner thimbles; 5 - krengels for the control end; b - stuffed: 1 - two-layer canvas cover; 2 - stuffed mat; 3 - firmware; 4 - angular thimble; c - lightweight: 1 - angular thimble; 2 - lyktros; 3 - pocket for rail; 4 - spacer rail from the pipe; 5.7 - layers of canvas; 6 - felt pad; g - chain mail: 1.2 - double layer of canvas cushion; 3 - patch lyktros; 4 – grid ring; 5 - canvas washer; 6 - mesh lyktros

Soft plasters (figure 3.16) are the main means for temporary sealing of holes, as they can fit snugly along the contours of the ship's hull in any place.

Literature:: p.36-47; : p.37-53, 112-119: : p.42-52; : With. 288-290.

Questions for self-control:

1. What are the main dimensions of the vessel?

2. Define the seaworthiness of a vessel?

3. Vessel's buoyancy?

4. Give a definition of all the volumetric operational characteristics of the vessel?

5. Draw a load line and decipher the letters at the comb?

6. What is called the unsinkability of the ship?

7. What organizational and technical measures ensure unsinkability?

8. What is called the stability of the vessel?

9. Give the definition of metacentric height?

Steering gear

Rudder designs

A modern ship's rudder is a vertical wing with internal reinforcing ribs, rotating around a vertical axis, the area of \u200b\u200bfor sea vessels is 1/10 - 1/60 of the area of \u200b\u200bthe submerged part of the DP (the product of the length of the vessel and its draft: LT).

The shape of the rudder is significantly influenced by the shape of the aft end of the vessel and the location of the propeller.

According to the shape of the feather profile, the rudders are divided into flat and profile streamlined. The profile rudder consists of two convex outer shells with ribs and vertical diaphragms on the inside, welded to each other and forming a frame to increase rigidity, which is covered on both sides with steel sheets welded to it.

Profile rudders have a number of advantages over lamellar ones:

Higher value of the normal force of pressure on the steering wheel;

Less torque required to turn the steering wheel.

In addition, the streamlined rudder improves the propulsion qualities of the vessel. Therefore, he found the greatest use.

The inner cavity of the rudder blade is filled with a porous material that prevents water from entering inside. The rudder blade is attached to the ruderpiece along with the ribs (Figure 4.1). Ruderpieces are cast (or forged) along with hinges for hanging the rudder on the ruder post (casting is sometimes replaced by a welded structure), which is an integral part of the sternpost.

The size of the rudder blade area depends on the type of vessel and its purpose. For an approximate assessment of the required rudder area, the S / LT ratio is usually used, which is 1.8-2.7 for sea transport ships with one rudder, and 1.8-2.2 for tankers;

for tugboats - 3-6; for ships coastal navigation - 2,3-3,3.

By connection method with body and number of supports pen passive rudders are divided into:

Simple (multi-support) (Figure 4.2, a, 6);

Semi-suspended (single-support - suspended on a stock and supported on the body at one point) (Figure 4.2, c);

Suspended (unsupported, suspended on a stock) (Figure 4.2, d).

By axis position baller relative to the pen are distinguished:

The rudders are unbalanced (ordinary), in which the axis of the stock passes near the leading edge of the pen;

Balancing, the axis of the baller in which is located at some distance from the leading edge of the rudder. Semi-suspended balancing rudders are also called semi-balancing.

Unbalanced rudders are installed on single-rotor ships, semi-balanced and balanced - on all ships. The use of outboard (balanced) rudders makes it possible to reduce the power of the steering machine by reducing the torque required to shift the rudder.

Figure 4.1 - Steering device with a semi-suspended balanced streamlined steering wheel: 1 - rudder blade; 2 - ruderpis; 3 - lower thrust bearing of the baller; 4 - helmport pipe; 5 - upper support-thrust bearing of stock; 6 - steering machine; 7 - spare roller steering gear; 8 - stock; 9 - lower pin of the rudder blade; 10 - ruderpost

Rudder stock- this is a massive shaft with which the rudder blade is rotated. The lower end of the stock usually has a curvilinear shape and ends with a paw - a flange that serves to connect the stock with the rudder blade with bolts, which makes it easier to remove the rudder during repairs. Sometimes instead of a flange (or a cone connection is used. The attachment of the rudder blade to the stock and the hull on many types of ships has much in common and differs slightly.

The rudder stock enters the aft clearance of the hull through a helm port tube, which ensures the impermeability of the hull, and has at least two supports (bearings) in height. The lower support is located above the helm port pipe and, as a rule, has a stuffing box seal that prevents water from entering the ship's hull; the upper support is placed directly at the place where the sector or tiller is fixed. Usually, the upper support (thrust bearing) takes the mass of the stock and rudder blade, for which an annular protrusion is made on the stock.

In addition to rudders, thrusters are used on ships. By means of a propeller installed in the transverse channel of the ship's hull, they create a traction force in the direction perpendicular to its DP, provide controllability when the ship is not moving or when it is moving at extremely low speeds, when conventional steering devices are ineffective. Fixed or variable pitch propellers, vane propellers or pumps are used as propellers. Thrusters are located at the bow or stern ends, and on some ships two such devices are installed at both the bow and stern ends. In this case, it is possible not only to turn the vessel on the spot, but also to move it sideways without using the main propellers. To improve handling, there are also rotary nozzles fixed on the stock and special balancing rudders.

Control post

Part control schemes steering gear includes:

Control post with servo electrical system;

Electrical transmission from the control station to the electric motor.

For remote control of electro-hydraulic steering machines on ships, the Aist control system is widely used. Together with a gyrocompass and a steering machine, it provides four types of control: "Automatic", "Tracking", "Simple", "Manual".

Types of control "Automatic", "Tracking" are the main ones. In the event of a malfunction of these types of control of the steering machine, they are transferred to "Simple". In case of failure in the operation of the remote electrical transmission system, they switch to the “Manual” view.

Components systems "Aist" are the control panel (PU) - the autopilot "Aist", the actuator (IM-1) and the steering sensor (RD).

The main control post is located in the wheelhouse near the steering compass and gyrocompass repeater. The steering wheel or steering control panel is usually mounted on the same column with the autopilot unit. The main element of the electrical transmission is a system of controllers placed in the steering column and connected by electrical wiring to the main drive motor in the tiller compartment.

steering machines

Steering machines. Currently, two types of steering machines are widely used - electric and hydraulic. The operation of the steering machines is controlled remotely from the wheelhouse, using a cable, roller, electric or hydraulic transmission. On modern ships, the last two are most common.

Steering gears

On ships navy various steering gears are used, among which steering gears with electrical and hydraulic drives of domestic and foreign production. They provide the transmission of the forces of the steering motor to the stock.

Among them, two main types of drives are widely known.

Mechanical sector-tiller drive from an electric motor (Figure 4.3) is used on ships of small and medium displacement.

In this drive, the tiller is rigidly fastened to the rudder stock. The sector, freely mounted on the stock, is connected to the tiller with the help of a spring shock absorber, and with the steering motor - by a gear.

The rudder is shifted by an electric motor through the sector and tiller, and dynamic loads from wave shocks are damped by shock absorbers.

Figure 4.3 - Steering device with a mechanical sector tiller drive

from electric motor:

1 - manual (emergency) wheel drive; 2 - tiller; 3 - reducer; 4 - steering sector; 5- electric motor; 6 - spring, 7 - rudder stock; 8-profile figured steering wheel; 9 - segment of the worm wheel and brake; 10 - worm.

The control scheme of the sector-steering machine with electric transmission is shown on

figure 4.4

Figure 4.5 - Hydraulic steering control scheme

two-plunger steering machine:

1 - steering wheel position sensor; 2 - cable network; 3 - drive electric motor of the oil pump; 4 - oil pump; 5 - steering column; 6 - rudder position repeater; 7- telemotor receiver; 8- hydraulic cylinders of the steering machine; 9- rudder stock; 10 - oil pipeline; 11 - adjusting rod feedback tracking system; 12 - telemotor sensor; 13 - oil pipeline.

Power plunger drive from hydraulic cylinders is used on modern ships (Figure 4.5). It consists of two hydraulic cylinders, an oil pump, a telemotor and a hydraulic system.

The operation of the device is as follows. When the steering wheel located in the wheelhouse is rotated, the teledynamic sensor of the control station generates a command signal in the form of oil pressure, which is pumped into the telemotor cylinder by the hydraulic system. Under the action of this signal, the telemotor drives

lever feedback system, which opens the access of power oil to one of the hydraulic cylinders. At the same time, oil under pump pressure is transferred from one cylinder to another, moving the piston and turning the tiller, stock and rudder in the right direction. After that, the adjusting rod returns to the zero position, and the sensor and repeater fix the new position of the steering wheel.

So that the oil pressure in the hydraulic cylinders does not increase when a strong wave or a large ice floe strikes the rudder, the hydraulic system is equipped with safety valves and shock-absorbing springs.

In the event of a failure of the telemotor, the steering machine can be controlled manually from the tiller compartment.

When both oil pumps fail, they switch to manual rudder shifting, for which the hydraulic system pipes are directly connected to the hydraulic cylinders, creating pressure in them by rotating the steering wheel in the control station.

The layout of the units of a two-plunger steering machine with a similar principle of operation is shown in Figure 4.6. These machines are most widely used on modern ships, as they provide the highest efficiency of the entire steering gear. In them, the pressure of the working oil in the hydraulic cylinders is directly converted first into the translational movement of the plunger, and then through a mechanical transmission into the rotational movement of the rudder stock, which is rigidly connected to the tiller. The required oil pressure and power of the steering gear are generated by radial piston pumps of variable capacity, and it is distributed over the cylinders by a telemotor, which receives a command from the steering wheel from the wheelhouse.

The utilization factor of the vessel's net carrying capacity (formula, its explanation and limits for changing this indicator).

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 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 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 a ship is related to its balance, which is 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

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 ship instantly leads to the appearance of angular acceleration and inertial forces. Stability, which 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 arrangement of 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. 4.

Rice. 4

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 a vessel having a positive initial transverse 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 ;

h = Z m – Z G .

The transverse metacentric height is often determined using the last equation. 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;
C – 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 is the 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.

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:

full pressing of tanks to avoid free surfaces
if this is not possible, filling under the neck, or vice versa, only at the bottom. In this case, any inclination sharply reduces the free surface area.
control of the number of tanks with free surfaces
breakdown of tanks by internal impenetrable bulkheads in order to reduce the moment of inertia of the free surface i x
When a heeling moment is applied to the ship m cr, constant in magnitude, it receives a positive acceleration with which it begins to roll. As the inclination increases, the restoring moment increases, but at the beginning, up to the angle θ st, at which m cr = m θ, it will be less heeling. Upon reaching the angle of static equilibrium θ st, the kinetic energy of rotational motion will be maximum. Therefore, the ship will not remain in the equilibrium position, but due to the kinetic energy it will roll further, but slower, since the restoring moment is greater than the heeling one. The previously accumulated kinetic energy is repaid by the excess work of the restoring moment. As soon as the magnitude of this work is sufficient to completely extinguish the kinetic energy, the angular velocity will become equal to zero and the ship will stop heeling.

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

Referring to the static stability diagram, work is expressed as the area under the restoring moment curve m in. Accordingly, the dynamic bank angle θ dyn can be determined from the equality of areas OAB And BCD corresponding to the excess work of the restoring moment. Analytically, the same work is calculated as:
,
on the interval from 0 to θ dyn.

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

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

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

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

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

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

Vessel inclinations can occur from the action of oncoming 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.

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 θ and ψ

The stability that a ship has with longitudinal inclinations is called longitudinal. It is, as a rule, quite large, and the danger of capsizing the vessel through the bow or stern never arises.

The stability of the vessel with transverse inclinations is called transverse. It is the most important characteristic of the ship, which determines its seaworthiness.

There are initial transverse stability at small angles of heel (up to 10 - 15 °) and stability at large inclinations, since the restoring moment at small and large angles of heel is determined in various ways.

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

It can be seen from the formula that the value of the restoring moment is the greater, the greater h. Therefore, the metacentric height can serve as a measure of stability for a given vessel.

The value h of a given ship at a certain draft depends on the position of the center of gravity of the ship. If the weights are arranged so that the ship's center of gravity takes more than high position, then the metacentric height will decrease, and with it the static stability arm and the restoring moment, i.e. the ship’s stability will decrease. With a decrease in the position of the center of gravity, the metacentric height will increase, the stability of the vessel will increase.

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

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

On a built ship, the initial metacentric height is determined empirically - by heeling, i.e., the transverse inclination of the ship by moving a load of a certain weight, called roll-ballast.

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

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

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

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

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

The value of the angle of heel under the dynamic action of the heeling moment can be determined from the static stability diagram. The horizontal line of the heeling moment is continued to the right until the area ODSE (work of the heeling moment) becomes equal to the area of the figure OBE (work of the restoring moment). At the same time, the OACE area is common, so we can restrict ourselves to comparing the areas of ODA and ABC.

If the area bounded by the restoring moment curve is insufficient, the ship will capsize.

The stability of sea-going vessels shall comply with the Register requirements, according to which it is necessary to fulfill the following condition (the so-called weather criterion): К=Mopmin / Мднmax ≥ 1» the vessel will not yet lose stability; Mdnmax - dynamically applied heeling moment from wind pressure at the worst loading option in terms of stability.

In accordance with the requirements of the Register, the maximum arm of the static stability diagram lmax shall be not less than 0.25 m for ships of 85 m in length and not less than 0.20 m for ships over 105 m at a heel angle θ of more than 30°. The slope angle of the diagram (the angle at which the curve of the stability arms intersects the horizontal axis) for all vessels must be at least 60°.

Influence of liquid cargoes on stability. If the tank is not filled to the top, that is, it has a free liquid surface, then when tilted, the liquid will overflow in the direction of the roll and the center of gravity of the vessel will shift to the same side. This will lead to a decrease in the stability arm and, consequently, to a decrease in the restoring moment. At the same time, the wider the tank, in which there is a free surface of the liquid, the more significant will be the decrease in lateral stability. To reduce the influence of the free surface, it is advisable to reduce the width of the tanks and strive to ensure that during operation there is a minimum number of tanks with a free surface of the liquid.

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

To prevent spillage of grain in the holds, suspended longitudinal semi-bulkheads are installed - shifting boards or sacks of grain are placed on top of the grain poured in the hold (cargo bagging).

Effect of a suspended load on stability. If the cargo is in the hold, then when it is lifted, for example, by a crane, there is, as it were, an instantaneous transfer of the cargo to the suspension point. As a result, the ship's CG will shift vertically upward, which will lead to a decrease in the righting moment arm when the ship receives a roll, i.e., to a decrease in stability. In this case, the decrease in stability will be the greater, the greater the mass of the load and the height of its suspension.

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

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

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

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

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

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

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

h = z c + r - z g,

Where z c- elevation of the CV over the OL; r- transverse metacentric radius, i.e., the elevation of the metacenter above the CV; z g- elevation of the ship's CG above the OL.

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

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

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

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

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

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

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

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

Rice. 150. Scheme of inclining experience.

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

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

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

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

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

The following are approximate transverse metacentric heights for different types of fully loaded ships:

Large passenger ships …………………………… 0,3-1,5

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

Large dry cargo ships …………………………….. 0,7-1,0

Medium ………………………………………………….. 0.5-0.8

Large tankers ………………………………… 2.0-4.0

Medium …………………………………………………... 0.7-1.6

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

Barges ……………………………………………………… 2.0-10.0

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

Tugs …………………………………………………… 0.5-0.8

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

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

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

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

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

Rice. 152. Diagram of static stability

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

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

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

Characteristics of wind and sea waves

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

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

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

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

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

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

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

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

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

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

in a squall (sail area is shaded)

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

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

The free surface of liquid cargoes always remains horizontal.

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

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

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

for stability

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

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

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