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

Abstract

Harbour tugs are usually used to moor ships if large ships do not have their own additional propulsion devices (thrusters). Alternatively, during ship loading operations, ships sometimes have to be transferred from one quay to another, and in some cases, port users (shipping companies or other companies) have to pay for port tug services. In such cases, it is very important to guarantee the safety of shipping during mooring operations and to use tugboats optimally and at the same time reduce the cost of tugboat services for ship operators and other companies. For the optimal use of tugboats, it is very important to accurately estimate the required traction force (bollard pull) of tugboats and their quantity, taking into account the parameters of moored ships, the locations of berths, hydro-meteorological and hydrological conditions, and clearance (the gap between the ship’s hull and the bottom of the water area), in order to guarantee the safety of navigation and not to order an excess of tugboats in terms of their quantity and powers. This article presents a methodology developed for estimating the required bollard pull and the number of tugs, taking into account the parameters of the ship, hydro-meteorological and hydrological conditions, clearance, and the locations of berths. The developed methodology for estimating the number of tugboats and their traction force (bollard pull) was tested in real conditions (with real ships and tugboats) and using a calibrated simulator, and we found that it can be successfully applied in any port or other complex shipping area by adapting it to specific conditions. The developed methodology for calculating the traction power (bollard pull) of tugboats allows us to determine the required traction force of tugboats in advance with sufficient accuracy, achieved by assessing the specific parameters and environmental conditions of the vessel served by tugboats. In the most difficult areas of the port, in terms of the use of tugboats, this methodology allows us to make reasonable decisions regarding the number of tugboats and the traction force (bollard pull) required and at the same time reduces the risk of emergency situations.

1. Introduction

Mooring ships in harbours and other places is often quite difficult, especially under the influence of external forces such as currents, wind, and in some cases waves and shallow depths, which are very common in harbours, when the space between the hull of the moored ship and the bottom of the water area is small [1]. Ship mooring operations often resemble an art, although they can be measured quantitatively.

Many large ports have harbour tugboats to help ships manoeuvre in harbour approaches and harbour navigational channels and to assist ships in berthing operations, but some ports do not have them or have a limited number of tugboats, and in such situations, it is very important to use tugboat assistance correctly and accurately. Harbour tugboats help to ensure the safe manoeuvring of ships in harbour navigational channels, by mooring ships to quays and unmooring them from quays, as well as turning ships in port turning basins and assisting with other manoeuvres [2,3].

Today, two main types of harbour tugboats can be distinguished: conventional tugboats with a standard fixed-pitch propeller (use in modern ports relatively rarely) and tugboats with an azimuth steering mechanism, named tractor tugs or otherwise known as Voith–Schneider tugs [4]. Each type of tugboat has certain technical characteristics and a spectrum of applicability, so when choosing the optimal tugboat that will serve ships the most efficiently, several main aspects are taken into account: the geographical conditions of the port, the size and characteristics of the ships served, and the prevailing meteorological and natural conditions [5]. Many modern ships have additional steering mechanisms (thrusters) that partially replace some of the functions of tugboats [6]. Ships such as big oil, chemical, and liquefied natural gas tankers and large dry cargo ships often do not have additional steering mechanisms, so their manoeuvring in the port and navigational safety are ensured by tugboats [1,5,7]. In order to improve the manoeuvrability of ships in ports, the number of tugboats and their capacities (traction forces or bollard pull) are determined based on the available experience, and often, this does not lead to optimal solutions [4]. In ports, tugboats additionally carry out firefighting and rescue work, and in freezing ports, port tugboats perform icebreaker functions in the water area and canals, as well as other operations required.

The necessity of solving the theoretical and practical problem discussed in this article is related to the restrictions on the number of tugboats in some ports. This is especially relevant when there are many ships that have to be serviced by tugboats (during ship mooring operations), severe hydro-meteorological conditions (storms), or when ships need to be taken out of certain parts of the port where they cannot stay during a storm. Some of the world’s ports have a limited number of harbour tugboats, and researching their optimal use and creating a methodology for calculating this by assessing ship parameters and external conditions, such as the effects of wind, currents, and shoaling, are very important from a scientific and practical point of view. Previously conducted studies on the use of port tugboats have shown that in some ports, an excess number of tugboats is used in terms of pulling power in mooring operations, and some tugs “participate” in towing operations, although in reality, their role is minimal or absent. At the same time, in individual ports, due to the lack of port tugboat capacity, excessive risk is often taken by using an insufficient pulling power of tugboats or an insufficient number of tugboats. Accordingly, the methodology presented in this article is very important from a scientific and practical point of view, for many ports, to guarantee the safety of navigation in ship mooring operations.

In this article, a great deal of attention was paid and a lot of research was conducted in the study of the ship’s inertial forces associated with the allowable contact of the ship with quay fenders, and as a result of these studies, it was possible to find acceptable practical solutions related to the assessment of the necessary towing force of tugboats.

In many scientific and practical studies related to the improvement of port navigational safety by using tugboats, it has been noted that the research on this topic is insufficient [1,4,7,8].

To address that research gap, our theoretical and experimental studies, presented herein, on the use of tugboats in ports make it possible to more accurately assess the characteristics of the work of tugboats in ship mooring operations and, based on that research, to develop methods for determining the necessary traction force of tugboats and the appropriate number of tugboats under various conditions, which is very important for increasing the safety of shipping in ports.

This article presents our methodology developed for assessing the necessary traction force (bollard pull) of harbour tugboats and, accordingly, the number of tugs, when mooring and unmooring ships and when turning ships in port turning basins, which is based on evaluating the features of the port (the arrangement of quays in relation to external impact forces), the effects of wind and the current on moored ships, and shoals’ impact on the mooring vessel.

The novelty and innovativeness of this article is manifested in the assessment of the necessary traction force of tugboats under various ship manoeuvring conditions, as well as external impact forces: wind, current, waves, shoaling effects, the development of a methodology and its adoption for specific ships and port conditions. The developed methodology has been tested on real ships and specific ports, based on relatively easily obtained initial data in real conditions.

2. Ship Mooring Operations with Tug Assistance in Ports and Literature Analysis

Maritime transport is the most important mode of transport and is one of the fastest developing modes of transport in the world. Navigational safety in ports is often helped by port tugboats, which help ships manoeuvre when they enter and leave the port, navigate the port channels, turn ships in port turning basins, moor ships to quays and unmoor them from quays [3]. Based on tradition and experience, the selection of port tugboats often leads to overbooking of tug power and volume or, even worse, in individual cases, under-booking of tug power and tow volume, which unjustifiably increases the risk to ships [8].

The optimal use of tugboats in ports is important for ensuring the safety of shipping, performing various support operations in ports and their approaches, such as emergency towing of ships, carrying out various ship and people rescue operations and other port operations.

Many scientific studies are devoted to research on the use of port tugboats, in particular, the human factor [8,9], evaluations of the necessary force of tugboats for increasing the manoeuvrability of ships in ports [3,10], and research on the more efficient use of tugboats [3], but at the same time, not enough attention has been paid to the tugboat system or evaluating possible internal and external impact studies. The lack of research affects the still-occurring ship accidents in ports, when port tugboats are used [11], which the authors of the article drew attention to.

Most often, tugs are classified according to the following categories: pulling power, propulsion type, functionality, and ice class. The pulling force of tugboats usually starts from 50 kN (in small ports) to 700–1000 kN in large ports that serve mega-type vessels such as E or G class container ships, SUEZMAX class or larger oil tankers, and dry bulk or other purpose vessels with a length reaching 300 m and more [12,13]. Today, the most common and popular tugboats with pulling capacities in ports are 500–600 kN. For example, in the port of Klaipeda, where up to 48 million tons of cargo are handled per year and more than 6500 ships enter the port, including G and E class container ships and SUEZMAX and larger oil tankers, currently 8 tugboats with a pulling power of up to 650 kN are used in the port for tug operations [11,14,15].

In some ports, when ships are moored and unmoored, the tugboat fee does not depend on the number of tugboats, so ship captains and pilots unreasonably order too many tugboats, while at the same time in other parts of the port, the tugboats’ specific operations are hindered, and unreasonable risks are caused [3,6,16,17]. When mooring ships in many ports, the number of tugboats and their traction force are not accurately calculated, which reduces the economic results for ship operators, and for ports, it decreases the attractiveness of the ports.

Accidents and emergencies in ports or seas lead to huge financial and ecological losses, so their prevention is one of the most important areas of ongoing scientific research. The most frequent locations of shipping accidents and incidents are in port approach channels, as well as during ships mooring and unmooring operations [18,19,20]. Therefore, it is especially important to ensure navigational safety during ships mooring and unmooring operations. So, based on scientific research, with the help of an optimal number and bollard pull of port tugboats, the number of accidents and other incidents can be reduced and material losses and damage to the environment can be minimized [9,10,11].

With the rapid increase in the scale of international trade and the construction of larger ships, such as very large crude carrier (VLCC) and ultra large crude carrier (ULCC) tankers and ultra large container ships (ULCSs), many ports face problems in accepting limited-size ships, as well as port tugboat availability [12,13,21,22]. At the same time, the correct use of port tugboats to service the largest vessels, under limiting conditions, is the optimal solution possible for the port entry and safe manoeuvring of ships [1,3,11]. In most cases, modifying and expanding the port infrastructure requires time and large investments, so in order to maximize the use of the port’s capacity by serving the largest possible ships and to ensure the safety of the port, the effective application of tugboats is one of the possible solutions [23].

Since tugboats have to compensate for the resulting external forces acting on the ships, these operations must be carefully planned and the port tugboat possibilities accurately calculated [1,4,16]. The research carried out and the methodology for the optimal use of port tugs presented in the article are universal, and this methodology is innovative and new.

Port tugs are particularly important for improving port navigational security, so various methods are applied to estimate their number and bollard pull necessary for a specific situation [8,16]. One of the research directions is related to the optimization of bollard pull of port tugs and the improvement of control systems [24,25].

Much research has been directed to the solution of the problem of planning the work and employment of port tugboats. This is especially relevant in large ports where VLCS (up to 15 thousand TEU) and ULCS (up to 24 thousand TEU) type container ships are served. The need to properly plan and allocate the capacity of tugboats, in order to avoid delays and downtimes, is determined by the incurred material losses and the risk of aligning port operations. By applying an ad hoc algorithm, it is possible to solve the problem of the load of port tugboats by programming the mutual chains of their activities and thus aiming to use them as efficiently as possible [21,22,24].

Ship mooring operations are described in the literature, but the actions of tugboats when mooring ships at quays with low clearance are not well studied, which in some cases creates dangerous situations when there is insufficient horizontal pulling force of tugboats.

These problems are generally studied in order to determine the optimal conditions for the use of tugboats in ports from the aspect of ensuring port safety and security, including the use of various simulation methods [26,27].

When planning ports and their separate parts, efforts are made to make optimal use of natural and available or possible technical conditions, as well as standards and recommendations that combine the latest achievements, so that by taking advantage of natural conditions, there would be a need to limit the use of assistance from port tugboats to a minimum [28,29,30,31], but completely dispensing with using port tugboats in mooring and unmooring large ships and in other port operations is in many cases impossible.

It can be said that research on the use of tugboats in ports is important and must consider various conditions of ship manoeuvring in ports, especially during ship mooring operations, which have not yet been sufficiently studied. As a review of scientific research shows, much attention is paid to studying the manoeuvring characteristics of tugboats and their interaction with the serviced ship, but little attention is paid to the research and proper assessment of external forces, which, as shown by various statistical and research data presented, have a significant impact on port safety when various towing operations are carried out.

The methodology for evaluating the maximum pulling force of tugboats and, accordingly, the number of tugboats required for mooring, unmooring and turning ships in the port’s turning basins, presented in the article, is innovative, and its use allows one to solve the challenges of increasing navigational safety in ports and optimally use the available capacities of port tugboats.

3. Theoretical Basis for Tug Bollard Pull Evaluation During Ship Mooring Operations in Ports

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:

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Collection and analysis of the aforementioned primary data;

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Assessment of the manoeuvrability of the ship and the tugboats in the port area during various operations;

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Optimum selection of the number of tugboats and the required pulling power (bollard pull) of the tugboats;

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Planning the timing of towing operations and possible costs;

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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]:

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

(1)

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

(2)

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

(3)

where $X_{in}, Y_{in}, M_{in}$ 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 $X_{\beta }, Y_{\beta }, M_{\beta }$ are the ship’s hull as the acting “wing” related forces and the moment, which could be calculated using the methodology stated 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); $X_{sh}, Y_{sh}, M_{sh}$ 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 $X_{tug}, Y_{tug}, M_{tug}$ 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) ($Y_{tug}$) 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]:

$$x_k=A{x}_{k-1}+{Bu}_k+{\omega }_k,$$

(4)

with observations $z_k$ (Equation (5)):

$$z_k=H{x}_k+{\upsilon }_k,$$

(5)

where: $A$, $B$, $H$—coefficients; ${\omega }_k$, ${\upsilon }_k$—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]:

$$t_P=t_y\pm {\mathrm{P}}^{\prime }·\Delta t·k_t,$$

(6)

where:$t_y$—average of the experimental data; ${\mathrm{P}}^{\prime }$—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); $\Delta t$—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 ($Y_{tug}$), 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:

$$Y_{tug}=Y_{in}+Y_k+Y_p+Y_a+Y_c+Y_{sh}+\cdots ,$$

(7)

where: $Y_{in}$—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; $Y_{sh}$—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:

$$Y_{tug}=1.3C{\displaystyle \frac{\rho }{2}}LT{v}_y^2(1+4.95({\displaystyle \frac{T}{H}}{)}^2)+C_a{\displaystyle \frac{{\rho }_1}{2}}{S}_x{v}_a^{2}sin{q}_a+C{\displaystyle \frac{\rho }{2}}LT{v}_c^{2}sin{q}_c,$$

(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]; $\rho$—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].

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

4. Case Study of Tug Bollard Pull Evaluation During Ship Mooring Operations

A calculation program was created to calculate the traction force (bollard pull) and number of tugboats required for various situations in the port at different quays. The maximum pulling power (bollard pull) of tugboats is required to bring a ship to or from a berth when the current and wind coincide or are in a similar direction. To assess a specific situation, berths were chosen to be placed at an angle to the current and the wind in various wind directions. At specific locations in the port of Klaipeda, for example, berths No. 67a and No. 72 (Figure 5), the current usually flows from the Curonian Lagoon to the Baltic Sea, and only in specific periods (during spring tides or after long-term strong westerly winds, when a lot of seawater enters the Curonian Lagoon), and currents from the Curonian Lagoon to the Baltic Sea are observed. The angle of the current course with berth No. 72 is about 70 degrees, and with berth No. 67a, about 80 degrees [39,40] and the wind and current flow in the same directions at the same time (direction about 330 deg., N is north direction) (Figure 5). The speed of the current from Curonian Lagoon to the Baltic Sea at the tops of the aforementioned berths is up to 1.0 m/s, and in exceptional cases, up to 1.5 m/s [39,40].

For POST PANAMAX ship mooring and removal from quay No. 67a, the trajectory with a wind speed of 12 m/s (wind direction towards the shore) and a current speed of 1.5 knots (direction 345 degrees), obtained with the help of the SimFlex Navigator simulator, is presented in Figure 6. The time for bringing the ship away from the quay was about 5 min, and the maximum power of the tugs’ engines was used for about 4 min when bringing the ship away from the quay and about 4 min when turning the ship into the channel.

At quay No. 72, ships up to the HANDY SIZE type with a deadweight of up to 35,000 tons are moored; at berth No. 67a, ships up to the POST PANAMAX type (Figure 7) with a deadweight of up to 100,000 tons are moored. The length of POST PANAMAX ships is up to 230–250 m, the width is up to 40 m, and the draft of a loaded ship can be up to 13.5 m (at zero or plus water level).

Leading from quay No. 67a, large ships sometimes have situations where three or four tugs are needed, each with a pulling force (bollard pull) of up to 500 kN (50 T). This quay is located in the most difficult harbour in terms of the use of tugboats, so it has been used for theoretical and experimental studies with real PANAMAX and POST PANAMAX type vessels.

In the course of detailed studies of the specified situations, a calculation program was prepared based on the developed methodology, and calculations of the necessary pulling force (bollard pull) of tugboats in various situations at the selected quays were performed.

With the help of the developed methodology and calculation program, the assessment of the necessary traction force (bollard pull) of tugboats in various hydrometeorological and hydrological situations was prepared, and graphic material, easily adapted for practical purposes, was prepared. The graphic material, as an example in this article, is presented for the direction of the current from the Curonian Lagoon to the Baltic Sea at the current speeds of 0.5 m/s (1.0 knot) and 1.0 m/s (2.0 knots), and the direction of the current is about 80 degrees to the pier.

Wind directions are assumed (with respect to the berth) from 0 to 180 degrees in every 30 degrees, and wind speeds are assumed at the wind speed measured at the hydrometeorological station at the port gate: 5 m/s; 10 m/s: 15 m/s; 20 m/s (taking into account the actual wind speed at the selected quays, and assessing the decrease in wind speed due to the effect of the Curonian Spit in the case of westerly winds and the effect of the buildings in the case of easterly winds). The calculation results, as examples, are presented in Figure 8 and Figure 9. In Figure 8 and Figure 9 are presented the minimum number of tugs and their power (bollard pull). As an example, in the entry shown: 10 m/s, 1 × 300 kN, 1 × 500 kN tugs means that the wind speed is 10 m/s, one tug has a pulling force (bollard pull) of 300 kN and one tug has a pulling force (bollard pull) of 500 kN.

A PANAMAX-type ship with a length of about 215 m was accepted for analysis. Its width was about 32.5 m; draft about 12.5 m (in ballast, about 7.0 m); the area of the projection of the underwater part to the DP was about 2500 m²; and the above-water surface area to DP was about 2700 m² (in ballast, about 3600 m²) (indicative deadweight of about 65,000 t) (Figure 8 and Figure 9).

In this way, the necessary traction force (bollard pull) of tugboats, when the current speed is up to 0.5 m/s (1 knot) and 1.0 m/s (2 knots), allows for a more accurate assessment of the required number of tugboats in specific situations, and if the ship has its own steering devices (thrusters), in individual cases, it is possible to completely or partially refuse the help of tugboats.

For practical purposes, the calculations also accept the traction (bollard pull) reserve of tugs or thrusters, i.e., no more than 75 percent of the pulling power (bollard pull) of the tugs or thrusters is used.

Similar calculations used the developed methodology for calculating the traction force of tugboats, and experiments used real ships and a calibrated visual simulator. Calculations and studies were carried out on different ships (deadweight from 15,000 tons to 110,000 tons), with wind speeds from 5 m/s to 15 m/s and various directions relative to the quay, current speeds from 0.5 m/s to 1.5 m/s and various directions relative to the quay, and ratios of draft to depth of the ship from 0.6 to 0.95. Analysis of the obtained results using the Kalman filter for filtering the obtained data [36] and the maximum distribution method for the accuracy assessment of the obtained data, showed that the difference between the obtained calculations and experimental data was no more than 10–12 percent.

5. Discussion

Harbour tugboats are very important in ensuring the navigational safety of the harbour during the mooring and unmooring of ships and other shipping operations. The methodology for assessing the maximum traction forces (bollard pull) required by tugboats and the number of tugboats during the mooring and unmooring of ships, as well as during other operations in the port, such as turning of ships in the port areas, is focused on increasing the safety of shipping in ports [4,6,21]. The developed methodology makes it possible to increase shipping safety in ports and optimize the required number of tugboats for specific ship mooring operations, which allows not only the optimal distribution of tugboats for various port operations, but also optimization of costs for tugboat services, which increases the attractiveness and competitiveness of ports.

At the same time, it should be noted that there are still many different problems related to the use of harbour tugboats that need to be solved, since port tugboats are used to solve various tasks in the port, so the estimation of the required tugboat pull (bollard pull) is very important for ports, especially if a port has a limited fleet of tugboats and a limited number of tugboats with large traction forces.

Additional power (ship pushers or tugboats) is required for mooring, unmooring and turning ships in limited water areas. With the help of the developed methodology, it is possible to estimate the required pulling or pushing force of tugboats to perform ship mooring operations, and at the same time, the required number of tugboats and the pulling force justified under certain hydrological and hydrometeorological conditions.

The prepared graphs of the required pulling power (bollard pull) of tugboats and their quantity, as an example of the purposeful use of the developed methodology, can be easily applied to real situations and at the same time reasonably assess the necessity of ordering tugboats, their quantity and traction force (bollard pull).

The validity of the use of tugboats in ports, ensuring the safety of navigation, was investigated, and it was found that under non-standard (marginal) conditions, tugboats are not always used effectively due to insufficient research; therefore, scientific research on the use of tugboats in ports, guaranteeing the safety of navigation, is very important and should be conducted [3,10].

The developed methodology for calculating the traction force (bollard pull) of port tugs and determining the number of tugboats required on that basis may be more difficult to apply in various exceptional cases: for example, when wind parameters (speed and direction) change due to nearby structures, or current parameters (speed and direction) undergo sudden change due to the cross-sectional area of the channel. This can be accepted as a partial limitation of the developed methodology, and such exceptional conditions should be the subject of further research under rapidly changing external influences.

6. Conclusions

When conducting experiments while mooring real ships and using a calibrated simulator, it was found that after using data filtering with the help of the Kalman filter and the maximum distribution method to determine the accuracy of the obtained results, the difference between the results of the theoretical calculations and experiments did not exceed 10–12%.

It is appropriate to inform the responsible employees of shipping and port administrations and shipping companies, who make decisions about the mooring and unmooring of ships, so that they can reasonably assess the necessity of port tugboats and their pulling force and quantity, especially in cases where a specific company or shipping company has to pay for tugboat services.

When using tugboats in ports, the maximum use of their power is short-term (e.g., when mooring and unmooring ships to and from quays, and in some cases when turning ships in port water areas), and it is very important to have sufficient traction power (bollard pull) calculated in advance to avoid emergency situations.

The developed methodology for calculating the traction power (bollard pull) of tugboats allows determining the required pulling power of tugboats with sufficient accuracy in advance for vessels of specific parameters and environmental conditions.

Carrying out case studies of the most difficult places in the port, from the point of view of the use of tugboats (for example, berths No. 67a and No. 72 in Klaipeda port), and other difficult places allows us to make reasonable assessments of the number of tugboats and pulling force (bollard pull) required, and at the same time minimize the risks of emergency situations.

The developed methodology for calculating the number of tugboats and their traction force (bollard pull) can be applied (with appropriate adaptation) in any port and at the same time increase the safety of navigation, especially in difficult conditions.