Steady-state circulation diameter. Vessel circulation

To quantify the circulation, geometric and time-velocity characteristics are used.

The geometric characteristics include the following quantities:

1. Steady-state circulation diameter – D c \u003d 2R c.

The diameter of the steady circulation is the diameter of the trajectory of the C.T. vessel in a steady circulation period.

For a comparative assessment of the agility of various ships, the value D c(or R c) is usually expressed in ship hull lengths L. This ratio is called the main measure of the ship's agility and this value is the relative circulation diameter ( D CTC).

For inland navigation vessels D CTC lies within 2.5 3.5.

2. Tactical circulation diameter D T- the distance between the diametrical plane of the ship on a straight course and its position when turning 180 about.

D T = (6.5)

Where L– vessel length, m;

T– vessel draft, m;

S P- steering wheel area, m 2;

K OP- experience factor.

usually the value D T = (0,9 – 1,2)D c.

Rice. 6.3 Vessel circulation scheme

3. Retract l 1– The distance by which the ship's center of gravity shifts in the direction of the original heading from the point of origin of the circulation to the point corresponding to a change in the ship's heading by 90 degrees. For various ships l 1 fluctuates within l 1 = (0,6 -1,5)D C.

4. Forward displacement l 2- the shortest distance from the line of the initial course of the vessel to the point with which the center of gravity (CG) coincides at the time of the course change by 90 °; usually l 2 = (0,25 -0,50)D c.

5. Reverse bias l 3– the greatest distance by which the C.T. is displaced. vessel in the direction opposite to the direction of turn; usually l 3 = (0,01 – 0,1)D c.

The speed-time characteristics include:

1. Circulation period T C- time for the ship to turn 360 degrees.

2. Linear speed of movement of Ts.T. ship in steady circulation V c.

3. Angular speed of rotation of the ship on the steady circulation ω.

The drift angle of the ship on the circulation is determined by C.T. on the stern and on the bow, respectively β C , β K And β C. .

Evaluation of the reaction of the vessel to the shifting of the steering body is determined by the coefficient of recall k ref, which is expressed as the ratio of time t o from the beginning of the shifting of the ship's steering gear to the required shifting value, by the time the ship starts turning.

To otz = (6.7)

For single ships, this coefficient, as a rule, tends to unity, and for pushed convoys it is much less, since the pushed convoys after the end of the shifting of the control body still continue to move on the same course for some time.

The width of the channel required for movement is determined by the circulation parameters along the aft end of ships and trains, since the aft end of the vessel moves along a curve of a larger radius than its C.T.

In accordance with (Fig. 6.4) the elements of the trajectory of the aft end of the vessel on the circulation, it is advisable to evaluate the maximum reverse displacement of the aft end. largest diameter, called the circulation diameter at the stern of the ship, will characterize the circulation motion of the extreme point of the aft end of the vessel. The circulation diameter along the stern of the vessel will be

D K \u003d D C + L R sinβ (6.8)

Where L P - distance from C.T. ship to the point of application of forces Р Р (to the stern).

Knowing the magnitude D K, the boatmaster can estimate the size of the water area required for the turn.

Fig.6.4. Change of the drift angle along the length of the ship and the radius of circulation.

Table 6.1. data on the relative radii of the steady circulation of some inland navigation vessels are given.

Table 6.1.

6.2.3 Heel of the ship in turning.

In the process of circulation, the ship gets a roll (Fig. 6.5). The magnitude and side of the angle of heel depends on the period of circulation in which the vessel is located. In the maneuvering period of circulation, under the action of the steering force (P Y), the roll is directed towards the side, on which transferred steering wheel. During the evolutionary period, the ship first straightens out, as a result of the action of the restoring moment of stability, and then acquires the maximum dynamic roll outside circulation, as the centripetal force begins to act. After one or two oscillations, by the beginning of the period of steady circulation, the ship acquires static roll directed outside circulation, which can be determined by the formula of G.A. Firsov

θ o max = 1.4 (6.9)

Where θ o max- the maximum value of the angle of heel at the steady circulation;

V o is the speed of the vessel on a straight course, m/s;

Z D is the ordinate of the ship's center of gravity relative to the main plane, m;

h- initial metacentric height of the vessel, m;

T And L- draft and length of the vessel, m.

Metocentric height ( h) is the distance between the meteorological center and the center of gravity (C.G.) of the vessel

Metocenter ( M) is the point of intersection of the resultant forces of water pressure with the DP.

The most dangerous list occurs when the circulation is at full speed, when the rudder is shifted on board.

The dynamic roll in the evolutionary period of circulation can exceed the roll in the steady-state period by more than 2 times.

For vessels with low stability, the list on the circulation at full speed can reach 12 - 15 degrees. On passenger ships, a turning roll of more than 7 degrees is not desirable, and more than 12 degrees is considered unacceptable.

To reduce the ship's heel angle on the turn, it is necessary to reduce the speed of movement before entering the turn. The navigator can determine the limits for changing the speed of the vessel before entering the circulation according to the information on stability available on the vessel.

Fig.6.5 Roll of the vessel during circulation.

Failure to take these factors into account can lead to tragic consequences and catastrophes. An example is the disaster of the ship "Bulgaria", which occurred on the Kuibyshev reservoir.

The ship "Bulgaria", which was cruising along the route Kazan - Bolgar-Kazan, sank on July 10, 2011 in the Volga near the village of Syukeyevo, Kamsko-Ustinsky district of Tatarstan.

According to the Rostransnadzor report, “At about 12:25 on July 10, the ship was hit by a strong gust of wind from the port side, a heavy downpour with a thunderstorm began. At this moment D/E "Bulgaria" entered the left turn. It should be noted that when the rudders are shifted to the left, all motor ships acquire an additional dynamic roll to starboard.

As a result, the roll angle was 9 degrees. “With such a roll, the portholes of the starboard side entered the water, as a result of which about 50 tons of outboard water entered the compartments of the vessel through the open portholes in 1 minute. In order to reduce the area of ​​wind impact on the port side, the captain decided to lie downwind. For this, the rudders were set 15 to the left. As a result, the roll increased and the total amount of water entering the ship's compartment reached 125 tons per minute. After that, all the windows and part of the main deck on the starboard side sank into the water. In the last 5-7 seconds, there was a sharp increase in list from 15 to 20 degrees, as a result of which the ship capsized to starboard and sank.

The commission concluded that one of the causes of the accident was the fact that the maneuver to turn to the left was carried out without taking into account the stability of the vessel, which already had a list of 4 about to starboard; an additional roll to starboard caused by centrifugal force during circulation to the left; a strong wind blowing to the port side and a large windage of the vessel.

Changes in the speed of the ship on the circulation can be achieved by regulating the mode of operation of ship propulsion by reducing the speed of the propulsor before the circulation and during its process, as well as by using the propulsors in different directions - "fight" (which is possible with a multi-shaft installation on a ship).

Reducing the speed of the vessel before the circulation causes a decrease in the advance of the circulation l 1 and its tactical diameter D T, which clearly illustrates (Fig. 6.6).

Fig.6.6. The circulation of the ship at different initial speeds.

After the ship has entered the steady circulation, in order to increase the intensity of the turn, the rotational speed of the propellers can be increased, which will not significantly change the geometric characteristics of the circulation.

A significant reduction in the required water area for the production of circulation can be achieved by applying a maneuver called "turning from a place." In this case, the vessel is stopped before the start of the maneuver, the rudders are shifted to the maximum angle of the corresponding side and the propellers are given full speed to the forward course. The vessel immediately enters the circulation, the dimensions of which are smaller than when moving at low speed, and the maneuver time is reduced.

The circulation diameter is affected by:

a) the area of ​​the rudder blade; the larger it is, the smaller the circulation diameter.

To increase the area of ​​the steering wheel, several rudders are installed, active rudders and steering nozzles are used.

b) the distribution of cargo on the ship; if the loads are concentrated in the middle part of the vessel, then it turns faster, with a smaller circulation diameter, and if at the ends, it turns more slowly, with a larger circulation diameter;

c) in relation to the length of the vessel to its width; the larger the ratio, the larger the circulation diameter;

d) the area of ​​the immersed part of the diametral plane; the larger it is, the larger the circulation diameter;

e) ship trim; when trimmed to the bow, the ship has slightly better agility than when trimmed to the stern.

As a conclusion, it can be said that when sailing along the GDP, the ship constantly moves along curvilinear trajectories and makes a large number of circulations. Therefore, knowledge of the elements of circulation is of great importance for ensuring the safety of navigation of ships.

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

For large-capacity vessels, you can use the formulas of G. Hammer:

or
,

where  is the rudder angle, rad;

V - volumetric displacement, m 3

F p - rudder area

C y is the rudder lift coefficient, C y = C p, calculated in the first part of the work, at α = 35˚;

L is the length of the vessel between perpendiculars;

B is the width of the vessel;

K is an empirical coefficient depending on the ratio:

,

where S is the area of ​​the submerged part of the ship's DP, is determined by the formula:

(m 2),

where d is the ship's draft, m.

The coefficient K is determined by interpolation from table 2.

table 2

V/(S L)

2.2. Circulation diameter described by aft end

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

where L is the length of the vessel, m;

 – drift angle, deg;

D t - tactical circulation diameter, m.

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

.

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

The tactical diameter of circulation (at a rudder angle of 35˚) is found by the formulas:

- in ballast

- in cargo

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

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

Using this formula, find the tactical diameter of circulation at a half-board rudder angle (15˚). The rudder angle is set in degrees.

The data for calculating the circulation diameters are presented in Table 3.

2.4. Promotion of the ship on the circulation

The propulsion of the vessel on the circulation can be determined by the formula:

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

T mp - dead time, s;

R c - the average radius of circulation (R c \u003d D t / 2);

K = IK 2 - IK 1 - angle of rotation, deg (90 o);

B is the width of the vessel, m.

2.5. Lane width vessels on circulation

The width of the ship's traffic lane on the circulation is determined by the formula:

2.6. Period of steady circulation

The period of steady circulation is determined by the formula:

, (seconds),

where V c - the speed of the vessel in the steady circulation m / s;

V c \u003d 0.58V 0 when the rudder is shifted "on board" and

V c \u003d 0.79V 0 when the rudder is shifted to "half-board" ( \u003d 15 °).

The procedure for calculating circulation elements:

We calculate the coefficient K;

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

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

We calculate the tactical diameter of circulation for a vessel in cargo with a rudder shifted on board;

We calculate the tactical circulation diameter for a vessel with a rudder shifted to half aboard;

We calculate the diameter of the circulation of the stern;

We determine the extension of the vessel in the cargo;

We calculate the width of the ship's lane;

We determine the period of the ship's steady circulation in the cargo, using D C for our version of the ship.

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
	"Hud. Moor"
	"Atlantic"
	"A. Kaverznev"
	Tanker No. 4
	Dry cargo ship No. 1
	Dry cargo ship No. 2
	Dry cargo ship No. 3
	Tanker No. 4
	Container ship
	Ro-Ro vessel

ship circulation.

Circulation and its periods.

circulation the process of changing the kinematic parameters of a vessel moving rectilinearly evenly in response to a stepped rudder shift, starting from the moment it was set for testing, is called. 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 rectilinear motion the vessel is called its movement in one course at a constant speed.

Steady rotary motion represents the rotation of the ship relative to the CM with a constant angular velocity.

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

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

Focusing on the boundary between evolutionary and steady-state movement accepted in the theory of automatic control, we can assume that the circulation motion 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 on the circulation is not measured, and the linear speed of the vessel is measured with a large error, the moment after which the course change 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 rotated 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 ship reach 3-5% of the approach to their established values ​​later.

Now we can define the circulation periods.

maneuver period (
) is the rudder shift period 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 end of the rudder shift to the moment when the curvilinear motion of the ship becomes steady.

The steady-state period begins at the end of the second period and continues as long as the rudder remains in the predetermined shifted position.

To assess and compare the controllability of ships, circulation under reference conditions. The beginning of the circulation corresponds to the moment when the rudder is set, and the end corresponds to the moment the ship's DP turns through an angle of 360°. Schematically, the trajectory of such circulation is shown in Figure 3.1

Fig. 3.1 Scheme of the circulation of the ship.

circulation parameters.

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

The main ones are such circulation parameters.

Steady-state circulation diameter - distance between ship's DP positions on opposite courses in steady circulation, usually between DP at the time of a 180° turn and DP at the time 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. The tactical diameter can be (0.9-1.2)

promotion - the distance between the positions of the ship's CM at the moment the rudder was started and at the moment after the DP turn by 90, measured in the direction of the initial heading. Approximately

Forward bias - the distance from the line of the initial course to the CM of the ship, which has turned 90°. It is of the order
.

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

drift angle - the angle between the DP and the ship's velocity vector.

Circulation period - the time interval from the moment the rudder is shifted to the moment the ship turns 360°.

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

Half-width of swept strip - the distance from the circulation trajectory, at which the most distant points of the hull are located during the circulation;

Distance - the distance from the position of the ship's CM 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 the end of the vessel - the greatest distance along the initial course from the position of the vessel's CM at the initial moment of circulation to the extreme end of the vessel during the maneuver (similarly, one can determine maximum extension of the center of mass ship, called simply maximum extension);

Maximum Forward Offset of Vessel End - the greatest lateral deviation from the line of the initial course to the extreme end of the ship in the process of circulation (similarly, it can be determined maximum direct displacement of the center of gravity ship, called simply maximum forward displacement).

The main parameter of the ship's agility, the diameter of the steady circulation , little depends on the speed of the ship before the start of the maneuver. This circumstance is confirmed by numerous full-scale tests. However, the extension of the ship does not have this property and depends on the initial speed of the ship. When circulating from a slow stroke, the extension is about 10-5-20% less than the extension from a full stroke. Therefore, in a limited water area in the absence of wind, it is advisable to slow down before making a turn through a large angle.

METHODOLOGICAL INSTRUCTIONS

on the implementation of course work in the discipline "Ship Management"

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

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 the Training, Certification and Watchkeeping of Seafarers, 1978, information on maneuvering characteristics must be provided on board each ship.

The course work on the discipline "Ship Management" provides for a deeper study of issues related to the definition of the maneuvering elements of the vessel.

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

Course work is carried out by cadets of the 5th year of the Faculty of Navigation in the 10th semester after studying Section 3 (topics 13-17) of the standard program of the discipline "Ship Management".

Coursework includes the following topics:

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

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

3. Calculation of the increase in the ship's draft when sailing in shallow water and in channels.

4. Drawing up a table of maneuvering elements of the vessel based on the results of the calculation (calculated and graphical part of the work).

Coursework is drawn up in accordance with existing requirements.

The dimension of physical quantities in the formulas used must correspond to that given in the section "Conventions", 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 is the length of the vessel between perpendiculars, m

B is the width of the vessel, m

d - draft, m

V 0 - full speed, m / s

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

From in - to-t of the general completeness

C m - set of fullness of the midship frame

C d - set of completeness of DP

C y - set of rudder lift

η - propulsion factor

λ 11 - coefficient of added mass

α is the angle of the ship's turn, deg

β is the drift angle of the vessel on the circulation, deg

δ r – rudder angle, deg

θ – roll angle, deg

ψ - trim angle, deg

l p - length of the rudder blade, m

h p – rudder blade height, m

λ p - relative elongation of the rudder blade

And r - the area of ​​\u200b\u200bthe rudder blade, m 2

A d - the area of ​​the submerged part of the ship's DP, m 2

A m - the area of ​​​​the submerged part of the midship frame, m 2

D in - propeller diameter, m

H in - screw pitch, m

n 0 - screw speed, 1/s

N i is the indicated power of the main engine, h.p.

N e - effective power, hp

M w - mooring moment

Р зх - screw stop on mooring lines in reverse, tf

T 1 - time of the first period, s

T 2 - time of the second period, s

T r - the reaction time of the vessel to the rudder shift, s

T c - circulation period, s

D 0 - diameter of the steady circulation, m

D t - tactical circulation diameter, m

D c - diameter of the circulation of the aft end of the vessel, m

l 1 - extension, m

l 2 - forward displacement, m

ΔS – lane width on the circulation, m

S 0 - inertial constant, m

S t - braking distance with active braking, m

t t - active braking time, s

S p - braking distance with passive braking, m

t p - passive braking time, s

S p - way of dispersal of the vessel, m

t p - ship acceleration time, min

g - free fall acceleration, m / s 2

3. Task for the section "Determination of the elements of the ship's circulation"

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

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

3.1 Method for calculating circulation elements

The diameter of the steady circulation, with some assumptions, is calculated using the empirical Shencher 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 lift coefficient C y can be found by the formula:

,

(assuming to accept).

The tactical circulation diameter can be determined by the formulas:

- in cargo: ;

– in ballast: ,

where D t is the tactical diameter of the circulation 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 forward displacement are calculated by 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 submerged part of the DP:

.

The trim angle is determined by the formula:

.

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

,

The translational speed at steady circulation is determined by the approximate formulas:

when shifting the rudder "on board";

when shifting the rudder "half board"

The period of steady circulation is determined by the formula:

The width of the ship's traffic lane on the circulation is determined by the formula:

3.2 Methodology for constructing the ship's circulation

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

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

The relative values ​​of the radii of unsteady circulation, depending on the angle of the ship's turn and the rudder angle, are shown in the table:

Table of values ​​R n / R c

where R n is the radius of unsteady circulation;

R 0 is the radius of the steady circulation.

The order of building circulation:

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

2. Calculate the average turning radius of the vessel by an angle of 10° according to the table. To do this, for example, we select from the table the ratio of the radii R n /R c at angles of rotation 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 ship's circulation curve from a series of arcs of circles of different radii up to the angle of rotation by 180°.

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

Rice. 1. Scheme of constructing the ship's circulation

4. Task for the section "Determination of the inertial characteristics of the vessel"

The inertial characteristics must be calculated during the maneuvers SPKh-PZKh, SPKh-PZKh, SPKh-PZKh, PPKh-STOP, SPKh-STOP, SPKh-STOP, acceleration from the STOP-PZKh position.

The listed characteristics are presented in the form of graphs for ship displacements 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
R0, t	xxx	xxx	xxx	xxx
S 1 , m
V 2 , m/s
M 1, t	xxx	xxx	xxx	xxx
S2, 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 cf, s
S sv, m
WITH	xxx	xxx	xxx	xxx
T r, min.	xxx	xxx	xxx	xxx
S p, kb.	xxx	xxx	xxx	xxx

4.1 Methodology for determining the inertial characteristics of the ship

4.1.1 Active braking

Active braking is calculated in three periods.

The calculation is carried out until the ship stops completely (V to = 0).

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 ship, taking into account the added mass:

Reverse screw thrust:

,

Where ;

N e \u003d η ∙ N i;

η can be determined from Emerson's formula:

.

Path traveled in the first period:

S 1 \u003d V n ∙ T 1

Vessel speed at the end of the second period:

.

The distance traveled by the vessel in the second period:

The path traveled by the ship in the third period:

.

Third period time:

Total distance and braking time:

S t \u003d S 1 + S 2 + S 3

t t \u003d t 1 + t 2 + t 3

4.1.2 Passive braking

The calculation is carried out up to the speed V k \u003d 0.2 ∙ V 0.

Determine the passive braking time:

,

4.2 Acceleration of the vessel

The calculation of the vessel is carried out up to the speed V k \u003d 0.9 ∙ V 0

We determine the path and acceleration time according to the empirical formula:

S p \u003d 1.66 ∙ C

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

,

where V to, nodes;

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

5.1 Draft increase in shallow water

The magnitude of the increase in the ship's draft in shallow water can be calculated using the formulas of the Institute of Hydrology and Hydromechanics of Ukraine (G.I. Sukhomel's formula), modified by A.P. Kovalev:

at

where is the ratio of the sea depth to the average draft;

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

Table for k definitions:

The results of the calculation are presented in the form of a dependence graph d to = f (V) at a ratio of h / d = 1.4 and A to /A m = 4; 6; 8.

5.2 Increase in ship's draft due to heel

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

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

5.3 Determination of the depth margin for wind waves

The wave depth margin is determined in accordance with Appendix 3 of RShS-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 the vessel "Man overboard" is a turn with access to the 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 value of the angle α is determined by the formula:

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

V cf is the average circulation speed, determined from the expression:

The construction of the maneuver scheme is carried out according to the circulation data calculated in Section 3.

Literature

1. Voitkunsky Ya.I. etc. Reference book on the theory of the ship. - L .: Shipbuilding, 1983.

2. Demin S.I. Approximate analytical definition of ship's circulation elements. - CBNTI MMF, express information, series "Navigation and Communication", 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 the maneuvering elements of the vessel of the "Prometheus" type. Sat. Safety of navigation and fishing, vol. 79. - L .: Transport, 1987.

5. Mastushkin Yu.M. Handling of fishing vessels. - M .: Light and food industry, 1981.

7. Handbook of the captain (under the general editorship of Khabur B.P.). - M .: Transport, 1973.

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

9. Tsurban A.I. Determination of the maneuvering elements of the vessel. - M.: Transport, 1977.

10. Vessel management and its technical operation (under the general editorship of Shchetinina A.I.). – 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. To the question of the "subsidence" of the vessel in shallow water and in the channel. Express Information, Safety of Navigation Series, 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 the maneuvering of large-capacity vessels. Express information, series "Navigation Communications and Safety of Navigation", no. 11 (240). – M.: Mortekhinformreklama, 1990.

16.Experimental and theoretical determination of the maneuvering elements of NMP vessels for compiling forms of maneuvering characteristics. Report on R&D UDC. 629.12.072/076. - Novorossiysk, 1989.

The agility of the vessel means its ability to change the direction of movement under the influence of the rudder (controls) and move along the trajectory of this curvature. The movement of the ship with the rudder shifted along a curvilinear trajectory called. circulation. (Different points of the ship's hull during circulation move along different trajectories, therefore, unless otherwise specified, the ship's trajectory - means the trajectory of its CG.)

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

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

On fig. 1 shows that different points along the length of the ship move along trajectories with different radii of curvature with a common CC and have different drift angles. For a point located at the aft end, the circulation radius and the drift angle are maximum. On DP vessel has a special point - turn pole(RP), where the drift angle is equal to zero, The position of the RP, determined by the perpendicular lowered from the CC to the DP, is shifted from the CG along the DP forward by approximately 0.4 of the ship's length; the magnitude of such a shift on different ships varies within small limits. For points on the DP located on opposite sides of the SP, the drift angles have opposite signs. The angular velocity of the ship in the process of circulation first increases rapidly, reaches a maximum, and then, as the point of application of the force Y o shifts towards the stern, it decreases somewhat. When the moments of forces P y and Y o balance each other, the angular velocity acquires a steady value.

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

Extension l 1 - the distance that the ship's CG moves in the direction of the initial course from the moment the rudder is shifted to the course change by 90 °;

Direct offset l 2 - the distance from the line of the initial course to the ship's CG at the moment when its course changed by 90 °;

Reverse displacement l 3 - the distance by which, under the influence of the lateral force of the rudder, the ship's CG is displaced from the line of the initial course in the direction opposite to the direction of rotation;

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

Steady circulation diameter D set - the distance between the positions of the ship's DP for two successive courses that differ by 180 °, with steady motion.

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

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

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

The circulation elements of a conventional transport vessel for a given rudder angle are practically independent of the initial speed in the steady state of the engine. However, if the propeller speed is increased when shifting the rudder, the ship will make a steeper turn. , than in the unchanged mode of the main engine (ME).

Attached are two drawings.