Dependence of Ships Turning at Port Turning Basins on Clearance under the Ship’s Keel

1. Introduction

2. Ships turning in ports situation and literature analysis

3. Theoretical justification of turning ships in port turning basins with low clearance

3.2. Mathematical model

The literature review, the results of simulators and real ship tests, when different clearances were used between the ship's hull and the bottom of the channels and port basins, were used to develop mathematical models of shipping navigational safety, energy (fuel) consumption and emission generation during ships turning in ports turning basins [3,24,35,38,52]. When conducting research and creating mathematical models, it was assumed that ships in port ships turning basins safe maneuvering independently using thrusters or using port tugs assistance, and the controllability of the ship is ensured by the ship's own steering equipment, thrusters or/and port tugs. In ship turning basins, ships turn with help of their control equipment (propulsion complex), and if necessary, they can use the help of ship steering devices (thrusters) and tugboats [40,47]. It is also assumed, that when ship turns and moves to quay wall or from quay wall due to the effect of low depth, the latitudinal and longitudinal resistance of the ship changes, the resistance of the ship's lateral and longitudinal movement additionally appears [40,47].

The safe depth of the port turning basin, so that the largest ship (with the largest draft) does not touch the bottom of the basin with its hull, can be calculated according to the following formula [17,40]:

$$H_{min}=T+{\Delta T}_v+{\Delta T}_{Ɵ}+{\Delta T}_{\Psi }+{\Delta H}_m+{\Delta H}_{VL}+{\Delta H}_{\Delta VL}+{\Delta H}_n,$$

(1)

where $T$ is the maximum draught of the calculated vessel; ${\Delta T}_v$ is the increase in draught due to settlement (speed) [3,17,40]. Ship’s speed during ship’s turning process is very low or clause to 0 and this factor could be excluded; ${\Delta T}_{Ɵ}$ is the increase in draught due to heeling as acting of the tugs [40]; ${\Delta T}_{\Psi }$ is the increase in draught due to the effect of pitch (change in the different) [40]; ${\Delta H}_m$ is the accuracy of the depth measurement [3]; ${\Delta H}_{VL}$ is the level of the water in the particular port [3]; ${\Delta H}_{\Delta VL}$ is the accuracy of the measurement of the water level [3,40]; ${\Delta H}_n$ is the navigational margin, which can be decomposed into a direct navigational margin, which is assumed to be about 2 - 3 % of the ship's draught, by means of accurate bottom depth measurements (using modern depth measurement techniques), and a layer of sediment, which has to be periodically removed (cleaned). The above elements of formula (1) can be calculated using the methodology presented in [3,17].

External forces and moments acting on ship sailing by port navigational channels and port waters shall be compensated by forces and moments created by the ship’s rudder, or if the ship uses tugs assistance—created by additional tugs forces and moments. Thus, the calculation of the forces and moments can be conducted using the following mathematical model, based on the D’Alembert principle [3,40]:

$$X_{in}+X_k+X_{\beta }+X_P+X_N+X_a+X_c+X_b+X_{sh}+X_T+X_{tug}+\cdots =0$$

(2)

$$Y_{in}+Y_k+Y_{\beta }+Y_P+Y_N+Y_a+Y_c+Y_b+Y_{sh}+Y_T+Y_{tug}+\cdots =0$$

(3)

$$M_{in}+M_k+M_{\beta }+M_P+M_N+M_a+M_c+M_b+M_{sh}+M_T+M_{tug}+\cdots =0$$

(4)

Where $X_{in},Y_{in},M_{in}$ are the inertia forces and the moment; $X_k,Y_k,M_k$ are the forces and moment created by the ship’s hull, which could be calculated by using the methodology stated at [3,40]; $X_{\beta },Y_{\beta },M_{\beta }$ are the ship’s hull as the acting “wing” related forces and the moment, which could be calculated using the methodology stated at [17]; $X_P,Y_P,M_P$ are the forces and the moment created by the ship’s rudder or other steering equipment [40]; $X_N,Y_N,M_N$ are forces and the moments created by thrusters [3,40]; $X_a,Y_a,M_a$ are aerodynamic forces and the moment, which could be calculated using the methodology stated at [40]; $X_c,Y_c,M_c$ are forces and the moment created by the current, which could be calculated using the methodology stated in [40]; $X_b,Y_b,M_b$ are the forces and the moment created by waves, which could be calculated using the methodology stated in [40]; $X_{sh},Y_{sh},M_{sh}$ are the forces and the moment created by shallow water effect [39,40]; $X_T,Y_T,M_T$ are the forces and the moment created by ship’s propeller (propellers), which could be calculated using the methodology stated in [38,40]; and $X_{tug},Y_{tug},M_{tug}$ are the forces and moment created by tugs. Additional forces and moments could be created by anchor or mooring ropes or other factors.

Big ship turning in ports made mainly by port tugs, especially if ship have not own thrusters, ships turning basin is very limited and impossible use ship’s propulsion devises, no waves and no current or current is constant in basin area, and ship have not movement in X and Y directions, ship’s turning moment could be expressed as follows:

$$M_{in}+M_k+M_a+M_{sh}+M_{tug}+\cdots =0,$$

(5)

The inertia moment, under the baseline conditions of turning the ship in port ships turning basin, could be expressed as follow [40]:

$$M_{in}=(I_z+{\lambda }_{66})\frac{d\omega }{dt}$$

(6)

Where $I_z$ is the moment of inertia of the ship; ${\lambda }_{66}$ is added moment of inertia of the ship turning in water; $\frac{d\omega }{dt}$ is the acceleration of the ship's rotational angular velocity.

Inertia moment of the ship could be calculated as [53,54]:

$$I_z=\rho V{L}^2/12$$

(7)

Where $\rho$ is water density, $\frac{t}{m^3}$; $V$ - ships displacement, $m^3$; $L$ is ship’s length, $m$.

Inertia moment together with added inertia moment of the ship, could be calculate as follows [40,53,54]:

$${\lambda }_{66}=k_{66}{I}_z,$$

(8)

Where $k_{66}$ – added moment coefficient, which for the analyzed situation (ship turning in port turning basin in case of T/H = 0.90 – 0.95), is equal to 3 [40,47]. Finally, Inertia moment with added inertia moment could be calculated as follows:

$$\sum I_{in}={(1+k}_{66})\rho V{L}^2/12$$

(9)

In this way, $M_{in}$ can be written as follows:

$$M_{in}=\left({(1+k}_{66}\right)\rho V{L}^2/12\left)\right(\frac{d\omega }{dt}\left(exp\right(-3t/T_{in}\left)\right)$$

(10)

Where $T_{in}$ is ship’s inertia period, can be taken as$T_{in}\approx L/3$ (figure 4) ( experiments on real ships results).

Ship's hull moment ($M_k$ ) could be calculated as the resistance of the ship's hull to lateral movement at a large drift angle (about 90 degrees) [38,40]:

$$M_k={(k}_{22}\rho VL\frac{{dv}_y}{dt}(1-exp\left(-\frac{3t}{T_{in}}\right)))(1+\mathrm{4,95}(T/H{)}^2)$$

(11)

Where $k_{22}$ is the coefficient of the added water mass when the ship moves in the transverse direction;$v_y$ is the speed of the ship's movement in the transverse direction; $T$ is the average draft of the ship; $H$ is the depth of the port ships turning basin.

The aerodynamic moment when the ship is turning can be calculated as follows [17,38,40]:

$$M_a=C_a\frac{{⍴}_1}{2}\sqrt{S_x^2+S_y^2}{v}_a^2{x}_{a}sin{q}_a{\int }_0^t⍵dt$$

(12)

Where: $C_a$ is the aerodynamic coefficient of the above-water part of the ship; ${⍴}_1$ here is air density, 1.25 kg/m³ can be accepted for calculations; $S_x$ and $S_y$ here are the areas of the projections of the above-water part of the ship to the middle and transverse planes; $v_a$ here is the wind speed; $x_a$ is the abscissa of the aerodynamic force addition point with respect to the middle plane of the ship; $q_a$ is the wind heading angle at the start of the maneuver.

The ship will start turning when the moment created by the tugboats is greater than the moments of inertia and other external forces, i.e.:

$$M_{tug}>M_{in}+M_k+M_a$$

(13)

When multiple tugs are used, the total moment generated by the tugs can be calculated as follows [12]:

$$\sum M_{tug}=F_{tug1}{l}_{1}sin{q}_{tug1}+F_{tug2}{l}_{2}sin{q}_{tug2}+F_{tug3}{l}_{3}sin{q}_{tug3}+\cdots$$

(14)

Where $F_{tug1}$, $F_{tug2}$ ,$F_{tug3}$ are tugs 1, 2, 3 bollard pool; $q_{tug1}$, $q_{tug2}$, $q_{tug3}$ are the traction angles of tugs to the middle plane of the ship; $l_1$, $l_2$, $l_3$ are the distances from the middle plane of the ship of the towing ropes of the tugs fixed places on the ship, or the tugs pooling points to the ship's hull.

In this way, the part of the moment created by the tugs, which will act to turn the ship, will be [18]:

$$∆M_{tug}=\sum M_{tug}-M_{in}+M_k+M_a,$$

(15)

Finally, the obtained part of the moment created by the tractors can be written as follows:

$$∆M_{tug}=R{l}^{\prime }=C_R\frac{⍴}{2}{F}_d{v}_y^2{l}^{\prime }$$

(16)

Where $R$ is the total rolling resistance of the ship; $l^{\prime }$ the is relative length of the point of attachment of the tugboats from the middle plane of the ship; $C_R$ is the total resistance of the ship's hull to the rotation of the ship coefficient; $⍴$ here is the density of water; $F_d$ here is the area of the projection of the underwater part of the ship to the middle plane of the ship; $v_y$ the is speed of the ship's lateral movement at the point $l^{\prime }$ away from the center plane.

$F_d$ is the area of the projection of the underwater part of the ship onto the middle plane of the ship can be calculated as follows [3,40]:

$$F_d=\xi LT$$

(17)

Here,$\xi$ is the fullness coefficient of the projection of the ship's underwater area to the middle plane; $T$ is the average draft of the ship.

$l^{\prime }$ the distance of the point from the midline can be calculated as follows:

$$l^{\prime }=\frac{l_{1}sin{q}_{tug1}+l_{2}sin{q}_{tug2}+l_{3}sin{q}_{tug3}+\cdots }{n_{tug}}$$

(18)

Where $n_{tug}$ is number of tugs.

The speed $v_y$ of the lateral movement of the ship at the point far from the middle plane $l^{\prime }$ can be calculated as follows:

$$v_y=\sqrt{\frac{2∆M_{tug}}{C_R⍴F_d{l}^{\prime }}}$$

(19)

The angular velocity (${⍵}^{\prime }$) of the ship can then be calculated as follows:

$${⍵}^{\prime }=\frac{v_y}{l^{\prime }}$$

(20)

The turning of the ship in the turning basin course angle ($\mathit{\phi }$) can be calculated as follows:

$$\mathit{\phi }={\int }_0^{\mathit{t}}{⍵}^{\prime }dt$$

(21)

In this way, the methodology developed for turning ships in the port's turning basins at shallow depth allows to evaluate the possibilities of turning ships in various conditions and to select the optimal number of tugboats, the power they use, and at the same time to reduce the number of emissions. during such operations.

Tugboats engine power ($N$) and the amount of fuel consumed ($q_f$) over a given period of tugs working, during which ship is turn, time ($t$), e.g., an hour, and the relative fuel consumption ($q_f^{\prime }$) link as, [9,52,55]:

$$N=q_f/\left(q_f^{\prime }t\right)$$

(22)

The amount of fuel consumed by tugboats when turning a ship in a port's turning pool can be calculated as:

$$q_f={\int }_0^t{q}_f^{\prime }{N}_{av}dt$$

(23)

Here, $N_{av}$ is the average engines power of the tugboats during the turn of the ship.

Emissions from tugboats during ship’s turning in port ships turning basin directly depend on the quantity and quality of fuel used, engine power and engine running time [11,24,41,56,57,58]. The main emissions from tugboats constitute: carbon dioxide ($C{O}_2$), nitrogen oxides ($N{O}_x$), carbon monoxide ($CO$), sulfur oxides ($S{O}_x$) and particulate matter ($PM$) [41]. Thus, the carbon dioxide emissions are calculated according to the formula [24,41,52]:

$$C{O}_2=k_{{CO}_2}{q}_f$$

(24)

Here, $k_{{CO}_2}$ is carbon dioxide coefficient for petroleum products (diesel, fuel oil) is between 3.0 and 3.5, for LNG between 2.5 and 2.9.

The Sulphur oxide content can be calculated using the formula:

$$S{O}_x=k_{{SO}_x}{q}_f$$

(25)

Here, $k_{{SO}_x}$ is the Sulphur oxide coefficient, which depends on the type of fuel: for petroleum products it ranges from 0.001 to 0.035, for LNG it is around zero.

The carbon monoxide content can be calculated using the formula:

$$CO={\int }_0^t{N}_{av}{k}_{CO}dt$$

(26)

Here, $k_{CO}$ is carbon monoxide coefficient, which depends on the type of engine.

The amount of nitrogen oxides generated is calculated using the formula:

$$N{O}_x={\int }_0^t{N}_{av}{k}_{{NO}_x}dt$$

(27)

Here, $k_{{NO}_x}$ is nitrogen oxide coefficient, depending on engine type.

The particulate matter generation is calculated using the formula:

$$PM={\int }_0^t{N}_{av}{k}_{PM}dt$$

(28)

Here, $k_{PM}$ is the particulate matter coefficient, which depends on the type of engine and the type of fuel, up to 10 g/kWh for petroleum products and close to zero for LNG fuels [52].

Because of tugboats powerful engines, tugboats consume a lot of fuel when turn ship and decrease of the engines power can dramatically decrease fuel consumption and generated emissions quantities.

4. 4. Case study of the ship‘s turning in port ships turning basin. 

As case study was taken Klaipeda port South turning basin (figure 5) [32] and real POST PANAMAX container vessel, which have length 330.0 m, width 42.8 m and draft 13.2 m, which was turn by two tugs with bollard pull 500 kN, which have 3500 kW main engines. As well, there was used calibrated, on basis of the real ship (POST PANAMAX container vessel) experimental data SimFlex Navigator simulator [33], by which were made a lot of experiments. The simulator calibration is based on obtaining the calibration correction coefficients by comparing the analog parameters of the simulator with the parameters of real ships and later, with the help of the obtained calibration coefficients, correcting the parameters obtained with the help of the simulator. The obtained simulation results were compared with real experimental data of similar ships. The arrival of similar ships in the port of Klaipeda happens every week and part of the experimental data was obtained with the help of AIS (automatic identification system) [51] and pilot navigation devices. This made it possible to sufficiently reliably check the correctness of the developed methodology.

The selected vessels are usually turned in the port turn basin using two 500 kN tugs. The turning of the real ship and the turning trajectory of the POST PANAMAX container ship were obtained of the real ship (figure 6).

The turning trajectory of a POST PANAMAX container ship in a port ships turning basin using two 500 kN tugs. The wind speed of up to 10 m/s and a current of 0.3 knots and a ship draft to depth (T/H) ratio of about 0.93 was obtained using a calibrated simulator (Figure 7).

In similar conditions (wind up to 10 m/s, current 0.3 knots, ship's draft and depth ratio about 0.93), the turning parameters of the POST PANAMAX container ship were calculated and experimentally obtained: turning time, tugs bollard pull, angular turning speed and clearance (Figure 8).

The obtained results of experiments with real ships were used to calibrate the SimFlex Navigator simulator, and about 50 experiments were carried out with the help of a calibrated simulator. The obtained results confirmed the correctness of the developed methodology for turning ships, using tugs or own ship's thrusters, in the presence of low clearance. The maximum distribution method [50] and the Kalman filter [59] were used to process the obtained experimental results (with the help of real ships and a simulator). The turning time of the POST PANAMAX container ship was obtained by the developed theoretical method and experimentally (real ship and using a calibrated simulator) ( experiments on real ships results), depending on the clearance, using two 500 kN tugs, presented in Figure 9.

In ports, it is not always possible to use tugboats with extremely high pulling forces, and the use of lower engine power in tugboats offers the opportunity to reduce the environmental impact by reducing fuel consumption and emissions. Conducted studies using lower engine powers of port tugboats, i.e. reducing the power of the main tugboat engine by about 40-50 percent, showed that the turning time of ships in the port ships turning basin increases only by about 15-18 percent, but at the same time the number of emissions decreases by about 25-35 percent, which positively affects the development of “green” ports without the use of large investments ( experiments on real ships results) (figure 10).

The angular rotation speed of the ships when turning the ships in the port turning basin of the ships is important, but when turning large ships, i.e. PANAMAX and larger ships, from the point of view of navigation safety, it is not recommended to exceed the angular rotation speed of the ship 15 - 18 degrees per minute, so it is often possible to use smaller tugs (which is not very acceptable for navigation from the point of view of safety in emergency situations). However, with the use of more powerful tugs, it is possible to reduce the power of their main engines up to 25 – 50 % and at the same time reduce fuel consumption and the number of emissions generated during such operations and have a reserve of the main engines (and at the same time bollard pull) of port tugs ( experiments on real ships results) (figure 11).

The clearance has a significant influence on the lateral resistance of the ship and at the same time on the angular speed of the ship, turning the ship using tugs. Conducted research with real ships and using a calibrated simulator made it possible to verify the correctness of the developed methodology and at the same time to find the optimal bollard pull of the tugboats, depending on the size of the clearance, minimizing the possible power of the tugboat engines and at the same time the fuel consumption during the turning of the ships and the possible minimum generated emissions. The obtained maximum angular speeds of the POST PANAMAX container ship using two tugs with a pulling force of 500 kN, depending on the clearance, are presented in Figure 12 ( experiments on real ships results).

It is necessary to note that the angular speed of rotation of large ships should not exceed 15 degrees/min, therefore, using the developed methodology, it is possible to plan in advance the necessary bollard pull of tugboats and at the same time estimate the possible powers of the tugboats' main engines and, at the same time, fuel consumption and the number of generated emissions.

Conducted experiments with real ships have shown that the methodology developed and presented in this article for ship turning in port ship turning basins, with small clearances, allows not only to optimize ship turning in ports, but also to minimize the impact on the environment.

Theoretical calculations and experimental studies of turning ships in ports and environmental impact assessments using the developed methodology, using tugs with bollard pull from 250 kN to 500 kN, depending on the size of the clearance, showed that it is very important to find the optimal bollard pull to guarantee the safety of shipping during such operations and to have the least impact on the environment.

The theoretical and experimental studies of the emissions of port tugboats when turning POST PANAMAX container ships in the ships turning basins of port are presented in Figure 13, Figure 14, Figure 15 and Figure 16.

When the tugboats use different fuels during the turn of the ship, i.e. diesel or LNG, depending on the draft and depth ratio of the POST PANAMAX container ship, turning the ship 180 degrees, the results of calculating the fuel consumption and emission generation, using the methodology presented in the article and experimentally, are presented in Figure 13 ( experiments on real ships results).

The number of emissions generated by $C{O}_2$ and $S{O}_x$ directly depends on the amount and quality of fuel used (diesel, LNG, ammonia, etc.). Calculations of the number of emissions generated by $C{O}_2$ and $S{O}_x$ were performed and obtained during the experiment when turning the POST PANAMAX container ship (a $C{O}_2$ measurement station was installed on one of the tugboats) depending on the draft and depth ratio of the turning ship, the results are presented in Figure 14 ( experiments on real ships results).

When turning the POST PANAMAX container ship with help of two tugs, the amounts of $C{O}_2$ and $S{O}_x$  generated by the tugs, using different powers (bollard pull) of the tugs depending on the draft and depth ratio of the turning vessel being turned, are presented in Figure 15 and Figure 16 (, experiments on real ships results).

$CO$, $N{O}_x$ and $PM$ the number of generated emissions depends on the power of the tugboat engines used and the working time when turning the ships. The results of emissions generated by tugboats when turning the POST PANAMAX container ship, depending on the bollard pull and the draft and depth ratio of the turning ship, are presented in Figure 17, Figure 18 and Figure 19.

When turning large ships in ports, it is necessary to maintain an angular rotation speed of not more than 12-15 degrees/min in order to be able to turn the ship safely and adjust to any non-standard situations in a timely and reliable manner and not to create large angles of inclination of the ship. Using the given case by case study, it can be seen from Figure 7 and Figure 8 that, assuming a turning angular speed of up to 15 degrees/min, with a ratio of the ship's draft to the depth of the turning basin of about 0.95, 2 tugs with a bollard pull of about 300 kN should be used and each tugboat ‘s main engine uses about 1900 kW. Under the specified conditions, the turnaround time of a POST PANAMAX container ship would be about 12 minutes and using diesel fuel for tugs would consume a total of about 170 kg of diesel fuel and would generate about: 540 kg of $C{O}_2$; 0.18 kg $S{O}_x$; 4.2 kg of $CO$; 9.0 kg $N{O}_x$; 0.43 kg $PM$.

As can be seen from the given example, by providing the necessary navigational safety, optimizing the turning of ships in ports with the help of tugs, the fuel consumption of tugs performing ship turning can be reduced by about 20-25% and the number of emissions generated by the same up to 20-30%, which is very important for ports especially located near large cities.

5. Discussions and conclusions

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