Vessel circulation diameter. Textbook: Calculation of circulation elements and inertial characteristics of a vessel. Methodology for constructing a vessel's circulation

The curvilinear trajectory described by the center of gravity of the ship when the rudder is shifted to a certain angle and then held in this position is called circulation.

There are three periods of circulation: maneuvering, evolutionary and the period of steady circulation. Maneuvering circulation period is determined by the beginning and end of the rudder shift, i.e. coincides in time with the duration of the rudder shift. During this period, the ship continues to move almost straight. Evolutionary period of circulation begins from the moment the rudder is shifted and ends when the elements of movement take on a steady character, i.e. will stop changing over time. The period of steady circulation begins from the end of the evolutionary period and lasts as long as the ship's rudder is in the reversed position.

The trajectory of the curvilinear movement of the vessel’s center of gravity, i.e. its circulation is characterized by the following elements:

Diameter of steady circulation (D c)- the diameter of the circle described by the ship during the steady period of circulation, which begins after the ship turns 90-180°; Tactical circulation diameter (D t)- the shortest distance between the position of the ship's centreline at the beginning of the turn and after changing the initial course by 180°. Extension l 1 the distance by which the ship's center of gravity shifts in the direction of the original course from the point at which the circulation begins to the point corresponding to a change in the ship's course by 90°. Forward displacement l 2- the distance from the initial course of the ship to the point of the center of gravity at the moment the ship turns 90°. Reverse bias l 3- the greatest distance by which the ship’s center of gravity shifts from the original course line in the direction opposite to the turn.

Circulation characteristics also include: the period of steady circulation T - the time the vessel turns 360°; angular speed of rotation of the vessel in steady circulation ω = 2π / T.

Steps to prepare the steering gear before leaving the vessel at sea

Gyrocompass directions. Gyrocompass correction

Gyrocompass meridian - the direction in which the main axis of the gyrocompass is installed

Hypocompass course - the direction of the centerline plane of the ship, measured by the horizontal angle between northern part gyrocompass meridian and the bow of the ship's center plane.

Gyrocompass bearing is the direction to a landmark, measured by the horizontal angle between the northern part of the gyrocompass meridian and the bearing line.

Reverse gyrocompass bearing is the direction opposite to the direction towards the object.

Gyrocompass correction is the angle in the plane of the true horizon between the true and gyrocompass meridians.

Types of ship motion. Elements of pitching

The rocking of the ship- oscillatory movements that a ship makes around its equilibrium position. There are three types of ship motion: a) vertical- vibrations of the vessel in the vertical plane in the form of periodic translational movements; b) onboard(or lateral) - oscillations of the ship in the plane of the frames in the form of angular movements; V) keel(or longitudinal) rolling - vibrations of the vessel in the center plane, also in the form of angular movements. When a ship is sailing on a rough water surface, all three types of motion often occur simultaneously or in various combinations.

Two types of oscillations of a ship when pitching: free(on still water), which occur by inertia after the cessation of the forces that caused them, and forced, which are caused by external periodically applied forces, for example, sea waves.

Pitching elements:

Amplitude of pitching (a) - the greatest deviation of the ship from its original position, measured in degrees. Pitching range(b) - the sum of two successive amplitudes (the inclination of the vessel on both sides).

Rolling period (in)- the time between two successive inclinations or the time during which the ship completes a complete cycle of oscillations, returning to the position at which the countdown began.

28 (10.1) Name the features of the steering control modes: “simple”, “following”, “automatic”

The agility of a vessel means its ability to change the direction of movement under the influence of the rudder (controls) and move along a trajectory of a given curvature. The movement of a vessel with the rudder shifted along a curved path is called circulation. (Different points of the ship’s hull during circulation move along different trajectories, therefore, unless specifically stated, the ship’s trajectory means the trajectory of its CG.)

With such a movement, the bow of the vessel (Fig. 1) is directed into the circulation, and the angle a 0 between the tangent to the CG trajectory and the center plane (DP) is called angle drift on circulation.

The center of curvature of this section of the trajectory is called the center of circulation (CC), and the distance from the CC to the CG (point O) - circulation radius.

In Fig. 1 it can be seen that different points along the length of the vessel move along trajectories with different radii of curvature with a common center of gravity and have different drift angles. For a point located at the aft end, the radius of circulation and the drift angle are maximum. On DP the vessel has a special point - turning pole (PP), for which the drift angle is equal to zero, The position of the PP, determined by the perpendicular lowered from the CC to the DP, is shifted from the CG along the DP to the bow by approximately 0.4 of the ship’s length; The magnitude of this displacement varies within small limits on different vessels. For points on the DP located along different sides from the PP, the drift angles have opposite signs. The angular velocity of the vessel during the circulation process first quickly increases, reaches a maximum, and then, as the point of application of the force Y o shifts toward the stern, decreases slightly. When the moments of forces P y And Y o will balance each other, the angular velocity acquires a steady value.

The vessel's circulation is divided into three periods: maneuvering, equal to the time of shifting the rudder; evolutionary - from the moment the rudder is shifted until the moment when the linear and angular velocities of the vessel acquire steady-state values; steady - from the end of the evolutionary period until the steering wheel remains in the shifted position. The elements characterizing a typical circulation are (Fig. 2):

Extension l 1 - the distance by which the ship's center of gravity moves in the direction of the initial course from the moment the rudder is shifted until the course changes by 90°;

Direct displacement l 2 - the distance from the initial position of the ship’s CG to its position after a 90° turn, measured normal to the original direction of the ship’s movement;

Reverse bias l 3 - the distance by which, under the influence of the lateral force of the rudder, the ship’s center of gravity shifts from the initial course line in the direction opposite to the direction of rotation;

Tactical circulation diameter D T - the shortest distance between the vessel’s DP at the beginning of the turn and its position at the moment of the course change by 180°;

The diameter of the steady circulation D mouth is the distance between the positions of the vessel's DP for two successive courses, differing by 180°, during steady motion.

It is impossible to define a clear boundary between the evolutionary period and the established circulation, since the change in the elements of movement fades out gradually. Conventionally, we can assume that after a rotation of 160-180° the movement acquires a character close to established. Thus, practical maneuvering of the vessel always occurs under unsteady conditions.

It is more convenient to express circulation elements during maneuvering in dimensionless form - in body lengths:

in this form it is easier to compare the agility of different vessels. The smaller the dimensionless value, the better the agility.

The circulation elements of a conventional transport vessel for a given rudder angle are practically independent of the initial speed at steady state engine operation. However, if you increase the propeller speed when shifting the rudder, the ship will make a sharper turn. , than with a constant mode of the main engine (MA).

Attached are two drawings.

Fig.1 Fig.2

Circulation call the trajectory described by the ship's center of gravity when moving with the rudder deflected at a constant angle. Circulation is characterized by linear and angular velocities, radius of curvature and drift angle. The angle between the linear velocity vector of the vessel and the DP is called drift angle. These characteristics do not remain constant throughout the maneuver.

Circulation is usually divided into three periods: maneuverable, evolutionary and steady.

Maneuvering period– the period during which the steering wheel is shifted to a certain angle. From the moment the rudder begins to shift, the ship begins to drift in the direction opposite to the rudder shift, and at the same time begins to turn in the direction of the rudder shift. During this period, the trajectory of the vessel's CG moves from a rectilinear one to a curved one with the center of curvature on the side opposite to the side of the rudder; the ship's speed drops.

Evolutionary period– the period starting from the moment of the end of the rudder shift and continuing until the end of the change in the drift angle, linear and angular velocity. This period is characterized by a further decrease in speed (up to 30 - 50%), a change in roll to the outer side and a sharp movement of the stern to the outer side.

Steady circulation period– the period that begins at the end of the evolutionary period is characterized by the balance of forces acting on the ship: the thrust of the propeller, hydrodynamic forces on the rudder and hull, centrifugal force. The trajectory of the ship's CG turns into the trajectory of a regular circle or close to it.

Geometrically, the circulation trajectory is characterized by the following elements:

D o – steady circulation diameter– the distance between the diametrical planes of the vessel on two successive courses, differing by 180° during steady motion;

D c – tactical circulation diameter– the distance between the positions of the vessel’s DP before the start of the turn and at the moment of changing course by 180°;

l 1 – extension– the distance between the ship’s CG positions before entering circulation to the circulation point at which the ship’s course changes by 90°;

l 2 – forward bias– the distance from the initial position of the ship’s CG to its position after a 90° turn, measured normal to the initial direction of the ship’s movement;

l 3 – reverse bias– the greatest displacement of the vessel’s CG as a result of drift in the direction opposite to the side of the rudder (the reverse displacement usually does not exceed the width of vessel B, and on some vessels it is completely absent);

T c–circulation period– time to turn the ship 360°.

Rice. 1.8. Trajectory of the vessel in circulation

The above-listed characteristics of the circulation of medium-tonnage sea transport vessels with the rudder fully on board can be expressed in fractions of the length of the vessel and through the diameter of the established circulation by the following relations:

D o = (3 ÷ 6)L; D c = (0.9 ÷ 1.2) D y; l 1 = (0.6 ÷ 1.2)D o;

l 2 = (0.5 ÷ 0.6)D o; l 3 = (0.05 ÷ 0.1)D o; T c = πD o /V c.

Usually the values D o; D c; l 1; l 2 ; l 3 expressed in relative form (divided by the length of the vessel L) – it is easier to compare the agility of different vessels. The smaller the dimensionless ratio, the better the agility.

Circulation speed for large-capacity vessels is reduced by 30% when the rudder is shifted to the side, and by half when turning 180°.

The following points should also be noted:

a) the initial speed affects not so much D o, how much for its time and extension, and only in high-speed ships are noticeable D o V big side;

b) when the vessel enters the circulation path, it acquires a list on the outer side, the value of which, according to the Register rules, should not exceed 12 °;

c) if during circulation the number of main engine revolutions is increased, the ship will make a sharper turn;

d) when performing circulation in cramped conditions, it should be taken into account that the stern and bow ends of the vessel describe a strip of considerable width, which becomes commensurate with the width of the fairway.

The curved line that the ship's center of gravity describes when the rudder is shifted to a certain constant angle is called circulation. There are the following three characteristic periods of vessel circulation. Maneuverable, during which the rudder is shifted (10-15 seconds when shifted on board). Evolutionary, during which the coordinate parameters of the vessel change (the angle of the vessel's drift and its angular and linear speeds).

It begins with the end of the rudder shift and ends approximately after the ship's course changes by 90-120°. Steady, during which the coordinate parameters of the vessel remain unchanged. In this case, the curve takes the shape of a regular circle, the diameter of which is called the diameter of the steady circulation Dc (Fig. 41). It is a measure of the ship's agility and is expressed in the length of the ship's hull.

The vessel's circulation is characterized by: tactical diameter DT - the distance in a straight line between the line of the initial course and the center line of the vessel when turning 180°, D = 1.1 Dts; advancement 11 - the distance between the position of the vessel’s center of gravity at the moment the rudder begins to shift and the centerline of the vessel when the course changes by 90°, l1 = 0.6 / 1.20 c; forward bias l2 - the distance by which the ship’s center of gravity shifts from the initial course line when turning 90°, l2 = 0.25 + 0.5 Dts, and reverse bias l³ - the distance by which the vessel’s center of gravity shifts from the line of the initial course during circulation in the direction opposite to the turn, l³ ~ up to 0.1 Dc.

A vessel in circulation always acquires a drift, while its center plane is not located tangentially to the circle (its bow is always located inside the circulation).

The angle between the centerline plane of the vessel and the tangent to the circulation is called drift angle As a result, the vessel in circulation occupies a strip significantly larger than the width of the vessel. The drift angle and reverse displacement must always be taken into account when performing maneuvers in limited water areas.

During circulation, the speed of the vessel decreases to 35% with a constant number of propulsion revolutions and a list appears. In displacement vessels, the roll occurs on the side that is located on the outside of the circulation, and can reach a significant value. The vessel's circulation is also characterized by its period.

This period is the period of time during which the ship describes a complete circulation, i.e., from the moment the turn actually begins until the ship returns to its original course.

During navigation, it is rarely necessary to perform a complete circulation, but its elements must be taken into account when changing course (turning the ship).

When calculating graphically, the value of the tactical circulation diameter Dt or its radius is taken into account

Definition of Circulation Elements

Circulation elements are usually determined during sea acceptance tests at three main forward speeds (full, medium and low) and when the rudder is shifted by 15° and “on board” (to the maximum angle) in both directions for ships with one and three propellers and in one - for ships with two and four propellers.

There are several ways to define circulation elements. The most common of them are: the moving base method; at two horizontal angles; along the alignment and horizontal corners.

Rice. 42

Movable base method is as follows. A buoy is installed in the testing area. On the ship, at a certain distance from each other (let's call it the basis), there are two observers with sextants (one in the bow and the other at the stern). The vessel moves at a certain distance from the buoy at a given speed, and at the command of the test director, usually 20-25 seconds from the moment the rudder is shifted, observers simultaneously measure the angles between the center plane and the buoy, at the same moment the compass heading is noted. Then, on the tablet, graphs of changes in angle values (heading and ship course) are plotted over time.

In Fig. Figure 42 shows the construction of the position of the vessel during circulation at the first moment of observation. Point O is the location of the buoy, line N0 is the meridian. In accordance with the course of the vessel KK at the time of the first observation, we draw line I through point O and on this line at point O we construct heading angles KUa1 AND KUv1, measured by observers. Then we set aside a segment of the OS, on a scale equal to the base.

Then from point C we draw a line CP parallel to OD. Next, from the point of intersection of lines CF with OE, draw line II, parallel to the course line, until it intersects with OD. The position of the segment AB will correspond to the position of the centerline plane of the vessel in circulation at the first moment of observation. If you make such constructions at every moment of observation - from the beginning of the maneuver to the turn to the opposite course, then you can draw the circulation, determine the size of its diameter, the width of the lane occupied by the vessel on the circulation, the drift angle, etc. The roll angle is determined by the inclinometer.

At two horizontal angles circulation elements can be determined in an area where there are three landmarks clearly visible from the ship. Moreover, their location must be such that the angles measured from the vessel in circulation between the middle and extreme landmarks vary within the range of no less than 30° and no more than 150°.

The ship must move at a given speed. From the moment the rudder is shifted, every 20-25 seconds, two observers on command simultaneously measure horizontal angles with sextants (Fig. 43, a) between objects AB (a) and BC (b). Then, on a large-scale map or plan, all observed points are plotted from the beginning of the circulation until the ship turns to the opposite course (P1, P2, etc.) and a smooth curve is drawn through them, which will be the circulation. Next, the diameter of the circulation and its other elements are determined.

Rice. 43

Along the alignment and horizontal corners it is possible to determine only the value of the tactical circulation diameter DT. To do this, it is necessary to have a target (Fig. 43, b) and another landmark located perpendicular to the target line at a known distance l. The vessel must approach the target line at a steady speed with a course perpendicular to it. At the moment of crossing the target, shift the rudder to the set angle, turn on the stopwatch and measure the angle a1 between the target line and landmark E. When the vessel arrives on a reverse course to the target line, stop the stopwatch, measure the angle a2 between the target line and landmark E.

The calculation of the tactical diameter is obtained from the expression

The accuracy of the calculated DT value will depend on the accuracy of the measured angles and the distance l.

The time counted by a stopwatch will give the duration half cycle of circulation, i.e. the time spent by the ship when turning 180°.

Circulation table

Suppose that on a ship sailing on course AK1 (Fig. 44), at point B the rudder was shifted to the starboard side and, having described an arc S, at point C it lay on a new course SK2. Let us take arc S as the arc of a circle, the center of which is located at point O. By connecting points B, E and C with the center of circulation O, we obtain two pairs of symmetrically located right triangles EBF = ECF and BOE = COE, from which we obtain

where

and

Rice. 44

When the radius of circulation Rt and the angle of rotation a are known, then using formulas (31) and (32) it is possible to calculate the length d of the intermediate course (IR cp) and the distance d1 to the point of intersection of the new course with the original one.

In addition to these quantities, in practice there is a need to know the length of the turning path (arc) S and the turning time. To calculate S, use the formula

or
Where

To calculate the time of rotation T at a given angle, use the formula
To speed up graphical constructions on the map associated with calculations of the turning path length S, turning time Г, turning angle by

The intermediate course α/2 of the length d of the intermediate course and the distance d1 at turning angles up to 150° are prepared in advance by circulation tables. They are compiled for different rudder angles, travel speeds and vessel loading (laden and empty).

An example of such a table for a rudder angle of 15° at a speed of 10 knots, D T = 3 kbt, T 180 = 4 min is presented in Table 4. For rotation angles of more than 150°, such tables are not compiled, since the value of d1 becomes too large (d1 = RC t g a/2, a tgl80°=~). intermediate course length d intermediate course and distance

Table 4

Table 30 (MT-63) makes it possible to select, based on the values of Rts and T 180, the circulation elements for different angles of rotation on a new course: S, d, d 1 T.

Circulation accounting methods

The moments of the vessel's turn to change course are usually calculated in advance and the turns are performed: abeam any lighthouse or sign; at the intersection of the secant alignment; upon arrival on the line of a pre-selected bearing of any landmark; according to the lag of a pre-calculated countdown or according to a pre-calculated point in time by the clock.

In all cases, the expected lag readings and clock time must be calculated for the intended turning moment. If it turns out that the actual log reading or clock time diverges from the pre-calculated ones, then it is necessary to immediately find an error in the calculations.

Having determined the moment of turning, they give a command to the helmsman, note the countdown of the log and the time on the clock. Then, on a map of scale 1:500,000 and larger, the necessary graphical constructions are made to plot the circulation. When sailing away from the coast, circulation elements are taken into account only with frequent course changes and when turning at an angle of more than 30°.

To calculate the angle of rotation a, use the following formulas: when turning to the right

and when turning left
Circulation elements can be taken into account using tabular or graphical techniques.

Table method. Let the ship follow course IR1 and make a turn at point A (Fig. 45, a). From this point at an angle a/2 to IR1, an intermediate course line is drawn, on which the value d selected from the table is plotted. 30 (MT-63). Point B will indicate the end of the turn. From this point a new course IR2 is carried out.

Rice. 45

In the case when the turning point A (Fig. 45, b) to the new course is unknown, proceed as follows. From point O (the point of intersection of courses), the distance dl9 selected from the table is set aside. 30 (MT-63) in the opposite direction along IK1 and IK2. The resulting points A and B will show the beginning and end of the turn, respectively. If the angle a > 150°, then the intermediate true course is preliminarily calculated using the formula
After this, from an arbitrary point F on the line IR1 (Fig. 45, c), a line IRsr is drawn and a segment FG = d is laid off from the same point on this line. Then they lay the line of the new course at such a distance from the line of the original course that between them above point F a segment equal in size to d can be accommodated. From point G, a parallel IRg is drawn, which, at the intersection with line IR2, will give point B - the end point of the turn to a new course, and a notch from point B with a compass with an opening equal to d, will give on line IR1 the starting point of turn A. In these cases Circulation curves (arcs) are usually not carried out, except in cases of navigation in narrow places, skerries, etc.

Graphic technique. Let us assume that the ship follows IR1 (Fig. 46, a), and from the starting point of the turn A sets a new course. From this point we restore the perpendicular to the line IR1 in the direction of the turn and on the perpendicular we plot the distance RC equal to the radius of circulation on the map scale. From the resulting point O as from the center with radius OA we describe the arc AB". To this arc we draw a tangent corresponding to the line IC2, the point of tangency B will be the end point of the turn.

Rice. 46

In cases where the starting and ending points of the turn are unknown, proceed as follows. Line IR2 is laid in the middle of the fairway or along the line of the target (Fig. 46, b), on which the ship should lie after the turn. Then, at arbitrary points on lines IR1 and IR2 (points A1 and B2), perpendiculars are restored, at which distances equal to the radius of circulation RC are laid. From the obtained points O1 and O2, lines are drawn parallel to the course lines. From the point of intersection of these lines (point O), as from a center with a radius equal to O1A1 (02B1), an arc is described; the points of tangency A and B with the true course lines will indicate the beginning and end of the turn.

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To judge the turning ability of a vessel, circulation is usually analyzed as the simplest type of curvilinear motion of a vessel.

The circulation of a ship is its movement with the control element deflected at a constant angle, as well as the trajectory described by the center of gravity of the ship.

In terms of time, the circulation movement of the vessel is divided into three periods:

1. Maneuvering period - during this period the control is shifted to a given angle; with further movement, the shift angle remains unchanged. During the maneuvering period, single vessels are just beginning to turn, while pushed convoys often continue to move in a straight line.

2. The evolutionary period (evolution) begins from the moment the control is transferred and continues until the moment when all parameters are established and the center of gravity of the vessel or convoy begins to describe a trajectory in the form of a circle.

3. The steady-state circulation period begins from the end of the evolutionary period and continues as long as the angle of shift of the ship's control remains constant.

The trajectory of the vessel in the third period of circulation is usually called steady circulation. A distinctive feature of the established circulation is the constancy of the movement characteristics and their small dependence on the initial conditions.

The diagram shows the following circulation characteristics used to quantify it:

− diameter of the established circulation along the CG of the vessel or train;

− diameter of the established circulation along the stern of the vessel or convoy;

− tactical circulation diameter (the distance between the ship’s DP on a straight course and after turning it by 180°);

− circulation advance (step) (displacement of the vessel’s CG in the direction of the initial straight-line motion until the vessel turns 90°);

− direct displacement of the vessel in circulation (distance from the line of the initial straight course to the CG of the vessel turned 90°);

− reverse displacement of the vessel during circulation (the greatest distance by which the CG of the vessel shifts in the direction opposite to the rudder shift);

− the angle of the ship's drift in the circulation (the angle between the vessel's DP and the speed vector in the circulation);

− pole of the ship’s turn (the point on the ship’s DP or its extension at which = 0).

In general, the picture of the vessel’s movement by circulation periods comes down to the following. If on a ship moving in a straight line, the controls are shifted to a certain angle, then a hydrodynamic force arises on the rudders or rotary nozzles, one of the components of which will be directed normally to the centerline plane of the ship (lateral force).

Under the influence of lateral force, the vessel shifts in the direction opposite to the direction of the control shift. A reverse displacement of the vessel occurs, the greatest value of which will be observed at the stern perpendicular point. The reverse displacement of the vessel leads to the appearance of a drift angle, and the flow, which initially ran along the center plane, begins to flow onto the side opposite to the direction of the control shift. This leads to the formation of a lateral hydrodynamic force on the ship’s hull, directed towards the repositioning of the controls and applied, as a rule, to the bow from the ship’s CG.

Under the influence of moments from lateral forces on the controls and the hull, the vessel rotates around a vertical axis in the direction of the shifted control. The centrifugal force of inertia arising in this case is balanced by the lateral steering and hull forces, and the moment of these forces is balanced by the moment of inertia forces.

During the evolutionary period, an intensive increase in the drift angle is observed, which leads to a decrease in the angle of attack of the steering wheel or rotary nozzle and a corresponding decrease in the magnitude of the steering force. Simultaneously with the increase in the drift angle, the force acting on the hull increases, and the point of its application gradually shifts towards the stern. During the same period, an increase in the angular speed of rotation and a decrease in the radius of curvature of the trajectory are observed, which, despite the decrease in the linear speed of movement, causes an increase in the centrifugal force of inertia.

Steady circulation occurs when the forces and moments acting on the controls, the ship's hull, as well as inertial forces and moments are balanced and cease to change over time. This determines the stabilization of the vessel’s motion parameters, which take constant values at an angle of rotation from the initial course line of 90÷130° for single vessels and 60÷80° for pushed convoys.

With this movement, the bow of the vessel (Fig. 1) is directed into the circulation, and the angle a0 between the tangent to the CG trajectory and the center plane (DP) is called angledrift on circulation.

The center of curvature of this section of the trajectory is called the center of circulation (CC), and the distance from the CC to the CG (point O) - circulation radius.

In Fig. 1 it can be seen that different points along the length of the vessel move along trajectories with different radii of curvature with a common center of gravity and have different drift angles. For a point located at the aft end, the radius of circulation and the drift angle are maximum. On DP the vessel has a special point - turning pole(PP), for which the drift angle is equal to zero, The position of the PP, determined by the perpendicular lowered from the CC to the DP, is shifted from the CG along the DP to the bow by approximately 0.4 of the ship’s length; The magnitude of this displacement varies within small limits on different vessels. For points on the DP located on opposite sides of the PP, the drift angles have opposite signs. The angular velocity of the vessel during the circulation process first quickly increases, reaches a maximum, and then, as the point of application of the force Yo shifts towards the stern, it decreases slightly. When the moments of the RuiYo forces balance each other, the angular velocity acquires a steady-state value.

Extension l1 is the distance by which the ship’s center of gravity moves in the direction of the initial course from the moment the rudder is shifted until the course changes by 90°;

Direct displacement l2 - the distance from the initial position of the ship’s CG to its position after a 90° turn, measured normal to the initial direction of the ship’s movement;

Reverse displacement l3 is the distance by which, under the influence of the lateral force of the rudder, the ship’s center of gravity shifts from the original course line in the direction opposite to the direction of rotation;

Tactical circulation diameter DT - the shortest distance between the vessel’s DP at the beginning of the turn and its position at the moment of a 180° course change;

The diameter of the steady circulation Dset is the distance between the positions of the vessel's DP for two successive courses, differing by 180°, during steady motion.

It is impossible to define a clear boundary between the evolutionary period and the established circulation, since the change in the elements of movement fades out gradually. Conventionally, we can assume that after a rotation of 160-180°, the movement acquires a character close to the steady state. Thus, practical maneuvering of the vessel always occurs under unsteady conditions.

It is more convenient to express circulation elements during maneuvering in dimensionless form - in body lengths:

in this form it is easier to compare the agility of different vessels. The smaller the dimensionless value, the better the agility.

Attached are two drawings.

Fig.1 Fig.2

Circulation is usually divided into three periods: maneuverable, evolutionary and steady.

Geometrically, the circulation trajectory is characterized by the following elements:

Do – steady circulation diameter– the distance between the diametrical planes of the vessel on two successive courses, differing by 180° during steady motion;

DC – tactical circulation diameter– the distance between the positions of the vessel’s DP before the start of the turn and at the moment of changing course by 180°;

l1 – extension– the distance between the ship’s CG positions before entering circulation to the circulation point at which the ship’s course changes by 90°;

l2 – forward bias– the distance from the initial position of the ship’s CG to its position after a 90° turn, measured normal to the initial direction of the ship’s movement;

l3 – reverse bias– the greatest displacement of the vessel’s CG as a result of drift in the direction opposite to the side of the rudder (the reverse displacement usually does not exceed the width of vessel B, and on some vessels it is completely absent);

TC–circulation period– time to turn the ship 360°.

Rice. 1.8. Trajectory of the vessel in circulation

Do = (3 ÷ 6)L; Dts = (0.9 ÷ 1.2)Dу; l1 = (0.6 ÷ 1.2)Do;

l2 = (0.5 ÷ 0.6) Do; l3 = (0.05 ÷ 0.1)Do; Tc = πDo/Vc.

Usually the values Do; DC; l1; l2; l3 expressed in relative form (divided by the length of the vessel L) – it is easier to compare the agility of different vessels. The smaller the dimensionless ratio, the better the agility.

Circulation speed for large-capacity vessels is reduced by 30% when the rudder is shifted to the side, and by half when turning 180°.

The following points should also be noted:

a) the initial speed affects not so much Do, how much for its time and extension, and only in high-speed ships are noticeable Do upward;

b) when the vessel enters the circulation path, it acquires a list on the outer side, the value of which, according to the Register rules, should not exceed 12 °;

c) if during circulation the number of main engine revolutions is increased, the ship will make a sharper turn;