When a submarine floats, the equality between its weight and the supporting force (buoyancy) is gradually violated. The weight of the bow and stern relative to each other also changes, which leads to the appearance of trim.

The supporting force is equal to the product of the density of water and the submerged waterproof volume of the submarine's pressure hull. Density sea water depends on salinity, temperature and pressure. The volume of the pressure hull also changes and depends on the depth of immersion and the temperature of the sea water, the weight of the submarine depends on the consumption of variable cargo: fuel, oil, ammunition, fresh water, provisions, etc. Most of these cargoes are replaced sea water, including fuel.

The difference in the densities of fuel and water leads to an imbalance. As a result, the equality between the weight of the submarine and the supporting force is violated, which leads to the emergence of so-called residual buoyancy. If the supporting force is greater than the weight of the submarine, then the residual buoyancy will be positive; if less, it will be negative. With positive residual buoyancy, the submarine tends to float, with negative residual buoyancy, it tends to sink.

Uneven consumption of variable loads in the bow and stern parts of the boat leads to the formation of trims.

Bringing residual buoyancy and trim to specified values by receiving (removing) water from overboard into the surge tank and moving water between trim tanks is called trimming.

The above and other reasons make it necessary to periodically trim the submarine.

Trimming can be done without moving or while moving.

Trim without travel

Trimming without stroke is performed:

When the submarine has not dived for a long time;

In areas where it is difficult to maneuver underwater;

At the sign;

For educational purposes.

When the sea state is no more than 3-4 points, trim without running is usually performed at periscope depth, and when the sea state is over 4 points - at safe depths.

The advantage of trim without running is that this method allows you to trim a submarine in an area with shallow depths. Disadvantages include: the need for trim when setting off and ensuring external security in areas that are difficult to maneuver.

It is advisable to trim at periscope depth with a obviously lightweight submarine, for which, before immersing in the surge tank, it is necessary to take in water that is 5-10 tf less than the calculated value (depending on the design of the submarine). The main ballast is received first in the end groups, then in the middle. If, after filling the end groups of the main ballast tanks, the submarine has a trim of more than 0.5°, the trim moment should be extinguished by distilling water from one trim tank to another. After filling the middle group of main ballast tanks, trim begins.

Positive buoyancy, depending on the value, is extinguished by the intake of water from overboard into the equalization tank through the kingston or precise filling valve. To remove air bubbles from the end groups of the main ballast tanks and from the superstructure, the submarine must be “rocked,” that is, the trim must be moved from one end to the other, distilling water between the trim tanks, and then the ventilation valves of these tanks must be closed. With the removal of air bubbles from the tanks of the end groups, the tanks of the middle group are ventilated in the same way. It is recommended to stop distilling water from one trim tank to another when the trim does not reach the specified value by 1.5-2°.

In a submerged position, the nature of the residual buoyancy is judged by the readings of depth gauges. If a submarine sinks, it has negative residual buoyancy. To bring the boat to zero buoyancy, water from the surge tank is pumped overboard. If a submarine floats, it has positive residual buoyancy. To bring it to zero buoyancy, water is taken into the surge tank from overboard. Trimming without progress is considered completed if the submarine maintains a constant depth with a given trim for some time. At the end of the trim, the actual amount of water in the auxiliary ballast tanks is measured and recorded, as well as the personnel available in each compartment and conning tower are checked and recorded.

Trim on the move

Performed in areas that allow the submarine to maneuver freely underwater. In calm sea conditions, trimming can be done at periscope depth, and in rough conditions - at safe depth.

To understand the essence of trim and control of a submarine in an underwater position, you need to know the principle of operation of horizontal rudders and the forces acting on the submarine.

When repositioning the horizontal rudders while moving (Fig. 3.1), hydrodynamic forces of the stern Rк and bow Rн horizontal rudders arise.

Rice. 3.1. Forces arising when shifting horizontal rudders

These forces are proportional to the square of the submarine's speed and the rudder angles. The forces Rк and Rн can be replaced by their components parallel to the GX and GY axes. The forces Rxk and Rxh increase the resistance of water to the movement of the submarine. The forces Ruk and Ryn change the trim and direction of the submarine in the vertical plane.

According to the well-known theorem of theoretical mechanics, the forces RyK and RyH can be represented as applied at the center of gravity of the submarine with the simultaneous action of hydrodynamic moments of the horizontal rudders Mk and Mn. Shifting the stern horizontal rudders to dive gives a moment - Mk, which trims the submarine to the bow, and a lifting force +Ruk. shifting the bow horizontal rudders to ascent gives a moment +Mn, which trims the submarine aft, and a lifting force +Ryn

Shifting the stern horizontal rudders for ascent gives a trimming moment at the stern +Mk and a sinking force _RyK, and shifting the bow horizontal rudders for a dive gives a trimming moment at the stern - Mn and a sinking force -Rk.

Rice. 3.2. Forces acting on a submarine while moving underwater

The joint use of horizontal rudders creates a trim moment and force applied to the center of gravity of the submarine, which are the resultant trim moments and forces created separately by the stern and bow horizontal rudders.

A submarine having a steady speed Vpl in a submerged position is subject to static and dynamic forces (Fig. 3.2). Static forces include the weight force, the supporting force and their moments, which act on the submarine constantly. These forces are usually replaced by the resultant - residual buoyancy Q and its moment Mq. With longitudinal inclinations (trim φ), a restoring moment Mψ occurs, which tends to return the submarine to its original position.

Dynamic forces and moments include thrust force, thrust moment of propellers and hydrodynamic forces and moments. The thrust force of the propellers Tt is proportional to the speed of rotation of the propeller. During steady motion, the thrust force of the propeller is balanced by the drag. The thrust moment of the propellers Mt arises due to the fact that the axes of the shaft line on a submarine usually do not coincide in height with the center of gravity and are located below it. Therefore, the moment of thrust force of the propellers trims the submarine to the stern.

Hydrodynamic forces arise when a submarine moves. For practical trimming, it can be assumed that at a constant depth the resultant of the hydrodynamic forces Rm acting on the hull is proportional to the speed and trim angle. Point K, applied to the resultant Rm, is called the center of pressure. The center of pressure does not coincide with the submarine's center of gravity and is usually located forward of it.

Based on the theorem of theoretical mechanics mentioned above, the effect on the submarine of the resultant hydrodynamic forces can be represented as a force Rm applied to the center of gravity G of the submarine and a moment MR. The force Rm can be broken down into its components. The component Rmх (drag) characterizes the resistance of water to the movement of a submarine. The Rm component plays an important role in the controllability of a submarine in the vertical plane. At a constant diving depth with a trim near zero or at the stern, the lifting force Rmu, and the moment MR trims the submarine to the stern; with a trim to the bow, the force Rtu is sinking, and the moment MR trims the submarine to the bow.

The basis for trim while moving is the movement of the submarine at a constant depth and on a straight course, as this makes it possible to determine the direction of forces and moments. Determining the direction of forces and moments in practice is facilitated by knowledge of the following characteristic positions of an undifferentiated submarine sailing at a constant depth, depending on the angles of the horizontal rudders and trim:

Trim 0° - the stern horizontal rudders are shifted to float;

Trim 0° - the stern horizontal rudders are shifted to submersion;

The trim is on the bow - the stern horizontal rudders are shifted to submersion;

The trim is on the bow - the stern horizontal rudders are shifted to float;

Trim to the stern - the stern horizontal rudders are shifted to float;

Trim to the stern - the stern horizontal rudders are shifted to submersion.

Examples of trim on the move

Example 1. The submarine on a direct course moves at low speed, maintains a constant depth with a trim of 0°.

Rice. 3.3. The submarine has a heavy bow

The stern horizontal rudders are shifted to float 12°, the bow rudders are at zero. It is possible to differentiate the submarine (Fig. 6.6).

The stern horizontal rudders create a trimming moment at the stern +MK and a sinking force - RyK. The +MK moment strives to create a trim to the stern, but the submarine has zero trim. It follows from this that there is some moment that counteracts the +MK moment to create trim aft. Such a moment can arise due to the fact that the bow of the submarine is heavier than the stern or, which is the same thing, the stern is light, i.e. the submarine has an excess trimming moment on the bow - Mid. To trim a submarine by moment, you should move water from the bow trim tank to the stern tank and at the same time move the stern horizontal rudders to zero.

It is impossible to determine in practice the nature of the residual buoyancy in this case, since the direction of the force Q, the resultant of the forces of weight and buoyancy, is unknown. Since the submarine maintains a given depth, the residual buoyancy can be:

Zero when the forces Rmy and Ryк are equal in magnitude;

Negative if Rmу > Rvк;

Positive if Rmu
Residual buoyancy in this case can only be revealed later in the process of differentiating the submarine according to new instrument readings.

Example 2. The submarine on a direct course moves at low speed, maintains a constant depth with a trim of 5° on the bow. The stern horizontal rudders are shifted to float 12° to the bow, the bow rudders are in the plane of the frame (at zero). It is necessary to trim the submarine (Fig. 3.4).

The stern horizontal rudders create a trimming moment at the stern +MK and a sinking force - RyK. The trim to the bow creates a sinking force - Rm, and a moment -MR, which trims the submarine to the bow. The submarine maintains a constant depth, but under the influence of sinking forces it must sink, therefore, there is a force that prevents it from sinking. In this case, such a force can only be residual positive buoyancy, i.e. the submarine is light. The +MK moment, as in example 1, is prevented from creating a trim at the stern by the excess trim moment at the bow - Mid, i.e. the submarine has a heavy bow.

With this characteristic position of an undifferentiated submarine, it is necessary to first move water from the bow to the stern, while moving the stern horizontal rudders to submerge to keep the submarine at a constant depth, and then take water from overboard into the surge tank for trimming by buoyancy.

Rice. 3.4. The submarine is light, the bow is heavy

An attempt to trim the submarine first by buoyancy and then level the trim may lead to the fact that it will not be possible to maintain it at a given depth. In fact, with the start of receiving water from overboard, the submarine will begin to sink due to an increase in its weight. To maintain a given depth, you will have to reduce the trim on the bow, i.e., reduce the sinking force -Rm, for which it is necessary to shift the horizontal rudders to ascent. But, since the horizontal rudders are shifted only to a limited angle and already have 12° for ascent, shifting them to the full angle for ascent (up to the limiter) may not reduce the trim on the nose to the required value. Consequently, the submarine will submerge.

In the same way, forces and moments are analyzed and trim is performed on the move in other characteristic positions of an untrimmed submarine.

In practice, trim on the move is performed as follows. After the personnel occupy the places according to the diving schedule, the conning hatch is battened down, the electric motors are given a low speed and the main ballast is received, after which the command is given: “Trim the submarine at a depth of so many meters, at such a speed, with a trim of so many meters.” degrees bow (aft).” The main ballast is received, as during trimming, without stroke. The ventilation of the middle group of main ballast tanks is closed at a depth of 5-7 m. The specified trim depth is maintained by the stroke and trim. When going to depth, significant trim should not be created. The ventilation of the end tanks of the main ballast is closed immediately upon the arrival of the submarine at a given depth (after transferring the trim from bow to stern).

If, after filling the middle group of main ballast tanks, the submarine receives negative buoyancy, you should create a trim to the stern with horizontal rudders and stroke and, holding the boat at a given depth, simultaneously pump out water from the surge tank.

If this turns out to be insufficient, give a bubble to the middle group of tanks or blow it out, pump out the required amount of water from the surge tank and, having removed the bubble from the middle group of tanks, continue trimming. These measures are taken depending on the speed of the submarine's descent.

If the submarine does not submerge, water should be taken into the surge tank through the seacock or precision filling valve. As soon as the depth gauge shows a change in depth, water intake is suspended.

To remove air bubbles from the end tanks of the main ballast and from the superstructure, it is necessary to alternately trim the submarine to the bow and stern (“rock” the submarine), and then close the ventilation valves of the end groups of the main ballast tanks.

In order to correctly and quickly differentiate the submarine by the position of the horizontal rudders and trim, the residual buoyancy and excess trim moment are determined, after which they begin trimming.

If the trimming officer does not have sufficient experience, the following rules must be followed:

1. If the submarine maintains a given depth and its trimming moment from the horizontal rudders coincides with the trim, you should first trim it by buoyancy, and then by trim.

2. If the submarine maintains a given depth, but the trim does not coincide with the trimming moment of the horizontal rudders, you should first trim it by trim, and then by buoyancy.

By draining or receiving water into the equalization tank and pumping auxiliary ballast between the trim tanks, a position is achieved so that the bow horizontal rudders are at zero, and the stern ones are with a slight deviation from the plane of the frame. In this case, the submarine with a slight trim to the bow should maintain depth. In this position it is considered differentiated.

At the end of the trim, the ventilation valves of the main ballast tanks are opened and closed (“slammed”) to bleed the remaining air cushion. Having made sure that at a given speed the submarine maintains a constant depth on a straight course with zero or a given trim, the shift of the stern horizontal rudders does not exceed ±5°, and the bow rudders lie at zero, the command “Trim is complete” is given. The compartment commanders report to the central post about the presence of personnel in the compartments and the amount of water in the auxiliary ballast tanks. This data is recorded in the log and trim logs.

Vessel trim (from Latin differens, genitive case differentis - difference)

tilt of the ship in the longitudinal plane. D. s. characterizes the landing of the vessel and is measured by the difference between its draft (deepening) stern and bow. If the difference is zero, the ship is said to be “sitting on an even keel”; if the difference is positive, the ship is trimmed to the stern; if it is negative, the ship is trimmed to the bow. D. s. affects the maneuverability of the vessel, operating conditions of the propeller, maneuverability in ice, etc. D.s. There are static and running, which occurs at high speeds. D. s. usually regulated by the intake or removal of water ballast.

Big Soviet encyclopedia. - M.: Soviet Encyclopedia. 1969-1978 .

See what “ship trim” is in other dictionaries:

TRIM of the vessel- Origin: from lat. differens, differentis the difference in the inclination of the vessel in the longitudinal plane (around the transverse axis passing through the center of gravity of the waterline area) ... Marine encyclopedic reference book

- (Trim difference) the angle of longitudinal inclination of the vessel, causing a difference in drafts of the bow and stern. If the depth of the bow and stern is the same, then the ship sits on an even keel. If the recess of the stern (bow) is larger than the bow (stern), then the ship has... ... Marine dictionary

- (Latin, from differe to distinguish). The difference in the depth of immersion in water between the stern and bow of a ship. Dictionary of foreign words included in the Russian language. Chudinov A.N., 1910. DIFFERENT lat., from differre, to distinguish. Difference in stern immersion in water... ... Dictionary of foreign words of the Russian language

- (ship) the inclination of the ship in the longitudinal vertical plane relative to the surface of the sea. It is measured by trim meters in degrees for a submarine or the difference between the recesses of the stern and bow for surface ships. Affects agility... ...Nautical Dictionary

- (from Latin differens difference) the difference in the draft (deepening) of the vessel bow and stern... Big Encyclopedic Dictionary

Marine term, the angle of deviation of the ship's hull from the horizontal position in the longitudinal direction, the difference in the draft of the stern and bow of the ship. In aviation, to denote the same angle that defines the orientation aircraft, the term is used ... ... Wikipedia

A; m. [lat. differens] 1. Special. The difference in the draft of the bow and stern of the ship. 2. Finance. The difference in the price of a product when ordering and receiving it during trading operations. * * * trim (from the Latin differens difference), the difference in the draft (deepening) of the vessel... ... encyclopedic Dictionary

Trim- DIFFERENT, the difference in the depth (landing) of the vessel bow and stern; if, for example, the stern is deepened by 1 ft. more than the bow, then they say: the ship has a depth of 1 ft at the stern. D. had a special meaning in the sail. fleet, where a good sailing ship d.b. have D. on… … Military encyclopedia

- [from lat. differens (differentia) difference] of the vessel, the inclination of the vessel in the longitudinal plane. D. determines the landing of the ship and is measured by the difference between the drafts of the stern and bow. If the difference is zero, the ship is said to be sitting on an even keel; if the difference... Big Encyclopedic Polytechnic Dictionary

Trim of the ship (vessel)- the tilt of the ship (vessel) in the longitudinal plane. It is measured using a trim meter as the difference between the draft of the ship and the stern in meters (for submarines in degrees). Occurs when rooms or compartments at the ends of a ship are flooded, unevenly... ... Glossary of military terms

Stability, which manifests itself during longitudinal inclinations of the ship, i.e., during trim, is called longitudinal.

Rice. 1

Despite the fact that the trim angles of the vessel rarely reach 10 degrees, and are usually 2 - 3 degrees, longitudinal inclination leads to significant linear trims with a large length of the vessel. Thus, for a ship with a length of 150 m, an inclination angle of 1 0 corresponds to a linear trim equal to 2.67 m. In this regard, in the practice of operating ships, issues related to trim are more important than issues of longitudinal stability, since transport ships with normal ratios longitudinal stability is always positive.

When the ship is longitudinally inclined at an angle Ψ around the transverse axis of the Ts.V. will move from point C to point C1 and the supporting force, the direction of which is normal to the existing waterline, will act at an angle Ψ to the original direction. The lines of action of the original and new direction of the supporting forces intersect at a point. The point of intersection of the line of action of the supporting forces at an infinitesimal inclination in the longitudinal plane is called the longitudinal metacenter M.

Radius of curvature of the displacement curve C.V. in the longitudinal plane is called the longitudinal metacentric radius R, which is determined by the distance from the longitudinal metacenter to the CV.

The formula for calculating the longitudinal metacentric radius R is similar to the transverse metacentric radius: R = I F /V, where I F is the moment of inertia of the waterline area relative to the transverse axis passing through its center of gravity. (point F); V is the volumetric displacement of the vessel.

The longitudinal moment of inertia of the waterline area IF is significantly greater than the transverse moment of inertia I X . Therefore, the longitudinal metacentric radius R is always significantly larger than the transverse radius r. It is roughly assumed that the longitudinal metacentric radius R is approximately equal to the length of the vessel.

The basic principle of stability is that the righting moment is the moment of the pair formed by the force of the weight of the vessel and the supporting force. As can be seen from the figure, as a result of the application of an external moment acting in the DP, called the trimming moment Mdif, the ship received an inclination at a small trim angle Ψ. Simultaneously with the appearance of the trim angle, a restoring moment MΨ arises, acting in the direction opposite to the action of the trim moment.

The longitudinal inclination of the ship will continue until the algebraic sum of both moments becomes equal to zero. Since both moments act in opposite directions, the equilibrium condition can be written as an equality:

M d and f = M Ψ

The restoring moment in this case will be:

M Ψ = D ‘ G K 1 (1)

where GK1 is the arm of this moment, called the longitudinal stability arm.

From the right triangle G M K1 we obtain:

G K 1 = M G sin Ψ = H sin Ψ (2)

The value MG = H included in the last expression determines the elevation of the longitudinal metacenter above the central temperature. of the vessel and is called the longitudinal metacentric height. Substituting expression (2) into formula (1), we obtain:

M Ψ = D ‘ H sin Ψ (3)

Where the product D'H is the longitudinal stability coefficient. Keeping in mind that the longitudinal metacentric height H = R - a, formula (3) can be written as:

M Ψ = D ‘ (R - a) sin Ψ (4)

where a is the elevation of the central temperature. ship over its Ts.V.

Formulas (3), (4) are metacentric formulas for longitudinal stability. Due to the smallness of the trim angle in the indicated formulas, instead of sinΨ, you can substitute the angle Ψ (in radians) and then:

M Ψ = D ' · H · Ψ and l and M Ψ = D ' · (R - a) · Ψ .

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

Vessel trim and trim angle

In the practice of calculating the inclination of a vessel in the longitudinal plane, associated with determining the trim, instead of the angular trim, it is customary to use a linear trim, the value of which is defined as the difference between the draft of the vessel bow and stern, i.e. d = T H - T K .

Rice. 2

The trim is considered positive if the vessel's draft at the bow is greater than at the stern; trim to the stern is considered negative. In most cases, ships sail with trim to the stern. Suppose that a ship floating on an even keel along the waterline of the overhead line, under the influence of a certain moment, received a trim and its new effective waterline took the position B 1 L 1. From the formula for the restoring moment we have:

Ψ = M Ψ D ‘ H

Let's draw a dotted line AB, parallel to VL, through the point of intersection of the stern perpendicular with B 1 L 1. Trim d is determined by leg BE of triangle ABE. From here:

t g Ψ = Ψ = d / L

Comparing the last two expressions, we get:

d L = M Ψ D ‘ · H , from here M Ψ = d L · D ‘ · H

Changing the trim during longitudinal movement of the load

Let us consider methods for determining the draft of a vessel under the influence of a trim moment resulting from the movement of cargo in the longitudinal-horizontal direction.

Rice. 3

Let us assume that a load of weight P is moved along the ship to a distance ιx. The movement of the load, as already indicated, can be replaced by the application of a couple of forces to the vessel. In our case, this moment will be differentiating and equal: M diff = P · l X · cosΨ. The equilibrium equation for the longitudinal movement of a load (equality of the trimming and restoring moments) has the form:

Р l x cos Ψ = D ‘ H sin Ψ

where:

t g ψ = P I X D ‘ H

Since small inclinations of the vessel occur around an axis passing through the C.T. waterline area (t.F), the following expressions can be obtained for changes in draft bow and stern:

∆ T H = (L 2 - X F) t g ψ = P I X D ‘ H (L 2 - X F)

∆ T H = (L 2 + X F) t g ψ = — P I X D ‘ H (L 2 + X F)

Consequently, the drafts bow and stern when moving cargo along the ship will be:

T n = T + ∆ T n = T + P I x D ‘ H (L 2 - X F)

T k = T + ∆ T k = T + P I x D ‘ H (L 2 - X F)

If we take into account that tan Ψ = d/L and that D’ · H · sin Ψ = МΨ, we can write:

T n = T + P I x 100 M 1 s m (1 2 - X F L)

T k = T - P I x 100 M 1 s m (1 2 + X F L)

where T is the draft of the vessel when positioned on an even keel;
M 1cm - moment that trims the ship by 1 cm.

The value of the abscissa X F is found from the “curves of the elements of the theoretical drawing”, and it is necessary to strictly take into account the sign in front of X F: when point F is located forward of the midsection, the value of X F is considered positive, and when point F is located aft of the midsection, it is negative.

Lever X is also considered positive if the load is transferred towards the bow of the vessel; when transferring the load to the stern, the l X arm is considered negative.

Scale of changes in draft of the ends due to receiving 100 tons of cargo

The most widely used are scales and tables of changes in draft bow and stern from receiving a single load, the mass of which, depending on the displacement, is selected equal to 10, 25, 50, 100, 1000 tons. The construction of such scales and tables is based on the following considerations. The change in the draft of the ends of the vessel when receiving cargo consists of an increase average draft by the value ΔТ and changes in the draft of the ends ΔТ H and ΔТ K. The value of ΔТ does not depend on the location of the accepted cargo, and the values of ΔТ H and ΔТ K for a given draft and fixed cargo mass P will change in proportion to the abscissa of the C.T. accepted cargo Chr. Therefore, using this dependence, it is enough to calculate the changes in the draft of the ends from receiving cargo, first in the area of the bow and then the stern perpendiculars and construct a scale or table of changes in the draft of the ends of the vessel from receiving a cargo weighing, for example, 100 tons. Values ΔТ, ΔТ H, ΔТ K are calculated using formulas.

Based on the resulting increments in the draft of the ends of the vessel, we construct a graph of changes in these drafts from the receipt of the specified cargo.

To do this, on straight line a - b, we mark the position of the midship frame and plot half the length of the ship on the selected scale to the right (to the bow) and to the left (to the stern). From the obtained points we restore perpendiculars to line a - b. On the bow perpendicular we put upward the segment b - c, depicting on the selected scale the calculated change in draft by the bow when receiving a load in the bow. Similarly, on the stern perpendicular we lay down the segment a - d, depicting the calculated change in draft by the bow when taking the load into the stern. By connecting straight points c - d, we obtain a graph of the change in draft by the bow from receiving a load weighing 100 tons.

Rice. 4

Δ T n = + 24 s m = 0.24 m;

Δ T k = + 4 s m = 0.04 m

In the same way, a graph of changes in the draft of the vessel stern from receiving cargo is constructed. Here, segment b - d on the accepted scale depicts the change in draft by the stern when receiving a load of 100 tons in the bow, and segment a - e - when receiving cargo in the stern.

We calibrate the scales. Above the graph (or below it) we draw two straight lines to plot draft scales: the upper one for the bow, and the lower one for the stern. On each of them we mark the points corresponding to divisions 0 (their position is determined by the points of intersection of line a - b with graphs c - d and f - e, i.e., points g - p). Then, between line a - b and graphs c - d and ed, we select such segments, the length of which on the accepted scale would be equal to 30 or 10 cm of change in precipitation. When calibrating the “nose” scale, such segments will be segments z - i and kl. As a result, we get 30 and 10 on the division scale. We divide the distances between 0 and 10, 10 and 20 into 10 equal parts. The sizes of these divisions on both sections of the scale should be the same.

Using the graph e - e, in a similar way we construct a scale for draft by the stern. In practical calculations, several scales of changes in the draft of the ends from receiving 100 tons of cargo are constructed. Most often, scales are built for three drafts (displacements): draft of an empty ship, draft of a ship with a full load, and intermediate.

Scales, diagrams or tables of changes in the draft of the ends of the vessel from receiving a unit cargo (for example, 100 tons) can have very different type. Several such examples are given below in Figures 5-7.

Rice. 5 Curves of changes in the draft of the ends from receiving 100 tons of cargo, combined with the corresponding points on the vessel

Rice. 6 Scale of changes in the draft of the ends of the vessel from receiving 100 tons of cargo, combined with the corresponding points on the vessel

Rice. 7

INTRODUCTION

Stability is the ability of a floating craft to withstand external forces that cause it to roll or trim and return to a state of equilibrium after the end of the influence of external forces (External influence can be caused by a wave blow, a gust of wind, a change in course, etc.). This is one of the most important seaworthiness qualities of a floating craft.

The stability margin is the degree of protection of a floating craft from capsizing.

Depending on the plane of inclination, a distinction is made between lateral stability during roll and longitudinal stability during trim. In relation to surface vessels, due to the elongated shape of the ship's hull, its longitudinal stability is much higher than transverse stability, therefore, for navigation safety, it is most important to ensure proper lateral stability.

Depending on the magnitude of the inclination, a distinction is made between stability at small angles of inclination (initial stability) and stability at large angles of inclination.

Depending on the nature of the acting forces, static and dynamic stability are distinguished.

Static stability - considered under the action of static forces, that is, the applied force does not change in magnitude.

Dynamic stability - considered under the action of changing (i.e. dynamic) forces, for example wind, sea waves, load movement, etc.

The most important factors affecting stability are the location of the center of gravity and the center of magnitude of the vessel (CV).

1. CONCEPT OF LONGITUDINAL STABILITY OF A VESSEL

Stability, which manifests itself during longitudinal inclinations of the ship, i.e., during trim, is called longitudinal.

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

When the ship is tilted longitudinally at an angle ψ around the transverse axis of the center of gravity, the water will move from point C to point C1 and the supporting force, the direction of which is normal to the existing waterline, will act at an angle ψ to the original direction. The lines of action of the original and new direction of the support forces intersect at a point.
The point of intersection of the line of action of the supporting forces at an infinitesimal inclination in the longitudinal plane is called longitudinal metacenter M.

The radius of curvature of the movement curve of the central wheel in the longitudinal plane is called longitudinal metacentric radius R, which is determined by the distance from the longitudinal metacenter to the C.V.
The formula for calculating the longitudinal metacentric radius R is similar to the transverse metacentric radius;

where IF is the moment of inertia of the waterline area relative to the transverse axis passing through its center of gravity (point F); V is the volumetric displacement of the vessel.

The longitudinal moment of inertia of the waterline area IF is significantly greater than the transverse moment of inertia IX. Therefore, the longitudinal metacentric radius R is always significantly larger than the transverse radius r. It is tentatively believed that the longitudinal metacentric radius R is approximately equal to the length of the vessel.

The basic principle of stability is that the righting moment is the moment of the pair formed by the force of the weight of the vessel and the supporting force. As can be seen from the figure, as a result of the application of an external moment acting in the DP, called trim moment Mdif, the ship has tilted at a small trim angle ψ. Simultaneously with the appearance of the trim angle, a restoring moment Mψ occurs, acting in the direction opposite to the action of the trim moment.

Mdif = Mψ.

The restoring moment in this case will be:

Мψ = D" × GK1 (1)

where GK1 is the shoulder of this moment, called shoulder of longitudinal stability.

From the right triangle G M K1 we obtain:

GK1 = MG × sinψ = H × sinψ (2)

The value MG = H included in the last expression determines the elevation of the longitudinal metacenter above the center of gravity of the vessel and is called longitudinal metacentric height.

Substituting expression (2) into formula (1), we obtain:

Мψ = D" × H × sinψ (3)

where the product D" × H is the longitudinal stability coefficient. Bearing in mind that the longitudinal metacentric height H = R - a, formula (3) can be written as:

Мψ = D" × (R - a) × sinψ (4)

where a is the elevation of the ship’s center of gravity above its center of elevation.

Formulas (3), (4) are metacentric formulas for longitudinal stability.

Due to the smallness of the trim angle in the indicated formulas, instead of sin ψ, you can substitute the angle ψ (in radians) and then:

Мψ = D" × H × ψ or Мψ = D" × (R - a) × ψ.

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

2. VESSEL TRIM AND TRIM ANGLE

The trim is considered positive if the vessel's draft at the bow is greater than at the stern; trim aft aft is considered negative. In most cases, ships sail with trim to the stern.
Let us assume that a ship floating on an even keel along the VL waterline, under the influence of a certain moment, received a trim and its new effective waterline took the position V1L1. From the formula for the restoring moment we have:

ψ = Мψ / (D" × H).

Let us draw a dotted line AB, parallel to VL, through the point of intersection of the stern perpendicular with V1L1. Trim d is determined by leg BE of triangle ABE. From here:

tg ψ ≈ ψ = d / L

Comparing the last two expressions, we get:

d / L = Mψ / (D" × H), hence Mψ = (d / L) × D" × H.

Let us consider methods for determining the draft of a vessel under the influence of a differential moment resulting from the movement of cargo in the longitudinal-horizontal direction.

Let us assume that the load p is moved along the ship to a distance lx. The movement of the load, as already indicated, can be replaced by the application of a couple of forces to the vessel. In our case, this moment will be differentiating and equal: Mdiff = P × lx × cos ψ the equilibrium equation for longitudinal movement of the load (equality of the trimming and restoring moments) has the form:

P × lx × cosψ = D" × H × sinψ

whence tanψ = (P × lx) / (D" × H)

Since small inclinations of the ship occur around an axis passing through the C. T. F of the waterline area, the following expressions can be obtained for the change in draft bow and stern:

Consequently, the drafts bow and stern when moving cargo along the ship will be:

If we take into account that tanψ = d/L and that D" × H × sinψ = Mψ, we can write:

where T is the draft of the vessel when positioned on an even keel;

M1cm is the moment that trims the ship by 1 cm.

The value of the abscissa XF is found from the “curves of the elements of the theoretical drawing”, and it is necessary to strictly take into account the sign in front of XF: when point F is located forward of the midsection, the value of XF is considered positive, and when point F is located aft of the midsection - negative.

Leverage lx is also considered positive if the load is transferred towards the bow of the vessel; when transferring the load to the stern, the lx arm is considered negative.

CONCLUSION

Stability is one of the most important seaworthiness qualities of a floating craft. In relation to ships, the clarifying characteristic of the stability of the vessel is used. The stability margin is the degree of protection of a floating craft from capsizing.

External impact can be caused by a wave blow, a gust of wind, a change in course, etc.

In the practice of calculating the inclination of a ship in the longitudinal plane, associated with determining the trim, it is customary to use a linear trim instead of an angular trim.

BIBLIOGRAPHY

1. I., A., S. Control of landing, stability and stresses of the ship’s hull: Textbook. manual - Vladivostok, Moscow State University. adm. G.I. Nevelskoy, 2003. - 136 p.

2. N. Operational calculations of the seaworthiness of a vessel - M.: Transport, 1990, 142 p.

3. K., S. General device ships. - Leningrad: "Shipbuilding". - 1987. - 160 p.

4. G. Theory and structure of the vessel. - Textbook for river schools and technical schools. M.: Transport, 1992. - 248 p.

5. G. Vessel structure: Textbook. - 5th ed., stereotype: - L.: Shipbuilding, 1989. - 344 p.