The vessel's circulation diameter is usually . Quantitative estimates of vessel circulation
METHODOLOGICAL INSTRUCTIONS
for completing coursework in the discipline “Ship Control”
Subject: « Calculation of circulation elements and inertial characteristics of the vessel »
1. General provisions 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
From in – general 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 – acceleration free fall, 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 circulation radius is constantly decreasing from highest value at the beginning of the turn to the value of the turn of the 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”
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 speed on circulation, 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 basis 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.
The change in engine load during ship acceleration can be illustrated in Fig. 2.19. In an installation with direct transmission to a fixed pitch propeller, in the absence of release clutches, during engine start-up, the propeller simultaneously begins to rotate. At the first moment, the ship's speed is close to zero, so the load on the diesel engine will vary according to mooring screw characteristic until it intersects with the engine regulatory characteristic (section 1-2), corresponding to a certain position of the control lever of the all-mode regulator. Further, as the speed of the vessel increases, the load decreases according to the regulatory characteristic of the engine (section 2-3). At point 3 the ship finishes accelerating to a speed determined screw characteristic II. Further acceleration until the required speed of the vessel is achieved is carried out according to the screw characteristic (sections 3-5 ÷ 13-14). For this purpose, the control handle of the all-mode regulator is installed in a number of intermediate positions corresponding to the regulatory characteristics of the engine. Typically, at each intermediate position of the engine's regulatory characteristic, a delay is made necessary to achieve the appropriate speed of the vessel and to establish the thermal state of the engine. The shaded areas correspond to the engine work required additionally to accelerate the ship. Stepwise acceleration of the vessel allows for less engine work and eliminates the possibility of engine overload.
Rice. 2.19. Change in engine load during ship acceleration
In cases of emergency acceleration of the vessel, the control handle of the all-mode governor, after starting the engine, is immediately moved from the position to the position corresponding to the nominal crankshaft rotation speed. The high pressure fuel pump rack is moved by the regulator to the position corresponding to the maximum fuel supply. This leads to the fact that the change in effective power and crankshaft rotation speed during the acceleration period occurs along a steeper screw characteristic (in Fig. 2.19 - along the characteristic corresponding to the relative speed of the vessel = 0.4). At point 15 the engine reaches the external rated speed characteristic of the engine. With further acceleration of the vessel, the load on the engine will change according to the external nominal speed characteristic of the engine (section 15-14). Point 14 characterizes the load on the engine at the end of the ship's acceleration.
In Fig. Figure 2.19 shows the dynamics of changes in the load on the engine during the acceleration of the vessel under the assumption that in one case (with slow acceleration of the vessel) the loads will be mainly determined by the position of the screw characteristic, and with rapid acceleration of the vessel the engine will reach the external nominal speed characteristic. In this case, the engine is overloaded in terms of effective torque.
Above, we considered the acceleration mode in the presence of a fixed propeller. An installation with a propeller propeller ensures a faster acceleration of the vessel due to the possibility of fully using the effective power of the engines and obtaining higher traction characteristics of the vessel.
The operating conditions of the engine during ship acceleration depend on the method of controlling the fuel supply and on the law of movement of the engine controls.
Change in load on engines during vessel circulation. According to the nature of the impact of the load on the main engines, the entire circulation maneuver of the vessel should be divided into sections of entry and exit from the circulation and a section of movement with a constant circulation radius. In the first two sections, the engines operate in unsteady modes caused by changes in the ship's speed, drift angle, and rudder angle. While maintaining the circulation radius, the engines operate in steady-state modes, which are different, however, from those that occurred during the ship's forward course. During circulation, the vessel moves not only along the radius, but also with drift; its speed drops at the same speed of rotation of the propeller shaft, propellers operate in an oblique water flow, and their efficiency decreases. In this regard, the load on the engine increases. The increase in engine load depends on the speed, the shape of the ship's hull, the design of the rudders and the angle of their shift.
The curvilinear trajectory of movement of the center of gravity G when the steering wheel is shifted to a certain angle and held in this position is called circulation
There are 4 circulation periods:
- Preliminary period- time from the moment the command is given to the helmsman until the rudder begins to shift.
- Maneuvering circulation period- determined by the beginning and end of the rudder shift. those. coincides in time with the duration of the rudder shift.
- Evolutionary period of circulation- begins from the moment the steering is completed and ends when the elements of movement take on a steady character.
- Steady circulation period- begins from the moment the center of gravity moves along a closed straight line, with the steering wheel in a constant position.
Elements of the vessel's movement on the circulation: dt - tactical diameter of the circulation; Dc is the diameter of the established circulation; l 1 - extension - the distance between the positions of the vessel’s center of gravity at the initial moment of circulation and after a turn of 90°: l 2 - reverse displacement; l 3 - forward displacement - the distance from the line of the initial course to the center of gravity of the vessel after a turn of 90°. B-drift angle
In the initial, evolutionary period of circulation, a hydrodynamic force acts on the rudder blade, removed from the DP, one of the components of which is directed perpendicular to the DP, and causes the ship to drift. Under the action of the propeller stop and lateral force, the ship moves forward and shifts in the direction opposite to the rudder. Therefore, along with drift, a reverse displacement of the vessel occurs in the direction opposite to the turn. The circulation trajectory is distorted at the first moment. The reverse displacement decreases as the centrifugal force of inertia increases, applied to the center of gravity of the vessel and directed to the outer side of the turn. The reverse displacement takes the vessel outside the circulation. And although it does not exceed half the width of the vessel, it must be taken into account, especially when sharp turns in narrowness.
During the period of steady circulation, the moments of forces acting on the rudder and hull of the ship are balanced and the ship moves in a circle. Violation of the ship's motion parameters can occur when the rudder angle, ship speed, or under the influence of external forces change.
The main elements of a vessel's circulation are diameter and period. The circulation diameter characterizes the maneuverability of the vessel. There are tactical circulation diameter Dt and steady circulation diameter Dc.
The tactical circulation diameter Dt is the distance between the initial course of the ship and after its turn by 180 ° and is 4-6 lengths of sea transport ships.
The diameter of the steady circulation Dc is the diameter of the circle along which the center of gravity of the vessel moves during steady circulation. The tactical circulation diameter is approximately 10% larger than the steady circulation diameter.
The circulation diameter depends on many factors: length, width, draft, loading, vessel speed, trim, roll, side and angle of laying, number of propellers and rudders, etc.
When circulating. The vessel's DP does not coincide with the tangent to the curvilinear trajectory of the center of gravity. As a result, a drift angle R is formed. The bow of the vessel moves inside the circulation curve, and the stern moves outward. As the speed increases, the drift angle increases, and vice versa. Due to the presence of a drift angle, a vessel in circulation occupies a strip of water larger than its size. This must be taken into account by navigators when maneuvering and passing in cramped navigation conditions.
The next element characterizing the maneuverability of the vessel is the circulation period. This is the time it takes for the ship to turn 360°. It depends on the speed of the vessel and the rudder angle. With increasing speed and rudder angle, the circulation period decreases. When the rudder is shifted, the ship initially rolls in the direction of the turn. It disappears at the beginning of the movement in the circulation and with further movement the ship begins to roll in the opposite direction of the turn. This is explained by the fact that at first the ship is affected by a heeling moment M"cr, arising from the force P - the water pressure on the rudder blade and the force R of lateral resistance. With further rotation of the ship, the centrifugal force of inertia K applied to the center of gravity of the ship begins to act on it. G) both directed to the outer side of the turn, and the lateral resistance force R. These two forces form a moment M"cr, significantly greater than M"cr, which heels the ship on the side opposite to the shifted rudder (the opposite side of the turn).
The circulation diameter at full speed and the rudder on board is directly proportional to the control arm ¾ (L – B) and inversely proportional to the lateral resistance arm 1/8 (L + 3B).
The value of the steady circulation diameter of a large-tonnage vessel will be approximately equal to:
Or 
(1.3)
where L and B are the length between perpendiculars and the width of the vessel, m.;
Circulation length C = πD. The drift angle β at the center of rotation will be equal to V = L/C. 180°. The given dependencies allow us to find circulation elements depending on the L/B ratio. This relationship is the reason for the different circulation diameters of ships of approximately the same deadweight. The calculation results are presented in table. 2.
Table 2.
Circulation elements depending on L/B
| L/B | Ts.V. | D | C | β |
| 1/3L | 4 L | 12.6 L | ||
| 1/32 L | 3.8 L | 12.0 L | ||
| 5/14 L | 3.6 L | 11.3 L | ||
| 3/8 L | 3.3L | 10.5 L | ||
| 2/5 L | 3.0L | 9.4 L |
The ship's center of rotation (CV), as a concept - the point around which the ship rotates, is discussed in the work of Henry H. Heuer. At the forward speed of the vessel Ts.V. be approximately ¼ of the boat's length from the bow. In astern it is located approximately ¼ of the length from the stern. On the circulation of C.V. located in the bow at the vessel lengths indicated in the second column of the table. 2.
When operating a vessel, it is more important to know the vessel’s largest circulation diameter (Dt), called tactical. Its value for a ship in ballast can be determined by the empirical formula:
(1.4)
for a loaded ship according to the formula:
(1.5)
where C in is the coefficient of displacement completeness.
In the work, based on the processing of full-scale tests, the following formula was obtained for an approximate estimate of the value of Dt:
where e is the base of natural logarithms.
In this work, the following formulas are given to determine the elements of steady circulation of a large-tonnage vessel.
Angular rotation speed:
where: V – linear speed at steady circulation, knots;
D C – diameter of the established circulation, m.
Circulation period:
The time of turning the vessel at a given angle φ° is determined from the expression:
T φ = T cφ ° / 360°, min.
The dependence of the circulation diameter D on the rudder angle can be expressed by the formula:
(1.9)
where D t is the tactical circulation diameter at the rudder angle α p = 35° “on board”.
The width of the ship's hull lane when turning is determined by the formula:
DS q = L sin β + B cos β (1.10)
where: β is the drift angle of the vessel in circulation;
S c - traffic lane width, m.
The drift angle of the vessel in circulation can be determined using the approximate formula:
(1.11)
For large-tonnage vessels, the reverse displacement on the circulation can be significant.
With some approximation, we find this value using the formula:
(1.12)
where l 3 is the reverse displacement of the vessel’s center of gravity, .
Then extreme point the stern, taking into account l 3, can deviate from the circulation curve by a distance determined by the formula:
;
The vessel's advance l p along the initial course, when turning at an angle of less than 90° (l 1 - the vessel's advance when turning by 90° is given in the table of maneuvering elements) can be approximately determined by the formula:
(1.13)
where: V 0 - speed of the vessel at the moment of the beginning of the turn;
R av - radius of curvature of the circulation in the turning section, R av = 1.2 D t /2 when the steering wheel is shifted to an angle of no more than 20°;
DK - angle of rotation of the vessel (IK 2 – IK 1 = DK);
t MP is the vessel’s reaction time to the shifted rudder (dead gap).
The value of the relative speed at steady circulation for a large-tonnage vessel can be determined using the following empirical formula:
(1.14)
To turn a vessel on a reverse course, the width of the fairway (the water area where the vessel turns) must be at least:
(1.15)
Calculation of circulation elements “manually”, according to the given formulas, under the conditions of a navigator working on the bridge, will take a lot of time, so it is necessary that information about turning ability be on a computer or on a poster in the form of a special tablet (Fig. 1.6).
Rice. 1.6. Performing turns using the circulation tablet
The circulation tablet is a grid of directions (radii) and distances (concentric circles), on which circulation curves are plotted at different rudder angles. For large-tonnage vessels, these curves are plotted taking into account the movement on the circulation of the ends of the vessel (in Fig. 1.4), this is shown for the circulation of the left side when the rudder is shifted by 10°.
The tablet can be used in the following ways. On tracing paper on a tablet scale, a diagram of the fairway (channel) in the area of the turn is drawn with marks of the old IR 1 and the new IR 2, as well as one or two of the most convenient landmarks. Then the tracing paper is placed on the tablet so that the IR line coincides with the radius of the tablet OO. By moving the tracing paper along this radius, select the required circulation and turn to a new course at the rudder angle of the selected circulation.
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 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.
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 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.
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:
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 for the vessel to turn 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:
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 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-tonnage 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;
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.
