Calculation of circulation elements. Vessel circulation and its elements Gyrocompass directions. Gyrocompass correction

Vessel circulation.

Circulation and its periods.

Circulation is the process of changing the kinematic parameters of a vessel moving rectilinearly and uniformly in response to a stepwise shift of the rudder, starting from the moment it was set for testing. Trajectory, which the ship's CM describes in this process is also called circulation.

The circulation movement in time is usually divided into three periods: maneuverable, evolutionary (transitional), established. Before defining these periods, let us clarify what is meant by the steady curvilinear motion of the vessel.

Steady linear motion The movement of a vessel is called its movement in one course at a constant speed.

Steady rotational motion represents the rotation of the vessel relative to the CM with a constant angular velocity.

The curvilinear movement of the vessel consists of translational and rotational. Under steady curvilinear movement refers to the movement of a vessel in which, over time, the angular and linear velocity of the vessel's CM does not change either in magnitude or direction relative to the axes rigidly connected to the vessel. Thus, the steady curvilinear motion of the vessel is characterized by a constant angular velocity , drift angle and ground speed vessel.

In the process of circulation motion, the linear speed of the vessel takes the longest to reach a steady value. At the final stage, the approach of the linear speed of the vessel to the steady value is monotonous and slow. For large-tonnage vessels in circulation, the linear speed can reach a constant value after turning through an angle greater than 270°. In addition, in a steady circulation, the ship may experience small fluctuations in the drift angle and angular velocity. Therefore, the question arises from what point in time the vessel’s circling motion is considered steady.

Based on the boundary between evolutionary and steady-state movement accepted in the theory of automatic control, we can assume that the circulation movement of the vessel is established, when current values , , begin to differ from their established values
less than 3-5%.

Due to the fact that the drift angle in the circulation is not measured, and the linear speed of the vessel is measured with a large error, the moment after which the change in course becomes almost uniform is usually taken as the beginning of the steady circulation period. For medium-tonnage vessels, this moment occurs after the vessel has turned approximately 130°. However, studies show that during circulation motion the angular velocity is established faster than And . The drift angle and especially the linear speed of the vessel reach 3-5% closer to their steady values ​​later.

Now we can give definitions of circulation periods.

Maneuvering period (
) - the period of shifting the rudder from zero to the selected value, starting from the moment the steering device is assigned to work out the selected value.

Evolutionary period ( ) - the time interval from the moment the rudder is shifted until the moment when the curvilinear movement of the vessel becomes steady.

The steady-state period begins from the end of the second period and continues as long as the steering wheel remains in the specified position.

To evaluate and compare the controllability of ships, they are used circulation under reference conditions. The beginning of the circulation corresponds to the moment the rudder is set, and the end corresponds to the moment the vessel's DP rotates through an angle of 360°. The trajectory of such circulation is shown schematically in Fig. 3.1

Fig. 3.1 Vessel circulation diagram.

Circulation parameters.

When considering circulation, its main and additional elements are distinguished.

The following circulation parameters are the main ones.

Steady circulation diameter - the distance between the positions of the ship's DP on opposite courses during steady circulation movement, usually between the DP at the moment of a 180° turn and the DP at the moment of a 360° turn

Tactical circulation diameter - the distance between the line of the initial course and the ship’s DP after turning it by 180. Tactical diameter can be (0.9-1.2)

Extension - the distance between the positions of the ship's CM at the moment the rudder begins to shift and at the moment after turning the DP by 90, measured in the direction of the initial course. Approximately

Forward offset - the distance from the initial course line to the center of gravity of the ship, turned 90°. It is about
.

Reverse bias - the greatest deviation of the ship's center of gravity from the initial course line in the direction opposite to the rudder shift. The reverse bias is small and amounts to
.

Drift angle - the angle between the DP and the ship's speed vector.

Circulation period - the time interval from the moment the rudder begins to shift until the ship turns 360°.

Of the additional circulation parameters, the most important from the point of view of ensuring maneuvering safety are.

Half-width of sweep strip - the distance from the circulation trajectory at which the points of the body most distant from it are located during circulation;

Distance - the distance from the position of the ship's center of gravity at the initial moment of circulation to the point at which the ship's hull leaves the line of the initial course;

Maximum extension of vessel tip - the greatest distance along the initial course from the position of the ship’s center of gravity at the initial moment of circulation to the extreme tip of the ship during the maneuver (can be determined similarly maximum center of mass extension vessel, simply called maximum extension);

Maximum forward displacement of the tip of the vessel - the largest lateral deviation from the initial course line to the extreme tip of the vessel during circulation (can be determined similarly maximum forward displacement of the center of mass a vessel simply called maximum forward displacement).

The main parameter of the vessel's turning ability, the diameter of the steady circulation , depends little on the speed of the vessel before the start of the maneuver. This fact has been confirmed by numerous field tests. However, the extension of the vessel does not have this property and depends on the initial speed of the vessel. When circulating at low speed, the extension is about 10-5-20% less than the extension at full speed. Therefore, in a limited water area in the absence of wind, before making a turn at a large angle, it is advisable to slow down.

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 vessel 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 vessel.

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 ship's drift angle during the circulation (the angle between the vessel's DP and the speed vector during 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.

For small-tonnage vessels (D< 10000 т), можно использовать формулу Шенхера:

For large-tonnage vessels, you can use G. Hammer’s formulas:

or
,

where  – rudder angle, rad;

V – volumetric displacement, m 3

F p – rudder area

C y – steering lift coefficient, C y =C р, calculated in the first part of the work, at α = 35˚;

L – length of the vessel between perpendiculars;

B – vessel width;

K – empirical coefficient depending on the ratio:

,

where S is the area of ​​the immersed part of the vessel’s DP, determined by the formula:

(m2),

where d is the vessel’s draft, m.

Coefficient K is determined by interpolation from Table 2.

table 2

V/(S L)

2.2. Diameter of circulation described by the aft end

The diameter of the circulation described by the aft end can be determined by the formula:

where L is the length of the vessel, m;

 – drift angle, degrees;

Dt – tactical circulation diameter, m.

The drift angle at steady circulation can be approximately found from the expression:

.

2.3. Tactical circulation diameter (at a rudder angle of 35˚)

The tactical circulation diameter (at a rudder angle of 35˚) will be found using the formulas:

- in ballast,

– in cargo,

where  is the coefficient of displacement completeness (Table 2);

The dependence of the circulation diameter on the rudder angle has the form:

Using this formula, find the tactical circulation diameter at a half-side rudder angle (15˚). Set the rudder angle in degrees.

Data for calculating circulation diameters are presented in Table 3.

2.4. Extension of the vessel in circulation

The vessel's advance during circulation can be determined by the formula:

where V o is the initial speed of the vessel, m/s;

Tmp – dead interval time, s;

R c – average radius of circulation (R c =D t /2);

K = IR 2 – IR 1 – rotation angle, degrees (90°);

B – width of the vessel, m.

2.5. Lane width vessels on circulation

The width of the vessel's traffic lane in circulation is determined by the formula:

2.6. Steady-state circulation period

The period of steady circulation is determined by the formula:

, (seconds),

where V c is the speed of the vessel at steady circulation m/s;

V c = 0.58V 0 when the rudder is shifted “on board” and

V c = 0.79V 0 when the steering wheel is shifted halfway ( = 15°).

The procedure for calculating circulation elements:

We calculate the coefficient K;

We calculate the diameter of the steady circulation using both formulas - Shenherr and Hammer;

We calculate the drift angle by substituting D C corresponding to the tonnage of the vessel;

We calculate the tactical circulation diameter for a loaded ship with the rudder on board;

We calculate the tactical circulation diameter for a ship with the rudder shifted halfway;

We calculate the diameter of the stern circulation;

We determine the extension of the vessel when loaded;

We calculate the width of the vessel's traffic lane;

We determine the period of steady-state circulation of the vessel while loaded, using D Ts for our version of the vessel.

Table 3

Tasks for calculating circulation elements

	Vessel name	, m 3	L, m		d,m	T mp, s
	"B. Butoma" OBO
	Tanker No. 1
	Tanker No. 2
	Tanker No. 3
	"A. Tupolev"
	“Hood. Moore"
	"Atlantic"
	"A. Kaverznev"
	Tanker No. 4
	Bulk carrier No. 1
	Bulk carrier No. 2
	Bulk carrier No. 3
	Tanker No. 4
	Container ship
	Ro-Ro vessel

Vessel circulation

Under agility vessel implied his ability change direction movement under influence steering wheel (funds management) And move By trajectories given curvature.

Movement vessel With rearranged driving By curvilinear trajectories called circulation.

Rice. 2.17

The vessel's circulation is divided into three periods: maneuverable , equal to the rudder shift time; evolutionary - from the moment the rudder is shifted until the moment when the linear and angular velocity of the vessel acquire steady-state values; steady - from the end of the evolutionary period until the steering wheel remains in the shifted position.

Rice. 2.18

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 gradually. Conventionally, we can assume that after a rotation of 160 - 180 O, the movement acquires a character close to 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:

circulation ship steering wheel maneuvering

L 1 = L 1 /L; L 2 = L 2 /L; L 3 = L 3 /L; D T = D T /L; D mouth = D mouth /L,

V like this form easier compare between yourself agility various ships. How less dimensionless size, those better 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 unchangeable main engine mode.

Determination of circulation elements from natural observations

When performing a circulation, you can determine its elements if you make sequential determinations of the ship’s position using some landmarks at short time intervals (15 - 30 s). At the time of each observation, the measured navigation parameters and the course of the vessel are recorded. By plotting the observed points on the tablet and connecting them with a smooth curve, the ship’s trajectory is obtained. From which circulation elements are removed on an accepted scale.

Determinations of the vessel's position can be obtained from the bearing and distances of a free-floating landmark, such as a raft. With this method, the influence of an unknown current is automatically eliminated, and a special testing ground is not required.

METHODOLOGICAL INSTRUCTIONS

for completing coursework in the discipline “Ship Control”

Subject: « Calculation of circulation elements and inertial characteristics of the vessel »

1. General provisions of the course work

In accordance with IMO Resolution A.160 (ES.IV) and paragraph 10 of Regulation II/I of the International Convention on Standards of Training, Certification and Watchkeeping for Seafarers, 1978, information on maneuvering characteristics must be provided on each ship.

Completing course work in the discipline “Ship Control” provides for a more in-depth study of issues related to the determination of maneuverable elements of the vessel.

The RC task includes calculations of the circulation elements and inertial properties of the vessel, as well as the compilation of a standard table of maneuvering elements based on the results obtained.

Course work is carried out by 5th year cadets of the Navigation Faculty in the 10th semester after studying Section 3 (topic 13–17) of the standard program of the discipline “Ship Control”.

Coursework includes the following topics:

1. Determination of the vessel's circulation elements by calculation.

2. Calculation of the inertial characteristics of the vessel, including passive braking, active braking and acceleration of the vessel under various motion modes.

3. Calculation of the increase in vessel draft when sailing in shallow water and in canals.

4. Drawing up a table of maneuverable elements of the vessel based on the calculation results (calculation and graphic part of the work).

Coursework is prepared in accordance with existing requirements.

The dimensions of physical quantities in the formulas used must correspond to those given in the “Conventions” section, unless otherwise specified in the text of the MU.

After checking the course work by the teacher, the student defends it at the department at the appointed time.

2. Conventions

Δ – volumetric displacement, m 3

D – weight displacement of the vessel, t

L – length of the vessel between perpendiculars, m

B – vessel width, m

d – draft, m

V 0 – full speed, m/s

V n – initial speed for a specific maneuver, m/s

C in – to-total completeness

C m - completeness of the mid-frame

C d – DP completeness level

With y - set of lifting force of the rudder blade

η – propulsive coefficient

λ 11 – coefficient of added mass

α – angle of rotation of the vessel, degrees

β – angle of drift of the vessel in circulation, degrees

δ р – rudder angle, degrees

θ – roll angle, degrees

ψ – trim angle, degrees

l р – rudder blade length, m

h r – height of the rudder blade, m

λ р – relative elongation of the rudder blade

A r – rudder blade area, m 2

A d – area of ​​the immersed part of the vessel’s DP, m2

A m – area of ​​the immersed part of the midship frame, m 2

D in – propeller diameter, m

H in – propeller pitch, m

n 0 – propeller rotation speed, 1/s

N i – indicated power of the main engine, hp.

N e – effective power, hp.

M w – moment on mooring lines

Рзх – screw stop on the mooring lines in reverse, tf

T 1 – time of the first period, s

T 2 – time of the second period, s

T r – vessel reaction time to shifting the rudder, s

Tc – circulation period, s

D 0 – diameter of steady circulation, m

Dt – tactical circulation diameter, m

D k – circulation diameter of the stern end of the vessel, m

l 1 – extension, m

l 2 – forward displacement, m

ΔS – circulation lane width, m

S 0 – inertial constant, m

S t – braking distance during active braking, m

t t – time of active braking, s

S p – braking distance during passive braking, m

t p – passive braking time, s

S р – vessel acceleration distance, m

t r – vessel acceleration time, min

g – free fall acceleration, m/s 2

3. Assignment for the section “Determination of vessel circulation elements”

All circulation elements are determined for two displacements of the vessel (loaded and in ballast) from full forward speed with the rudder position “on board” (35°) and “half on board” (15°).

The calculation results are summarized in a table and a circulation curve is constructed from them for two displacements and two rudder shifts.

3.1 Methodology for calculating circulation elements

The diameter of the steady circulation, with some assumptions, is calculated using the empirical Shenherr formula.

where K 1 is an empirical coefficient depending on the ratio;

.

Table of coefficient values ​​K 1

	0,05	0,06	0,07	0,08	0,09	0,10	0,11	0,12	0,13	0,14	0,15
K 1	1,41	1,10	0,85	0,67	0,55	0,46	0,40	0,37	0,36	0,35	0,34

The area of ​​the rudder blade is determined by the formula:

where A is an empirical coefficient determined by the formula:

The rudder blade lift coefficient C y can be found using the formula:

,

(calculated to accept ).

The tactical circulation diameter can be determined using the formulas:

– in cargo: ;

– in ballast: ,

where Dt is the tactical circulation diameter when the rudder is shifted “on board”.

The dependence of the tactical circulation diameter on the rudder angle is expressed by the formula:

.

Extension and direct displacement are calculated using the formulas:

,

,

where K 2 is an empirical coefficient determined by the formula:

,

where is the relative area of ​​the rudder blade, expressed as a percentage of the area of ​​the immersed part of the DP:

.

The trim angle is determined by the formula:

.

The circulation diameter of the stern end of the vessel can be determined by the formula:

,

The forward velocity in a steady circulation is determined by approximate formulas:

when shifting the steering wheel “on board”;

when shifting the steering wheel "half board"

The period of steady circulation is determined by the formula:

The width of the vessel's traffic lane in circulation is determined by the formula:

3.2 Methodology for constructing the vessel’s circulation

The curve of the evolutionary period of circulation can be constructed from arcs of circles of variable radii. After the vessel turns through an angle of 180°, the radius of circulation is considered constant.

The value of the circulation radius constantly decreases from the largest value at the beginning of the turn to the value of the rotation radius of the established circulation.

The relative values ​​of the radii of unsteady circulation depending on the angle of rotation of the vessel and the rudder angle are shown in the table:

Table of values ​​of R n / R c

where R n – radius of unsteady circulation;

R 0 – radius of steady circulation.

The procedure for constructing circulation:

1. We draw the line of the initial course and plot on it, on a selected scale, the segment of the vessel’s path covered during the maneuvering period:

2. Calculate the average turning radius of the vessel at an angle of 10° according to the table data. To do this, for example, we select from the table the ratio of radii R n /R c at rotation angles of 5° and 10° at p = 35. These values ​​will be equal to 4.4 and 3.2.

Then we calculate the average turning radii of the vessel in the intervals from 10° to 30°, etc.

3. We construct (approximate) the vessel’s circulation curve from a number of circular arcs of various radii up to a rotation angle of 180°.

4. Having constructed the circulation curve in the evolutionary period, we complete the construction by describing a circle with the radius of the steady-state circulation up to a rotation angle of 360° (Fig. 1)

Rice. 1. Scheme of constructing the vessel circulation

4. Assignment for the section “Determination of the inertial characteristics of a vessel”

The inertial characteristics must be calculated for the maneuvers PPH-PZH, SPH-PZH, MPH-PZH, PPH-STOP, SPH-STOP, MPH-STOP, acceleration from the STOP-PPH position.

The listed characteristics are presented in the form of graphs for the displacement of the vessel in cargo and in ballast. The calculation results are summarized in the table:

cargo			ballast
PPH	SPH	MPH	PPH	SPH	MPH
A m, m 2	xxx	xxx	xxx	xxx
R 0 , t	xxx	xxx	xxx	xxx
S 1, m
V 2, m/s
M 1, t	xxx	xxx	xxx	xxx
S 2, m
M w	xxx	xxx	xxx	xxx	xxx
R zx, t	xxx	xxx	xxx	xxx	xxx
S 3, m
T 3, s
S t, s
t t, s
T avg, s
S St, m
WITH	xxx	xxx	xxx	xxx
T r, min.	xxx	xxx	xxx	xxx
S r, kb.	xxx	xxx	xxx	xxx

4.1 Methodology for determining the inertial characteristics of a vessel

4.1.1 Active braking

Active braking is calculated in three periods.

The calculation is carried out until the vessel comes to a complete stop (Vc = 0).

We accept , .

We determine the resistance of water to the movement of the vessel at full speed using the Rabinovich formula:

,

Where .

Inertial constant:

where m 1 is the mass of the vessel taking into account the added mass:

Reverse screw stop:

,

Where ;

N e = η ∙ N i ;

η can be determined by Emerson's formula:

.

Path covered in the first period:

S 1 = V n ∙ T 1

Vessel speed at the end of the second period:

.

The path traveled by the ship in the second period:

The path traveled by the ship in the third period:

.

Third period time:

General distance and braking time:

S t = S 1 + S 2 + S 3

t t = t 1 + t 2 + t 3

4.1.2 Passive braking

The calculation is carried out up to the speed V k = 0.2 ∙ V 0 .

Determine the passive braking time:

,

4.2 Ship acceleration

The vessel is calculated up to speed V к = 0.9 ∙ V 0

We determine the acceleration path and time using the empirical formula:

S р = 1.66 ∙ C

where C is the inertia coefficient, determined by the expression:

,

where V k, nodes;

5. Calculation of additional data for the table of maneuverable elements

5.1 Increasing the vessel's draft in shallow waters

The amount of increase in the vessel's draft in shallow water can be calculated using the formulas of the Institute of Hydrology and Fluid Mechanics of Ukraine (G.I. Sukhomela formula), modified by A.P. Kovalev:

at

where is the ratio of sea depth to average draft;

k is a coefficient depending on the ratio of the length to the width of the vessel.

Table for definitions of k:

The calculation results are presented in the form of a graph of the dependence dk = f(V) with the ratio h/d = 1.4 and Ak /Am = 4; 6; 8.

5.2 Increase in ship draft due to heeling

The increase in draft at different heel angles is calculated by the formula:

The calculation results are presented in tabular form for roll angles up to 10º.

5.3 Determination of depth reserve for wind waves

The wave depth reserve is determined in accordance with Appendix 3 of RSS-89 ​​for wave heights up to 4 meters and is presented in tabular form.

5.4 Man overboard maneuver

One of the types of maneuver of a vessel “Man Overboard” is a turn with access to a counter course. The execution of this maneuver depends on the choice of the angle of deviation of the vessel from the initial course (α). The magnitude of the angle α is determined by the formula:

where T p is the time for shifting the rudder from side to side (T p = 30 sec);

V av – average circulation speed, determined from the expression:

The maneuver scheme is constructed using the circulation data calculated in Section 3.

Literature

1. Voitkunsky Ya.I. and others. Handbook on the theory of the ship. – L.: Shipbuilding, 1983.

2. Demin S.I. Approximate analytical determination of vessel circulation elements. – CBNTI MMF, express information, series “Navigation and Communications”, vol. 7 (162), 1983, p. 14–18.

3. Znamerovsky V.P. Theoretical foundations of ship control. – L.: Publishing house LVIMU, 1974.

4. Karapuzov A.I. Results of full-scale tests and calculation of maneuverable elements of a Prometheus-type vessel. Sat. Safety of navigation and fishing, vol. 79. – L.: Transport, 1987.

5. Mastushkin Yu.M. Controllability of fishing vessels. – M.: Light and food industry, 1981.

7. Captain's Handbook (under the general editorship of Khabur B.P.). – M.: Transport, 1973.

8. Ship devices (under the general editorship of Aleksandrov M.N.): Textbook. – L.: Shipbuilding, 1988.

9. Tsurban A.I. Determination of maneuverable elements of the vessel. – M.: Transport, 1977.

10. Ship management and its technical operation (under the general editorship of A.I. Shchetinina). – M.: Transport, 1982.

11. Management of ships and convoys (Solarev N.F. and others). – M.: Transport, 1983.

12. Management of large-capacity vessels (Udalov V.I., Massanyuk I.F., Matevosyan V.G., Olshamovsky S.B.). – M.: Transport, 1986.

13.Kovalev A.P. On the issue of “subsidence” of the vessel in shallow water and in the canal. Express information, series “Safety of Navigation”, issue 5, 1934. – M.: Mortekhinformreklama.

14. Gire I.V. and others. Testing the seaworthiness of ships. – L.: Shipbuilding, 1977.

15. Olshamovsky S.B., Mironov A.V., Marichev I.V. Improving maneuvering of large-capacity vessels. Express information, series “Navigation communications and navigation safety”, vol. 11 (240). – M.: Mortekhinformreklama, 1990.

16. Experimental and theoretical determination of maneuverable elements of NMP vessels for the compilation of maneuver characteristics forms. Research report on UDC. 629.12.072/076. – Novorossiysk, 1989.