What is the displacement and the coefficient of completeness of the vessel? Trim on the bow - the position of the vessel when the draft of the bow is greater than the draft of the stern. Trim on the bow reduces the speed of the ship See what "Trim the ship" is in other dictionaries

INTRODUCTION 2

1. THE CONCEPT OF THE LONGITUDINAL STABILITY OF THE SHIP.. 3

2. SHIP TRIM AND TRIM ANGLE.. 6

CONCLUSION. nine

REFERENCES.. 10

INTRODUCTION

Stability - the ability of a floating facility to withstand external forces that cause it to roll or trim and return to a state of equilibrium after the impact of external forces (External impact may be due to 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, there are transverse stability with roll and longitudinal stability with trim. With regard to surface vessels, due to the elongation of the shape of the ship's hull, its longitudinal stability is much higher than the transverse one, therefore, for the safety of navigation, it is most important to ensure proper transverse stability.

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

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 (that is, dynamic) forces, such as wind, sea waves, cargo movement, etc.

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

1. THE CONCEPT OF THE LONGITUDINAL STABILITY OF THE SHIP

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

Despite the fact that the trim angles of the vessel rarely reach 10 degrees, and usually amount to 2-3 degrees, the longitudinal inclination leads to significant linear trims with a large length of the vessel. So, for a ship with a length of 150 m, the angle of inclination is 1 deg. 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 for vehicles with normal ratios of the main dimensions, longitudinal stability is always positive.

With the longitudinal inclination of the ship at an angle ψ around the transverse axis, the C.V. will move from point C to point C1 and the support force, the direction of which is normal to the current waterline, will act at an angle 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 support forces at an infinitesimal inclination in the longitudinal plane is called longitudinal metacenter M.

The radius of curvature of the displacement curve of the C.V. 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 C. T. (point F); V - volumetric displacement of the ship.

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

The basic position of stability is that the restoring moment is the moment of the pair formed by the ship's weight force 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 trimming moment Mdif, the ship has received a small trim angle ψ. Simultaneously with the appearance of the trim angle, a restoring moment Mψ arises, acting in the opposite direction 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:

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 a right triangle G M K1 we get:

GK1 = MG × sinψ = H × sinψ (2)

The value MG = H included in the last expression determines the elevation of the longitudinal metacenter above the C.T. 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 coefficient of longitudinal stability. Keeping in mind that the longitudinal metacentric height H \u003d R - a, formula (3) can be written as:

Мψ \u003d D "× (R - a) × sinψ (4)

where a is the elevation of the C. T. of the vessel above its C. V.

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

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

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

Since the value of the longitudinal metacentric radius R is many times greater than the transverse r, the longitudinal metacentric height H of any ship is many times greater than the transverse one h. therefore, if the vessel is provided with lateral stability, then longitudinal stability is ensured without fail.

2. SHIP TRIM AND TRIM ANGLE

In the practice of calculating the inclinations of the vessel in the longitudinal plane, associated with the determination of the trim, instead of the angular trim, it is customary to use a linear trim, the value of which is determined as the difference between the draft of the vessel bow and stern, i.e. d = TN - TC.

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

ψ \u003d Mψ / (D "× H).

Let's draw a dotted line AB, parallel to VL, through the point of intersection of the aft perpendicular with V1L1. Trim d - is determined by the leg BE of the 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.

Consider methods for determining the ship's draft under the action of a trimming moment on it, which occurs as a result of the movement of cargo in the longitudinal-horizontal direction.

Let us assume that the load p is moved along the ship by a distance lx. The movement of cargo, as already indicated, can be replaced by the application of a moment of a pair of forces to the ship. In our case this moment will be trimming and equal:

P × lx × cosψ = ​​D" × H × sinψ

whence tgψ = (P × lx) / (D" × H)

Since small ship inclinations 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 fore and aft:

Consequently, drafts fore and aft when moving cargo along the ship will be:

Considering that tgψ = d/L and that D" × H × sinψ = Mψ, we can write:

where T is the ship's draft when positioned on an even keel;

M1cm - 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 the point F is located forward of the midship, the value of XF is considered positive, and when the point F is located aft of the midship - negative.

The arm lx is also considered positive if the cargo is carried towards the bow of the ship; when transferring cargo to the stern, the shoulder lx is considered negative.

CONCLUSION

Stability is one of the most important seaworthiness qualities of a floating craft. With regard to ships, a clarifying characteristic of the ship's stability is used. The stability margin is the degree of protection of a floating craft from capsizing.

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

In the practice of calculating the inclinations of the vessel in the longitudinal plane, associated with the determination of the trim, instead of the angular trim, it is customary to use a linear trim.

BIBLIOGRAPHY

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

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

3. K., S. The general arrangement of courts. - Leningrad: "Shipbuilding". - 1987. - 160s.

4. D. Theory and arrangement of the vessel. - Textbook for river schools and technical schools. M.: Transport, 1992. - 248s.

5. D. Device of the vessel: Textbook. - 5th ed., stereotype: - L.: Shipbuilding, 1989. - 344 p.

(from lat. differens, genitive case differentis - difference)

inclination of the vessel in the longitudinal plane. D. s. characterizes the landing of the vessel and is measured by the difference between its draft (recesses) stern and bow. If the difference is equal to zero, they say that the ship is “sitting on an even keel”, with a positive difference, the ship is sitting with a trim to the stern, with a negative difference, with a trim on the bow. D. s. affects the agility of the vessel, the operating conditions of the propeller, the patency in ice, etc. D. s. it can be static and running, occurring at high speeds. D. s. usually regulated by the intake or removal of water ballast.

  • - inclination of the ship in the longitudinal plane. It is measured with the help of an instrument - a trim gauge as the difference between the draft of the io-sa and the stern in meters ...

    Dictionary of military terms

  • - vessel - inclination of the vessel in the longitudinal plane. D. determines the landing of the vessel 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"...

    Big encyclopedic polytechnic dictionary

  • - the angle of longitudinal inclination of the vessel, causing a difference in drafts of the bow and stern ...

    Marine vocabulary

  • - from lat. Differences - the difference in the price of the goods when they are ordered and when they are received in trading operations...

    Glossary of business terms

  • - in trading operations, this is the difference in the price of the goods when ordering and when receiving ...

    Big Economic Dictionary

  • Economic dictionary

  • - in trading operations: the difference in the price of the goods when ordering and receiving ...

    Encyclopedic Dictionary of Economics and Law

  • - see Differentiation...

    Big Law Dictionary

  • - the difference between the deepening of the bow and stern; is of great importance for sailing ships, since the ship's agility largely depends on D. ...

    Encyclopedic Dictionary of Brockhaus and Euphron

  • - the difference in the draft of the vessel bow and stern ...

    Big encyclopedic dictionary

  • - ; pl. trims / nts, R ....

    Spelling Dictionary of the Russian Language

  • - husband, marine the difference between the loading of the stern and the bow; unloading, unloading. The trim starts on the stern, the loading of the stern is deeper. Differential male, mat. an infinitesimal amount...

    Dahl's Explanatory Dictionary

  • - trim I m. The difference in the draft of the bow and stern of the ship; pitch angle of the vessel. II m. The difference in the price of the goods when ordering and upon receipt ...

    Explanatory Dictionary of Efremova

  • - diff...

    Russian spelling dictionary

  • - DIFFERENT, DIFFERENT a, m. différent m. lat. differens 205. Each Captain tries to bring his ship into the best trim, in order to win the wind from the enemy. Kush. MS 2 310. // Sl. eighteen...

    Historical Dictionary of Gallicisms of the Russian Language

  • - The difference in the depth of immersion in the water of the stern and bow of the ship ...

    Dictionary of foreign words of the Russian language

"Ship trim" in books

V. Building a ship

From the book RUSSIAN IMPERIAL FLEET. 1913 author

V. Construction of the vessel In parallel with the production of detailed working drawings, an order is made for steel, stems and other necessary components of the vessel. Krom? In addition, directly after the preparation of the theoretical drawing, they proceed to the breakdown? ship to the plaza?, i.e.

ship board

From the book Great Soviet Encyclopedia (BO) of the author TSB

Vessel's board Vessel's board (from the German Bord), a set of framing and plating elements that form the side walls of the ship's hull. There are left (backboard) and right (starboard) B., if you look from the stern to the bow of the vessel. The cargo capacity of the ship depends on the height of the B.; tall

Sail (ship)

From the book Great Soviet Encyclopedia (PA) of the author TSB

ship pitching

From the book Great Soviet Encyclopedia (KA) of the author TSB

Hull

From the book Great Soviet Encyclopedia (KO) of the author TSB

Vessel trim

From the book Great Soviet Encyclopedia (CI) of the author TSB

ship drift

From the book Great Soviet Encyclopedia (DR) of the author TSB

Vessel course

From the book Great Soviet Encyclopedia (KU) of the author TSB

Vessel survivability

From the book Great Soviet Encyclopedia (GI) of the author TSB

ship plating

From the book Great Soviet Encyclopedia (OB) of the author TSB

Vessel circulation

From the book Great Soviet Encyclopedia (CI) of the author TSB

Refloating a ship by moving the ship's center of gravity

From the author's book

Removing the vessel from the shoal by moving the center of gravity of the vessel It is used if the vessel does not have a double keel.1. The whole team moves to one of the sides and drags all the heavy cargo there.2. With a maximum keel height in the stern, it is better

VI. PREPARATION OF THE SHIP FOR THE voyage AND SHOOTING ITS ANCHOR 1. Vessel's seaworthiness

the author Lugovoi S P

VI. PREPARATION OF THE SHIP FOR THE voyage AND ANCHORING IT 1. Seaworthiness of the ship Regardless of whether the ship goes on a voyage with or without cargo, in any case, the seaworthiness of the ship must be ensured both in the port of departure and throughout the entire future

VIII. GROUNDING (ON REEFS, ON STONES) AND MEASURES TO REMOVE THE SHIP 1. Reasons for landing and measures to prevent the ship from running aground

From the book Accidents of ships and their warning the author Lugovoi S P

VIII. GROUNDING (ON REEFS, ON ROCKS) AND MEASURES TO REMOVE THE VESSEL 1. Reasons for grounding and measures to prevent the vessel from running aground Grounding of vessels (on reefs or rocks) occurs most often during fog or at night, as well as when sailing in narrowness or in a place

Chapter IV. The crew of the ship. Vessel captain

From the book Labor protection in transport author Korniychuk Galina

Chapter IV. The crew of the ship. Vessel captain Article 52. Composition of the ship's crew1. The ship's crew includes the captain of the ship, other officers of the ship and the ship's crew.2. In addition to the captain of the ship, the commanding staff of the ship includes assistants to the captain of the ship, mechanics,

The stability of a cargo ship during movement is greatly influenced by its loading. The control of the vessel is much easier when it is not fully loaded. A vessel with no load at all is easier to steer, but since the propeller of the vessel is close to the surface of the water, it has increased yaw.

When accepting the cargo, and consequently, the increase in draft, the ship becomes less sensitive to the interaction of wind and waves and more steadily keeps on course. The position of the hull relative to the surface of the water also depends on the load. (i.e. the ship is heeling or trimming)

The moment of inertia of the ship's mass depends on the distribution of cargo along the length of the vessel relative to the vertical axis. If most of the cargo is concentrated in the stern holds, the moment of inertia becomes large and the ship becomes less sensitive to the disturbing effects of external forces, i.e. more stable on the course, but at the same time more difficult to bring to the course.

Improvement in agility can be achieved by concentrating the heaviest loads in the middle of the hull, but at the same time deteriorating driving stability.

Placing cargo, especially heavy weights, at the top causes roll and roll of the vessel, which negatively affects stability. In particular, the presence of water under the hold slips has a negative effect on controllability. This water will move from side to side even with rudder deflection.

The trim of the ship worsens the streamlining of the hull, reduces speed and leads to a shift in the point of application of the lateral hydrodynamic force on the hull to the bow or stern, depending on the difference in draft. The effect of this displacement is similar to changing the diametral plane due to a change in the area of ​​the bow or aft deadwood.

The trim on the stern shifts the center of hydrodynamic pressure to the stern, increases the stability of the movement on the course and reduces the agility. On the contrary, the trim on the nose, improving the agility, worsens the stability on the course.

When trimming, the effectiveness of the rudders may deteriorate or improve. When trimming to the stern, the center of gravity shifts to the stern (Fig. 36, a), the steering torque arm and the moment itself decrease, agility worsens, and driving stability increases. When trimming on the nose, on the contrary, when the “steering forces” and are equal, the shoulder and moment increase, so the agility improves, but the stability on the course becomes worse (Fig. 36, b).



With a trim on the bow, the ship's agility improves, the stability of movement on the oncoming wave increases, and vice versa, strong peals of the stern appear on the tail wave. In addition, when trimming on the bow of the vessel, there is a desire to go out into the wind in forward gear and stop bowing downwind in reverse gear.

When trimmed to the stern, the ship becomes less agile. On the forward course, the ship is stable on the course, but in the oncoming waves it easily evades the course.

With a strong trim to the stern, the vessel has a desire to bear with its bow to the wind. In reverse, the ship is difficult to steer, it constantly strives to bring the stern to the wind, especially when it is lateral.

With a slight trim to the stern, the efficiency of the propellers increases and most ships increase their speed. However, a further increase in trim leads to a decrease in speed. Trim on the nose due to increased water resistance to movement, as a rule, leads to a loss of forward speed.

In the practice of navigation, trim to the stern is sometimes specially created when towing, when sailing in ice, to reduce the possibility of damage to propellers and rudders, to increase stability when moving in the direction of waves and wind, and in other cases.

Sometimes the ship makes a voyage, having some list on any side. The roll can be caused by the following reasons: incorrect location of cargo, uneven consumption of fuel and water, design flaws, lateral wind pressure, crowding of passengers on one side, etc.

Fig.36 Effect of trim 37 Effect of roll

Roll has a different effect on the stability of a single-rotor and twin-rotor vessel. When heeling, a single-rotor ship does not go straight, but tends to deviate from the course in the direction opposite to the roll. This is due to the peculiarities of the distribution of the forces of water resistance to the movement of the vessel.



When a single-rotor vessel moves without a roll, two forces and equal to each other in magnitude and direction will resist on the cheekbones of both sides (Fig. 37, a). If we decompose these forces into components, then the forces and will be directed perpendicular to the sides of the cheekbones and they will be equal to each other. Therefore, the ship will go exactly on course.

When the vessel rolls over the area "l" of the submerged surface of the chin of the heeled side is greater than the area "p" of the chin of the raised side. Consequently, the cheekbone of the heeled side will experience more resistance of the oncoming water and less - the cheekbone of the raised side (Fig. 37, b)

In the second case, the water resistance forces and applied to one and the other cheekbones are parallel to each other, but different in magnitude (Fig. 37, b). When decomposing these forces according to the parallelogram rule into components (so that one of them is parallel and the other is perpendicular to the side), we will make sure that the component perpendicular to the side is greater than the corresponding component of the opposite side.

As a result of this, it can be concluded that the bow of a single-rotor vessel, when heeling, deviates towards the raised side (opposite to heel), i.e. in the direction of least water resistance. Therefore, in order to keep a single-rotor ship on course, you have to shift the rudder in the direction of the roll. If the rudder is in the “straight” position on a heeled single-rotor ship, the ship will circulate in the direction opposite to the roll. Consequently, when making revolutions, the circulation diameter increases in the direction of the roll, and decreases in the opposite direction.

For twin-screw vessels, course deviation is caused by the combined effect of the unequal frontal resistance of water to the movement of the hull from the sides of the vessel, as well as by the different magnitude of the impact of the turning forces of the left and right machines at the same number of revolutions.

For a ship without a roll, the point of application of the forces of water resistance to movement is in the diametrical plane, so the resistance from both sides has an equal effect on the ship (see Fig. 37, a). In addition, for a vessel without a roll, the turning moments relative to the center of gravity of the vessel, created by the thrust of the propellers and , are practically the same, since the arms of the stops are equal, and therefore .

If, for example, the ship has a constant list to port, then the recess of the starboard propeller will decrease and the recess of the propellers on the starboard side will increase. The center of water resistance to movement will shift towards the heeled side and take up a position (see Fig. 37,b) on the vertical plane relative to which the thrusters with unequal application arms will act. those. then< .

Despite the fact that the right screw will work less efficiently than the left one due to the smaller depth, however, with an increase in the shoulder, the total turning moment from the right machine will become much greater than from the left, i.e. then< .

Under the influence of a larger moment from the right car, the ship will tend to evade towards the left, i.e. tilted side. On the other hand, an increase in water resistance to the movement of the vessel from the side of the cheekbones will predetermine the desire to divert the vessel in the direction of increased, i.e. starboard.

These moments are comparable in magnitude. Practice shows that each type of vessel, depending on various factors, deviates in a certain direction when heeling. In addition, it was found that the values ​​of the evasive moments are very small and can be easily compensated by shifting the rudder by 2-3° towards the side opposite the side of the evasion.

Displacement completeness coefficient. Its increase leads to a decrease in force and a decrease in damping moment, and consequently, to an improvement in course stability.

The shape of the stern. The shape of the stern is characterized by the area of ​​​​the aft gap (undercut) of the stern (i.e., the area supplementing the stern to a rectangle)

Fig.38. To determine the area of ​​the aft undercut:

a) feed with an outboard or semi-outboard rudder;

b) stern with a rudder located behind the rudder post

The area is limited by the aft perpendicular, the keel line (base line) and the contour of the stern (shaded in Fig. 38). As a criterion for trimming the stern, you can use the coefficient:

where is the average draft, m.

The parameter is the coefficient of completeness of the DP area.

A constructive increase in the undercut area of ​​the aft end by 2.5 times can reduce the circulation diameter by 2 times. However, this will dramatically worsen the stability on the course.

Rudder area. An increase increases the lateral force of the rudder, but at the same time, the damping effect of the rudder also increases. In practice, it turns out that an increase in the rudder area leads to an improvement in agility only at large shift angles.

Relative elongation of the steering wheel. An increase with its area unchanged leads to an increase in the lateral force of the steering wheel, which leads to some improvement in agility.

Rudder location. If the rudder is located in a screw jet, then the speed of water flowing onto the rudder increases due to the additional flow velocity caused by the screw, which provides a significant improvement in agility. This effect is especially pronounced on single-rotor vessels in the acceleration mode, and as the speed approaches the steady value, it decreases.

On twin-propeller ships, the rudder located in the DP has a relatively low efficiency. If on such vessels two rudder blades are installed behind each of the propellers, then the agility increases sharply.

The influence of the ship's speed on its handling appears ambiguous. Hydrodynamic forces and moments on the rudder and hull of the ship are proportional to the square of the speed of the oncoming flow, therefore, when the ship is moving at a steady speed, regardless of its absolute value, the ratios between the indicated forces and moments remain constant. Consequently, at different steady speeds, the trajectories (at the same rudder angles) retain their shape and size. This circumstance has been repeatedly confirmed by natural tests. The longitudinal size of the circulation (advance) significantly depends on the initial speed of movement (when maneuvering from low speed, the run-out is 30% less than the run-out from full speed). Therefore, in order to make a turn in a limited water area in the absence of wind and current, it is advisable to slow down and turn at a reduced speed before starting the maneuver. The smaller the water area in which the vessel circulates, the lower should be the initial speed of its course. But if during the maneuver the rotational speed of the propeller is changed, then the speed of the flow on the rudder located behind the propeller will change. In this case, the moment created by the steering wheel. It will change immediately, and the hydrodynamic moment on the ship's hull will change slowly as the speed of the ship itself changes, so the previous ratio between these moments will be temporarily violated, which will lead to a change in the curvature of the trajectory. With an increase in the rotational speed of the screw, the curvature of the trajectory increases (the radius of curvature decreases), and vice versa. When the ship's speed matches the propeller's nose speed, the curvature of the trajectory will return to its original value.

All of the above is true for the case of calm weather. If the ship is exposed to wind of a certain strength, then in this case the controllability depends significantly on the speed of the vessel: the lower the speed, the greater the effect of wind on controllability.

When for some reason it is not possible to allow an increase in speed, but it is necessary to reduce the angular rate of turn, it is better to quickly reduce the speed of the propulsors. This is more efficient than shifting the steering body to the opposite side.

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

Rice. one

Despite the fact that the trim angles of the vessel rarely reach 10 degrees, and usually amount to 2 - 3 degrees, the longitudinal inclination leads to significant linear trims with a large length of the vessel. So, for a ship 150 m long, the angle of inclination 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.

With the longitudinal inclination of the vessel at an angle Ψ around the transverse axis Ts.V. will move from point C to point C1 and the support force, the direction of which is normal to the current waterline, will act at an angle 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 support forces at an infinitely small 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 C.V.

The formula for calculating the longitudinal metacentric radius R is similar to the transverse metacentric radius: R \u003d I F / V, where I F is the moment of inertia of the waterline area relative to the transverse axis passing through its C.T. (point F); V - volumetric displacement of the ship.

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

The basic position of stability is that the restoring moment is the moment of the pair formed by the ship's weight force 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 trim moment Mdiff, the ship received a tilt 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 \u003d D ‘ G K 1 (1)

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

From a right triangle G M K1 we get:

G K 1 \u003d M G sin Ψ \u003d H sin Ψ (2)

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

M Ψ \u003d D ‘ H H sin Ψ (3)

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

M Ψ \u003d D ‘ (R - a) sin Ψ (4)

  • where a is the elevation of the C.T. vessel over his C.V.

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

M Ψ \u003d D ‘ · H · Ψ and l and M Ψ \u003d D ‘ · (R - a) · Ψ.

Since the value of 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 one h, therefore, if the vessel has transverse stability, then longitudinal stability is certainly ensured.

Vessel trim and trim angle

In the practice of calculating the inclinations of the vessel in the longitudinal plane, associated with the determination of the trim, instead of the angular trim, it is customary to use a linear trim, the value of which is determined as the difference between the draft of the vessel bow and stern, i.e. d \u003d T H - T K.


Rice. 2

The trim is considered to be positive if the ship's draft is greater with the bow than with the stern; trim to the stern is considered negative. In most cases, ships sail with a trim to the stern. Suppose that a vessel 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 position B 1 L 1 . From the formula for the restoring moment, we have:

Ψ \u003d M Ψ D ‘ H

Let's draw a dotted line AB, parallel to VL, through the point of intersection of the aft perpendicular with B 1 L 1. Trim d - is determined by the leg BE of the 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

Trim change during longitudinal movement of the load

Consider methods for determining the ship's draft under the action 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 by a distance ιx. The movement of cargo, as already indicated, can be replaced by the application of a moment of a pair of forces to the ship. In our case, this moment will be trimming and equal to: M diff \u003d P · l X · cosΨ. The equilibrium equation for the longitudinal movement of the load (the equality of the trimming and restoring moments) has the form:

R l x cos Ψ = D ‘ H sin Ψ

  • where:

t g ψ = P I X D ‘ H

Since small ship inclinations occur around an axis passing through the C.T. area of ​​the waterline (point F), you can get the following expressions for the change in draft fore and aft:

∆ T H \u003d (L 2 - X F) t g ψ \u003d P I X D ‘ H (L 2 - X F)

∆ T H \u003d (L 2 + X F) t g ψ \u003d - P I X D ‘ H (L 2 + X F)

Consequently, drafts fore and aft when moving cargo along the ship will be:

T n \u003d T + ∆ T n \u003d T + P I x D ‘ H (L 2 - X F)

T k \u003d T + ∆ T k \u003d T + P I x D ‘ H (L 2 - X F)

Considering that tg Ψ = d/L and that D’ H sin Ψ = MΨ, we can write:

T n \u003d T + P I x 100 M 1 s m (1 2 - X F L)

T to \u003d T - P I x 100 M 1 with m (1 2 + X F L)

  • where T is the ship's draft when positioned on an even keel;
  • M 1cm - the moment trimming 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 the point F is located forward of the midship, the value of X F is considered positive, and when the point F is located aft of the midship - negative.

Shoulder l X is also considered positive if the cargo is carried towards the bow of the vessel; when transferring cargo to the stern, the shoulder l X is considered negative.

Scale of changes in the draft of the extremities due to the reception of 100 tons of cargo

The most widely used are scales and tables of changes in draft fore and aft from the reception of a single cargo, the mass of which, depending on the displacement, is chosen equal to 10, 25, 50, 100, 1000 tons. The following considerations underlie the construction of such scales and tables. The change in the draft of the ship's extremities when receiving cargo is composed of an increase in the average draft by the value ΔТ and a change in the draft of the ends ΔТ H and ΔТ K . The value of ΔТ does not depend on the location of the received cargo, and the values ​​of ΔТ H and ΔТ K at a given draft and a fixed mass of cargo Р will change in proportion to the abscissa C.T. accepted cargo Xr. Therefore, using such a dependence, it is sufficient to calculate the changes in the draft of the ship's ends from the acceptance of cargo, first in the area of ​​the bow and then the stern perpendiculars and build a scale or table of changes in the draft of the ship's ends from the acceptance of a cargo with a mass of, for example, 100 tons. Values ​​ΔТ, ΔТ H , ΔТ K calculated by formulas.

Based on the received increments of the draft of the ship's ends, we build a graph of changes in these drafts from the reception of the specified cargo.

To do this, on a straight line a - b, we outline the position of the midship - frame and set aside on the selected scale to the right (in the bow) and to the left (in the stern) half the length of the vessel. From the points obtained, we restore the perpendiculars to the line a - b. On the bow perpendicular, we lay off the segment b - c, depicting on the selected scale the calculated change in draft by the bow when receiving cargo 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 the straight points in - d, we get a graph of the change in draft by the bow from the reception of a load of 100 tons.


Rice. 4

Δ T n \u003d + 24 s m \u003d 0, 24 m;

Δ T k \u003d + 4 s m \u003d 0, 04 m

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

We calibrate scales. Above the graph (or below it), we draw two straight lines for drawing scales for draft changes: the upper one is for the bow, and the lower one is for the stern. On each of them we mark the points corresponding to the divisions 0 (their position is determined by the points of intersection of the line a - b with the graphs c - d and e - e, i.e., the points g - p). Then, between the line a - b and graphs c - d and unit, we select such segments, the length of which on the accepted scale would be equal to 30 or 10 cm of the change in draft. Such segments when grading the “nose” scale will be segments s - and and cl. 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 parts of the scale should be the same.

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

Scales, charts or tables of changes in the draft of the ends of the vessel from the reception of a single load (for example, 100 tons) can have very different views. Several such examples are given below in Figures 5-7.


Rice. 5 Curves of changes in the draft of the extremities from the reception of 100 tons of cargo, combined with the corresponding points on the ship
Rice. 6 The scale of changes in the draft of the ship's extremities from the reception of 100 tons of cargo, combined with the corresponding points on the ship
Rice. 7

Suggested reading:

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

The support force is equal to the product of the density of water and the submerged waterproof volume of the strong hull of the submarine. The density of sea water depends on salinity, temperature and pressure. The volume of the pressure hull also varies and depends on the depth of immersion and the temperature of the outboard water, the weight of the submarine - on the consumption of variable cargoes: fuel, oil, ammunition, fresh water, provisions, etc. Most of these cargoes are replaced by outboard 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 support force is violated, which leads to the appearance of the so-called residual buoyancy. If the support force is greater than the weight of the submarine, then the residual buoyancy will be positive, if less - negative. With positive residual buoyancy, the submarine tends to surface, with negative residual buoyancy, it tends to sink.

The uneven consumption of variable loads in the bow and stern of the boat leads to the formation of trims.

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

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

Trimming can be done without a move or on the move.

Trim without travel

Trimming without a stroke is performed:

When a submarine has not been immersed for a long time;

In areas constrained for maneuvering in a submerged position;

When signboard;

For educational purposes.

With sea waves of no more than 3-4 points, trimming without a move is usually performed at periscope depth, and with sea waves of more than 4 points - at safe depths.

The advantage of trimming without a stroke is that this method allows you to trim a submarine in an area with shallow depths. The disadvantages include: the need for trimming when moving and ensuring external security in areas that are cramped for maneuvering.

It is advisable to trim at the periscope depth of a obviously lightweight submarine, for which, before diving into the equalization tank, water should be taken less than the calculated one by 5-10 tf (depending on the design of the submarine). The main ballast is taken first to the end groups, then to the middle one. If, after filling the end groups of the tanks of the main ballast, the pl will have a trim of more than 0.5 °, the trim moment should be extinguished by distillation of water from one trim tank to another. After filling the middle group of tanks of the main ballast, they start trimming.

Positive buoyancy, depending on the value, is extinguished by receiving water from behind the side into the surge tank through a kingston or a fine filling valve. To remove air bubbles from the end groups of the main ballast tanks and from the superstructure, the submarine must be “rocked”, i.e., shift the trim from one end to the other, distilling water between the trim tanks, and then close the ventilation valves of these tanks. 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. The distillation of water from one trim tank to another is recommended to be stopped when the trim does not reach the set value by 1.5-2 °.

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

Trim on the go

It is carried out in areas that allow the submarine to maneuver freely underwater. When the sea is calm, trimming can be carried out at the periscope depth, and when the sea is rough, at a safe one.

To understand the essence of trimming and controlling a submarine in a submerged position, one must know the principle of operation of horizontal rudders and the forces acting on a submarine.

When shifting horizontal rudders on the move (Fig. 3.1), hydrodynamic forces of stern Rk and bow Rn horizontal rudders arise.

Rice. 3.1. Forces arising from the shifting of horizontal rudders


These forces are proportional to the square of the submarine's speed and the rudder angles. The forces Rk and Rn can be replaced by their components parallel to the axes GX and GY. The forces Rxk and Rxh increase the resistance of the 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 the hydrodynamic moments of the horizontal rudders Mk and Mn. Shifting the stern horizontal rudders for diving gives a moment - Mk, trimming the submarine to the bow, and lift + Ruk. shifting the bow horizontal rudders for ascent gives a moment + Mn, trimming the submarine to the stern, and lift + Ryn

Shifting the stern horizontal rudders for ascent gives a trim moment for the stern + Mk and drowning force _RyK, and shifting the bow horizontal rudders for diving gives a trim moment for os - Mn and drowning force - Ruk.


Rice. 3.2. Forces acting on a submarine under water


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

A submarine with 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 support force and their moments acting 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 arises, which tends to return the submarine to its original position.

Dynamic forces and moments include thrust force, propeller thrust torque, and hydrodynamic forces and moments. The thrust force of the propellers Tm is proportional to the rotational speed of the propeller. With steady motion, the propeller stop force is balanced by drag. The thrust moment of the propellers Mt arises due to the fact that the axes of the line of shafts on a submarine usually do not coincide in height with the center of gravity and are located below it. Therefore, the moment of thrust 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. The point K applied to the resultant Rm is called the center of pressure. The center of pressure does not coincide with the center of gravity of the submarine 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 decomposed into its components. The component Rmx (drag) characterizes the resistance of water to the movement of the submarine. The component Rm plays an important role in the controllability of the submarine in the vertical plane. At a constant immersion depth with a trim near zero or aft, the force Rmу is lifting, and the moment MR trims the submarine to the stern, with a trim to the bow, the force Rtu sinks, and the moment MR trims the submarine to the bow.

The trim on the move is based on the movement of the submarine at a constant depth and in a direct 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 knowing the following characteristic positions of an undifferentiated submarine sailing at a constant depth, depending on the angles of horizontal rudder and trim:

Trim 0 ° - stern horizontal rudders shifted to the ascent;

Trim 0° - stern horizontal rudders shifted to dive;

Trim on the bow - stern horizontal rudders shifted to dive;

Trim on the bow - stern horizontal rudders shifted to the ascent;

Trim to the stern - stern horizontal rudders shifted to the ascent;

Trim aft - stern horizontal rudders shifted to dive.

Examples of trim on the go

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


Rice. 3.3. The submarine has a heavy nose


The stern horizontal rudders are shifted to the ascent of 12 °, the bow rudders are at zero. 1reOuetsya to trim the submarine (Fig. 6.6).

Stern horizontal rudders create a trimming moment on the stern + MK and sinking force - RyK. Moment +MK tends to trim aft, but the submarine has zero trim. It follows from this that there is some moment that counteracts the +MK moment to create a trim to the stern. Such a moment may 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 trim moment on the bow - Mid. To trim the submarine in terms of moment, water should be moved from the bow trim tank to the stern tank and at the same time the stern horizontal rudders should be set to zero.

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

Zero if the forces Rmy and Ryk are equal in magnitude;

Negative if Rmu > Rvk;

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

Example 2 A submarine on a straight course moves at low speed, keeps a constant depth with a trim of 5 ° on the bow. Aft horizontal rudders are shifted to the ascent 12 ° on the bow, bow - in the plane of the frame (at zero). It is required to trim the submarine (Fig. 3.4).

Stern horizontal rudders create a trimming moment on the stern + MK and sinking force - RyK. The trim on the bow creates a drowning force - Rm, and a moment -MR, trimming the submarine on the bow. The submarine keeps a constant depth, and under the influence of sinking forces it must sink, therefore, there is a force that prevents it from sinking. Such a force in this case 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 on the stern by an excessive trimming moment on the bow - Mid, i.e., the nose of the submarine is heavy.

With such a characteristic position of an untrimmed submarine, you must first move the water from the bow to the stern, while retracting the stern horizontal rudders to dive to keep the submarine at a constant depth, and then take water from the side into the equalizing tank for buoyancy trimming.


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


An attempt to trim the pl first by buoyancy, then level the trim may lead to the fact that it cannot be kept at a given depth. In fact, with the beginning of receiving water from overboard, the submarine will begin to sink due to an increase in its weight. To maintain a given depth, it will be necessary to reduce the trim on the nose, i.e., reduce the drowning 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 a full angle for ascent (up to the limiter) may not provide a decrease in trim on the nose to the required value. Therefore, the submarine will sink.

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

In practice, trim on the go is performed as follows. After the personnel have occupied places according to the dive schedule, the wheelhouse hatch is closed, the electric motors are given a low speed and the main ballast is taken, after which the command “Trim the submarine at a depth of so many meters, at such and such a course, with a trim of so many degrees fore (aft)". The reception of the main ballast is carried out, as in trimming, without a stroke. The ventilation of the middle group of tanks of the main ballast is closed at a depth of 5-7 m. The specified trim depth is maintained by the stroke and trim. When going to depth, a significant trim should not be created. The ventilation of the end tanks of the main ballast is closed immediately with the arrival of the submarine at a given depth (after the trim is switched from bow to stern).

If, after filling the middle group of tanks of the main ballast, the submarine becomes negatively buoyant, you should create a trim to the stern with horizontal rudders and propulsion and, while 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 rate of submergence of the submarine.

If the pl is not immersed, water should be taken into the surge tank through a kingston or fine fill 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 trim the submarine according to the position of the horizontal rudders and trim, determine the residual buoyancy and excess trim moment, and then proceed to trim.

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

1. If the pl holds a given depth and its trim moment from the horizontal rudders coincides with the trim, you should first trim it in buoyancy, and then trim.

2. If the pl holds a given depth, but the trim does not match the trim moment of the horizontal rudders, you should first trim it along the trim, and then along the buoyancy.

By draining or receiving water into the surge tank and pumping auxiliary ballast between the trim tanks, such a position is achieved that the bow horizontal rudders are at zero, and the stern rudders are with a slight deviation from the plane of the frame. At the same time, a submarine with a slight trim on the nose should keep the depth. In this position, it is considered trimmed.

With the end of the trim, the ventilation valves of the main ballast tanks are opened and closed (“slammed”) to bleed the remaining air cushion. After making sure that at a given stroke, the submarine maintains a constant depth on a straight course with zero or a given trim, the shifting of the stern horizontal rudders does not exceed ± 5 °, and the bow rudders are at zero, the “Trim finished” command is given. Compartment commanders report to the central post on the presence of personnel in the compartments and the amount of water in the auxiliary ballast tanks. These data are recorded in the watch and trim logs.