Estimation of Tug Pulling Power (Bollard Pull) and Number of Tugs Required During Ship Mooring Operations

Tugs of various purposes and types are used to provide port navigational safety, which allows increasing the manoeuvring parameters (possibilities) of ships while sailing and manoeuvring in ports.

In order to determine the real parameters for ship manoeuvring in a port, at a shallow depth, it is necessary to develop and experimentally verify the possibilities for evaluating the manoeuvring of real ships. It is also possible to use calibrated simulators, recalibrated according to real port conditions and using tugboats in mooring operations, and check the suitability of the methodology. Experimental studies of ship manoeuvring parameters in real conditions, when a ship is sailing to the port and manoeuvring in it, using tugboats, allowed checking the reliability of the developed methodology. In modern ports, versatile, wide-purpose tugboats are used, which can not only perform towing operations and help ships enter and leave the port, but also take part in various operations when mooring and unmooring ships.

In order to create a research methodology, the collection of primary data, their analysis, assessment of the situation, and primary research were carried out. After analysing the available literature and scientific sources and conducting a review, information was collected and systematized about the novelty of the topic: shipping safety challenges faced by tugboats when mooring ships in ports. The developed methodology must allow for a more accurate assessment of the optimal number of tugboats and their traction force (bollard pull) and ensure safe manoeuvring of ships in the port using tugboats.

3.1. Research Methodology: Basic Ideas

The methodology consists of data from the literature and results obtained by monitoring the movement of ships in the port of Klaipeda and other ports, supported by theoretical and experimental research. This methodology takes into account the manoeuvrability of commercial ships and tugboats in various weather conditions; these conditions include wind speed, wind heading angle, current speed, current heading angle, etc. The study required additional data, such as the width of navigation channels (waterways), channel depths, tug equipment parameters during operation and the corresponding coefficients obtained from theoretical and experimental studies for the calibration of the full mission visual simulator (which was later used for further studies).

A methodology for calculating the manoeuvrability of the ship and the tugboats in the port’s water area has been developed, allowing accurate estimates of the optimal number of tugboats and the traction power (bollard pull) of the tugboats required to perform towing operations in difficult conditions. This model considers the implementation of the following steps:

–: Collection and analysis of the aforementioned primary data;
–: Assessment of the manoeuvrability of the ship and the tugboats in the port area during various operations;
–: Optimum selection of the number of tugboats and the required pulling power (bollard pull) of the tugboats;
–: Planning the timing of towing operations and possible costs;
–: Drawing conclusions and recommendations for specific conditions.

This study developed and presented a methodology that takes into account complex meteorological conditions in assessing the influence of wind, current and waves, as well as the effect of shallow depth, selecting the optimal number of tugboats and pulling power (bollard pull) to ensure safe and smooth work during mooring and unmooring operations, and safe manoeuvring of ships in the port water area. The main parameters were taken into account, such as ship size and hydrodynamic parameters, tugboat size and power, berth parameters, wind and current speed and direction, towing rope parameters, port depth, towing schemes, etc. (Figure 1).

The boundary conditions of the methodology and the model are as follows: hydro-meteorological conditions that avoid additional costs and risks, for example, not using icebreakers in the port area.

The developed methodology, based on the D’Alambare principle, covers all the main factors that affect ships during mooring operations. The aim of the article is to identify the main factors affecting the ship during mooring operations, to create a methodology that would be acceptable for scientific and practical purposes, using initial data that can be obtained in real conditions.

The optimization problem is important to provide navigational safety during the mooring of ships (theoretically, it can be an infinitely large number of tugboats) and at the same time, the traction force of tugboats and, accordingly, the number of tugboats must be optimal, considering the real number of tugboats and their potential traction force.

The proposed methodology was verified based on a case study. The work of tugboats in the port of Klaipeda and other ports was analysed in detail, and calculations based on real data were performed. Based on the research results, a methodology for selecting the optimal number and power of tugboats is proposed. At the same time, the proposed methodology could be applied in practically any port due to the universal calculation method, which is easy to adapt to the conditions and situations of a specific port, since the calculations use common parameters such as, e.g., wind and current parameters, and these data in most cases can be obtained by assessing the current situation directly and used as a basis for preparation of the best solution. Also, in most cases, no special equipment is needed to obtain the values used for the calculation methodology, and this information is collected and can be provided at any time by the departments of the port administration responsible for safe shipping.

3.2. Mathematical Model

Based on the presented principal methodology (Figure 1), a theoretical model of ship mooring and unmooring with the help of ship thrusters or tugboats was created, and experiments were carried out with real ships and with the help of a calibrated simulator. Finally, the theoretical model was improved on the basis of real ships and calibrated simulator experimental results [27]. After determining the possible optimal operations for mooring ships to the quay wall or unmooring them from the quay wall, in the case of low clearance, the estimated tugboat bollard pull or thrusters under various hydrological and hydro-meteorological conditions were calculated.

External forces and moments acting on ship mooring and unmooring shall be compensated by forces and moments created by the ship’s thrusters, or if the ship uses tugboat assistance, created by additional tugboats forces and moments. Ship motion mathematically is mostly described by the D’Alembert method [32]. Thus, the calculation of the ship’s forces and moments during mooring operations can be conducted using the following mathematical model, based on the D’Alembert principle [3]:

$X_{i n} + X_{k} + X_{β} + X_{P} + X_{N} + X_{a} + X_{c} + X_{b} + X_{s h} + X_{T} + X_{t u g} + \dots = 0;$

(1)

$Y_{i n} + Y_{k} + Y_{β} + Y_{P} + Y_{N} + Y_{a} + Y_{c} + Y_{b} + Y_{s h} + Y_{T} + Y_{t u g} + \dots = 0;$

(2)

$M_{i n} + M_{k} + M_{β} + M_{P} + M_{N} + M_{a} + M_{c} + M_{b} + M_{s h} + M_{T} + M_{t u g} + \dots = 0,$

(3)

where $X_{i n}, Y_{i n}, M_{i n}$ are the inertial 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 in [33]; and $X_{β}, Y_{β}, M_{β}$ are the ship’s hull as the acting “wing” related forces and the moment, which could be calculated using the methodology stated in [34], although if we analyse just the ship’s mooring and unmooring, these types of forces and moments are close to 0; $X_{P}, Y_{P}, M_{P}$ are the forces and the moment created by the ship’s rudder or other steering equipment [33]; $X_{N}, Y_{N}, M_{N}$ are forces and the moments created by thrusters [33]; $X_{a}, Y_{a}, M_{a}$ are aerodynamic forces and the moment, which could be calculated using the methodology stated in [33]; $X_{c}, Y_{c}, M_{c}$ are forces and the moment created by the current, which could be calculated using the methodology stated in [33]; $X_{b}, Y_{b}, M_{b}$ are the forces and the moment created by waves, which could be calculated using the methodology stated in [33] (in port conditions, this parameter is insignificant and often not applicable); $X_{s h}, Y_{s h}, M_{s h}$ are the forces and the moment created by shallow water effect [33,34] (in port conditions, this parameter is very important, especially when the ratio of the ship’s draft to the depth of the mooring and unmooring places is greater than 0.9); $X_{T}, Y_{T}, M_{T}$ are the forces and the moment created by the ship’s propeller (propellers), which could be calculated using the methodology stated in [33,34]; and $X_{t u g}, Y_{t u g}, M_{t u g}$ are the forces and moment created by tugs. Additional forces and moments could be created by the anchor or mooring ropes or other factors.

The resulting system of equations is important in that its use allows solving many problems of ship movement and controllability. In each case, the presented system of Equations (1)–(3) must be adapted to a specific task or tasks.

At the same time, it is necessary to note that for the practical purposes of mooring and unmooring ships in ports, using the adapted system of Equations (1)–(3), it is necessary to find a model acceptable for practical purposes, which would allow the calculation of the necessary maximum traction force (bollard pull) of the tugboats under the conditions of the ship or port, and to accordingly select the optimal number of tugboats. For that purpose, additional studies were conducted on the mooring of ships using tugboats, during which the maximum traction force (bollard pull) of the tugboats was recorded, depending on the ship’s parameters and external conditions (wind, current, depth, etc.). On the basis of research, it was decided that the main force when mooring and unmooring ships is the traction force (bollard pull) ( $Y_{t u g}$ ) of the tugs and the maximum traction time (period) of the tugs.

Experiments were carried out by mooring and unmooring real PANAMAX and POST PANAMAX type ships, which did not have their own steering devices, and turning them in ship turning basins. Harbour tugboats with a bollard pull of up to 550 kN were used. During the experiments, wind speeds and directions were recorded at the inner harbour hydrometeorological station, current speeds and directions were measured at the nearby current measuring station, located at quay No. 72 of the end (picture 5), and the depth during the experiments was measured by means of measuring the depth of the ship (sounders). Hydrometeorological and current measuring stations complied with IALA recommendations [35]. The bollard pull of the tugboats was recorded by the tugboat towing rope recorder every 1 s. Over 50 such experiments were carried out. It was found that tugboats with maximum power, i.e., at or near maximum bollard pull, operated from 4 to 15 min, while at all other times operating at no more than 50% of the rated power of their engines. Since the aim of the research was to investigate the maximum bollard pull of tugboats during ship mooring operations and when turning ships in the turning basin, the article was limited to 20 min in time (time window).

The obtained results of experiments with real ships were used for the calibration of the full-mission visual simulator SimFlex Navigator [27], with the help of which additional studies were later carried out. The principle of simulator calibration is as follows: ships in the simulator library that are similar to the real ships used during the experiments are selected, analogous external conditions (wind, current, depth parameters) are entered, and analogous experiments are performed in the simulator. After comparing the results of the experiments using real ships with those of the simulator and processing them using a Kalman filter [36], the calibration coefficients of the simulator were calculated, which aided in refining the bollard pull and other results obtained during further research with the help of the simulator.

Theoretical and experimental studies of the use of tugboats in ports to provide navigational safety have shown that the time period for the maximum pulling force (bollard pull) of tugboats, i.e., when turning a ship in port ship turning basins or other areas of the port water area or mooring and unmooring ships, is relatively short (Figure 2, Figure 3 and Figure 4).

Traction force (bollard pull) of tugboats obtained experimentally in relation to time, for example, when mooring, unmooring, and turning a real PANAMAX-type ship in the turning basin with the help of two tugboats, each of which had a bollard pull of about 500 kN, showed that the maximum pulling force of the tugboats was applied in the range of 7–12 min during the PANAMAX ship mooring operation, 5–8 min during the PANAMAX ship unmooring operation, and about 4–10 min during the PANAMAX ship turning operation in the port ship turning basin. At all other times, the pulling force of tugs was between 10 and 50% of their maximum pulling force (Figure 3, Figure 4 and Figure 5). All experiments were executed in conditions of wind velocity up to 12 m/s and current up to 0.8 m/s (1.6 knots).

Kalman filters are frequently used for processing experimental data obtained from real ships with the help of a calibrated simulator [36]. In cases where the analysed data were obtained from real ships and calibrated simulator experimental results, the fluctuations and differences in the obtained experimental results may be observed during data comparative analysis. This may be caused by differences in the experimental perspective of the problem area, as well as changes taking place among the analysed factors. Therefore, data filtration is needed. The filtration of data collected during the analysis of the experiments can be achieved using a Kalman filter by applying Equation (4) [36]:

$x_{k} = A x_{k - 1} + {B u}_{k} + ω_{k},$

(4)

with observations $z_{k}$ (Equation (5)):
where: $A$ , $B$ , $H$ —coefficients; $ω_{k}$ , $υ_{k}$ —sequence of noisy observations; $x_{k}$ , $u_{k}$ —control vectors.

The appropriate computational model to conduct simulations in order to analyse the experimental results has been developed. The proposed method for analysis of experimental results is focused on band analysis. To calculate the size of the random error or the received experimental results band, “maximal distribution” mathematical methods can be used [37]. With the help of the maximum distribution method, which was used in processing the results of experimental studies, the error values of the obtained results were obtained (bar). Assessing the accuracy of experimental results during this research was important in order to detect possible deviations and to confirm the correctness of the developed methodology for calculating the traction force (tugboat bollard pull).

The received experimental results band can be calculated using the “maximal distribution” method. For the research, experimental results band

t_{P}

is calculated by applying Equation (6); this can be expressed as follows [37]:

$t_{P} = t_{y} \pm P^{'} \cdot Δ t \cdot k_{t},$

(6)

where: $t_{y}$ —average of the experimental data; $P^{'}$ —probability coefficient (it has been proposed that in case of a probability of 63–68%, the coefficient should equal 1; in the case of a probability of 95%, the probability coefficient should be 2, and in the case of a probability of 99.7%, the probability coefficient equals 3); $Δ t$ —difference between maximum and minimum experimental values; $k_{t}$ —coefficient, which depends on the number of measurements (the number of possessed data): in case the number of data is 3, this coefficient will be 0.55; in case the data number is 4, this coefficient will be 0.47, and similarly depending on the data number 5–0.43; 6–0.395; 7–0.37; 8–0.351; 9–0.337; 10–0.329; 11–0.325; 12–0.322 and so on. The minimum value of this coefficient is about 0.315, in the case where the number of items of collected data is more than 15.

Evaluating the fact that when mooring ships and turning them in the turning basin or in another port area, the maximum traction force (bollard pull) of tugboats is needed to control the lateral movement of the ship, to improve the safety of shipping in the port, it is very important to calculate (evaluate), and it is appropriate to present the generalized necessary maximum traction force (bollard pull) of tugboats in the

Y

direction. For the assessment of the generalized necessary force of tugs (

Y_{t u g}

), it is necessary to take into account the resistance of the ship’s hull during lateral movement, aerodynamic (wind-generated) force, current-generated force, inertial force, and shoaling effect. In such a case, the required traction force of tugs can be calculated as follows:

$Y_{t u g} = Y_{i n} + Y_{k} + Y_{p} + Y_{a} + Y_{c} + Y_{s h} + \dots,$

(7)

where: $Y_{i n}$ —inertial force; $Y_{k}$ —developed hull force; $Y_{p}$ —forces generated by the ship’s propulsion mechanisms (thrusters); $Y_{a}$ —aerodynamic force; $Y_{c}$ —the force created by the current; $Y_{s h}$ —the force created by the impact of shallow water.

It may also be assessed if the ship’s steering and steering mechanisms are used: for example, for ships with two propellers and two rudder plates, the presence and use of steering mechanisms onboard.

The main operational criteria are the traction force of the tugboats, depending on the parameters of the ship, hydro-meteorological and hydrological conditions and the number of tugboats calculated on the basis of the traction force of the tugboats, depending on the parameters of the tugboats available in the port (traction force of the tugboats). The parameters of the ship’s mooring movement are related to the maximum absorption energy of the quay fenders and the permitted maximum contact speeds of the ship, depending on the water space and mooring conditions of the ship, respectively, and the maximum possible acceleration. The ship’s acceleration during contact with the quay is evaluated as the possible (allowable) speed of the ship’s contact with the quay fenders and the possible extent of fender deformation.

In this way, it is possible to assess what the permissible acceleration of the ship’s contact with the recoil can be, so that the ship’s hull is not damaged and the quay’s recoils are not damaged.

After evaluating the short-term necessary traction force (bollard pull) of the tugboats and the very low speed of the ship when turning the ship and mooring or unmooring it, the inertial force can be taken as about 1.3–1.5 times the resistance of the side hull of the ship. After carrying out a number of theoretical and experimental studies of the necessary traction force of the tugboats, evaluations of the accuracy of the obtained results, an evaluation of the main and secondary factors specified in Equations (1)–(3), as well as an evaluation of the forces generated by ship propulsion devices, without evaluating the side forces generated by the ship’s steering and steering devices, then Equation (7) can be expressed as follows:

$Y_{t u g} = 1.3 C \frac{ρ}{2} L T v_{y}^{2} (1 + 4.95 (\frac{T}{H})^{2} + C_{a} \frac{ρ_{1}}{2} S_{x} v_{a}^{2} s i n q_{a} + C \frac{ρ}{2} L T v_{c}^{2} s i n q_{c}),$

(8)

where: $C$ —the hydrodynamic coefficient of the hull of the ship; for marine ships during mooring or turning at relatively low speeds in the $Y$ direction, this can be taken as about 1.3–1.5 (as a plate with rounded edges placed across the flow) [33,34]; $ρ$ —water density; $L$ —ship length; $T$ —mean draft of the ship; $H$ —depth; $S_{x}$ —the area of the projection of the above-water part of the ship to the middle plane; $C_{a}$ —aerodynamic coefficient, for bulk cargo ships; for tankers, it can be taken as about 1.1, and for container ships, about 1.3 [33,34]; $v_{y}$ —the speed of the ship moving to the quay; for medium-sized ships (displacement up to 15,000 tons), it can be accepted as about 0.15 m/s, and for PANAMAX and larger ships—about 0.08 m/s [38]; $v_{a}$ —wind velocity; $v_{c}$ —modified average current speed, which can be accepted at the quays at about 0.3–0.6, and depends on the configuration of the quays and the current speed in the channel; $q_{a}$ —the angle of the wind course to the berth; $q_{c}$ —the angle of the course of the current to the berth.

The methodology for calculating and evaluating the traction force (bollard pull) of tugboats, necessary for manoeuvring ships in the port and for mooring operations, developed in this way can be adapted to a specific port location and specific ships. By using the developed methodology, it is possible to optimize the selection of the number of tugboats and their traction force (bollard pull), and at the same time increase the safety of shipping in the port and optimize the costs of mooring and manoeuvring operations for ships in ports.

Figure 5.
The central part of Klaipėda port [38].

Source link

Vytautas Paulauskas www.mdpi.com

Greenberg News

Estimation of Tug Pulling Power (Bollard Pull) and Number of Tugs Required During Ship Mooring Operations

3.1. Research Methodology: Basic Ideas

3.2. Mathematical Model

Greenberg

3.1. Research Methodology: Basic Ideas

3.2. Mathematical Model

Related Posts

Earth911 Inspiration: Nature, a Source of Inspiration

Oregon invites public participation in offshore wind energy ‘roadmap’ after feds pause plans

Environmental Factor – April 2024: Sequencing RNA and its modifications will chart a new era for biology

Greenberg