Issue №30

In work is specified, that navigation safety of sailing to a great extent depends on the errors of the navigation measuring, and also from operating reliability of sensors of navigation information. It is also marked that descriptions of exactness of gyroscopic compass influence on navigation safety. Because sizes of his errors the requirements providing the set exactness of determination of azimuthal directions are produced. At maneuvering of ship there are inertia errors which cause appearance of lateral displacement of ship after his turn, that can lead to the navigation failure of ship. Therefore, there is the problem of decline of lateral relocation bias of ship which appears after his turn, that conduces to the decline of navigation accident rate.
The analysis of the last achievements and publications is resulted in work, the decision of the considered problem and selection of parts unsolved before is begun in which.
Within the framework of theory endless rapid maneuver, expression for total inertia deviation which depends on character of maneuver and breadth of sailing of ship is resulted in the publication.
It is shown that transversal relocation bias of ship is an integral function in relation to the function of deviation and for estimation of its size analytical expression is resulted, which it is visible from, that transversal displacement also depends on speed of ship after a maneuver.
It is marked in the publication, that transversal displacement is more complete description of exactness of gyrocompass on the protracted time domains, as it represents the consequences of influencing of maneuvering on a gyrocompass in the «smoothed» kind out. From these positions, obviously, that inertia deviation is the index of instantaneous exactness of gyrocompass.
Two methods of decline of transversal displacement of ship are offered, thus for estimation of efficiency of the offered procedure of indemnification of lateral displacement of ship the computer program allowing to produce the calculation of the crooked dependence of total inertia error from time with the subsequent graphic reflection was developed. The program also expects and builds the graphs of dependence of lateral displacement without indemnification, total lateral displacement with partial indemnification and with complete indemnification.
The results of computer graphic design are resulted, which it ensues from, that total inertia error and lateral without indemnification is multiplied displacements with growth of breadth, during partial indemnification total lateral displacement diminishes approximately in 5 times, and at the variable additional amendment of course lateral displacement of ship is absent.
Keywords: safety of navigator, ship gyrocompass, inertia deviation, lateral displacement of ship, imitation design.

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161 с.
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The safety of marine navigation in coastal areas and narrow waters, which account for 80% of total navigational accidents, remains a pressing concern. These circumstances indicate the need to improve traditional and automated methods of passage planning and control of navigation and traffic management processes, based on the assessment of the actual navigation accuracy and navigation safety parameters. According to current industry recommendations, the main parameters of safe navigation are safety depth, safety contour, permissible cross-track limit, and accuracy of position fixing.

This study deals with the development of a general practical approach to the calculation of the safety depth, as one of the main safety parameters in the ECDIS system, with an increased focus on those aspects of calculation where navigators tend to make mistakes.

Analysis of data obtained during the training on the ECDIS simulator for navigators directly involved in the passage planning process (master, navigation officer) showed systematic mistakes in assessing the route safety, which can lead to ship grounding in real world. At the same time, navigators often do not recognize the danger, misinterpret it or make mistakes when checking the passage plan for safety. The results of the competence assessment showed that 40% of masters and 30% of navigation officers make mistakes in calculating the safety depth.

The most common mistakes are the incorrect application of category zones of confidence (CATZOC), miscalculation of the minimum depth on the route, miscalculation of the tide height, tidal window period, the neglect of corrections for increased draught due to roll and pitch.

The paper suggests that the UKC (under keel clearance) company policy shall take into account the accuracy of chart information. Furthermore, the research further develops the method of calculating the safety depth, implemented in the software, which makes it possible to systematically assess the safety of a route with multiple legs with heterogeneous parameters.

Keywords: ECDIS, ECDIS simulator, grounding, safety depth, safety contour, deck officers` errors leading to grounding, E-navigation.

1. Becker-Heins, R. (2017) Voyage Planning with ECDIS. Practical Guide for Navigators. Geomares Publishing.
2. Burenkov, O., Pipchenko, O. (2020) Monitoring and identification of errors during training on ECDIS simulators // Slovak international scientific journal: Vol. 1, №43, 46 – 50
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5. Idris Turna, Orkun Burak Öztürk (2019) A causative analysis on ECDIS-related grounding accidents, Ships and Offshore Structures, DOI: 10.1080/17445302.2019.1682919 https://doi.org/10.1080/17445302.2019.1682919
6. IMO (2017) MSC circ. 1503 ECDIS – Guidance for Good Practice
7. IMO (1999) resolution A. 893 (21) Guidelines for Voyage Planning
8. IMO (2006) resolution MSC 232 (82) Adoption of the Revised Performance Standards for Electronic Chart Display and Information Systems
9. INTERTANKO (2017) Guide to Safe Navigation (Including ECDIS)
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11. Pipchenko, O. (2019) Passage Planning with ECDIS. Module 4: Safety limits and use of navigational functions. https://learnmarine.com/library/EP04/Safety_limits_and_use_of_
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19. Пипченко А. Д. Расчет крена судна на циркуляции / Науковий вісник Херсонської державної морської академії № 1 (16), Херсон: ХГМА, 2017 – С. 61-67

In the article is specified, that a decision-making process contains the following stages: control of environment, including relative position and parameters of relative motion, the exposure of situation of rapprochement of vessels, in the case of rapprochement of vessels it is necessary to produce estimation of degree of his danger, at dangerous rapprochement is needed to define the type of co-operation, depending on the degree of danger of situation of rapprochement the choice of strategy of divergence is produced.

On the first stage of process of decision-making surrounding mobile objects come to light by ARPA or AIS, for which is measured parameters of motion and relative position. It is shown that on the second stage of process of decision-making, using the measured parameters, it is necessary to expect the value of speed of change of distance between vessels, taking into account that at its negative value ships are drawn together. On the third stage of process of decision-making at rapprochement of vessels estimation of degree of his danger is produced, what development of situation of rapprochement to the moment of time of their shortest rapprochement is forecast for.

On the fourth stage of decision-making it is necessary to define the type of cooperation of the drawn together vessels, taking into account principle their process control of divergence. It is especially substantial for principle of locally-independent management by the process of divergence, when coordination of co-operation of vessels at dangerous rapprochement is needed. The fifth stage of decision-making is characterized by the choice of strategy of divergence, thus at the locally-independent process control of divergence the choice of strategy of divergence is produced depending on the degree of danger of situation of rapprochement, by the standard maneuver of divergence or for excessive rapprochement of vessels it is necessary to use the maneuver of urgent divergence.

In work as the index of efficiency of the analytical collision avoidance systems vessels probability of safe completion of process of divergence, which is work of probabilities of successful end of stages of process of decision-making on the choice of strategy of divergence, is offered.

It is shown that first three stages of decision-making on the choice of strategy of divergence are characterized by general probability of absence of danger of collision on condition that distance of the shortest rapprochement is equal to the set minimum-possible distance of rapprochement. For determination of the mentioned probability the error of distance of the shortest rapprochement is considered and expression is got for the closeness of its distributing. To that end collected dependence of error of distance of the shortest rapprochement from the errors of measuring of distance and bearing.

By the got expression for the closeness of distributing of error of distance of the shortest rapprochement probability is certain of that at equality of distance of the shortest rapprochement with limit-possible distance of rapprochement there will not be the collision.

Keywords: safety of navigation, warning of collision of vessels, index of efficiency of the analytical collision avoidance systems vessels, probability of absence of danger of collision.

1. Бурмака И.А. Управление судами в ситуации опасного сближения / И.А Бурмака.,
   Э.Н Пятаков, А.Ю. Булгаков – LAP LAMBERT Academic Publishing, – Саарбрюккен (Германия), – 2016. – 585 с.
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10. Бурмака И.А. Экстренная стратегия расхождения при чрезмерном сближении судов / Бурмака И.А., Бурмака А. И., Бужбецкий Р.Ю. – LAP LAMBERT Academic Publishing, 2014. – 202 с.
11. Пятаков Э.Н. Оценка эффективности парных стратегий расходящихся судов / Э.Н. Пятаков., С.И. Заичко // Судовождение: Сб. научн. трудов. / ОНМА, – Вып.15. – Одесса: “ИздатИнформ”, 2008. – С. 166 – 171.
12. Бурмака И.А. Маневр расхождения трех судов изменением курсов/ И.А. Бурмака, А.Ю. Булгаков // Автоматизация судовых технических средств: науч. -техн. сб. – 2014. – Вып. 20. Одесса: ОНМА. – С. 18 -23.

An algorithm is proposed for determining the set of corresponding to the COLREG variants of combined action (alteration course with the speed) to avoid collision with several vessels. When establishing compliance with COLREG, 11 types of meeting of the dangerous target and own ship and four stages (planning of maneuver, early, possible and urgent measures) at the segment of COLREG performance in relation to this target were distinguished. It was assumed that the action to prevent a collision is determined at the first stage. We used the general and particular indicators of the COLREG compliance for each of possible variants of combined action. Due to the large number of such options, the formulas used in their analysis for forecasting, assessment of safety and other goals were simplified so that the calculation time was acceptable. On this basis, the danger domain for the targets was selected simple, circular in shape, with the center shifted relative to the target to take into account the greater risk of crossing its course along the bow than at the stern. It was supposed acceptable to replace the trajectories of combined actions with a combination of a straight segment and an arc of a circle; to represent the change in speed during braking by a second-order polynomial; to consider as unrelated the course and speed changes in the joint operation.

An algorithm has been developed for obtaining a matrix of general COLREG compliance estimates of possible combined action variants and flow chart of this algorithm is given. By the elements of this matrix, it is possible to search for an effective variant of the passing by under various assumptions and criteria. As an example, an algorithm for calculating the combined action to avoid a collision with a minimum reduction of the speed is given. The reliability of the proposed algorithms was confirmed by simulation modeling of ships collision avoiding processes in various situations.

Key words: collision avoidance, combined action, compliance with COLREG, collision avoidance algorithm.

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Principle of action of semiconductor two-collector magnetic transistors and possibility of creation on their basis of electronic compass is covered in the article. Level of automation of marine ships navigation, appearance of the autonomous fully automated ships without a crew, requires presences aboard the ship of device giving out a not visual, but electronic signal about direction of motion. An electronic compass on the basis of magnetic sensor semiconductor elements can decide this task.

There is of most interest an electronic compass, a consisting of semiconductor magnetic sensor element, electric signal on the output of which is proportional to the level of the external magnetic field, and electronic chip processing a signal. In this article the example of laboratory construction of such electronic compass is described and his descriptions over are brought. Important, that this electronic device does not have mobile mechanical parts and mechanisms.

For the increase of sensitiveness of electronic sensor of the magnetic field application of reflector-absorbers of the magnetic field is offered. Ferrite bars are used in this case. Bars are disposed both-side sensor, parallell to optimum direction of the magnetic field. In the experiments it was succeeded to get the increase of sensitiveness of sensors in 400 times. The reflector-absorbers of the magnetic field also allow to improve correlation signal to noise in 100 times.

An electronic compass on the basis of magnetic transistors can be also used and as an element to control the course of marine ship. If a magnetic transistors is set to direction of motion, the change of loading resistances sets the zero of tension between the collectors of magnetic transistor. At deviation of axis from the set direction, tension of one polarity appears between collectors, and in other – opposite. This tension through the system of autopilot can directly control a steering gear and automatically to maintain the set direction of motion of marine ship.

Experimental descriptions over of pre-productions models of magnetic transistors and flows diagrams of compasses are brought. An experiments show that on the basis of two-collector magnetic transistors can be created electronic compass not containing mechanically moving details, that sharply promotes his reliability and durability.

An electronic compass will become the obligatory attribute of future autonomous ships without a crew. He will be able not only to replace a classic magnetic compass but also to allow to realize the span-new functions of ships control.

Keywords: safety of navigator, magnetic compass, navigation, unmanned ships, magnetic transistors, reflector-absorbers of the magnetic field, electronic control chip

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In the article is specified, that marine ships considerable part of the operating time work in the straitened districts, in which the width of free passage-way for vessels is limited in the navigation relation by dangers, or intensive navigation. It is marked that in the case of dangerous rapprochement of vessels in the straitened waters at the choice of maneuver of divergence by an operating ship besides a dangerous target it is necessary to take into account preventing ships and navigation dangers in the district of maneuvering, and the existent methods of simultaneous account of dangerous aims and navigation dangers carry analytical character and are bulky and ineffective. The necessity of development of operative and evident methods of warning of collisions of vessels at sailing in the straitened waters is caused to these.

The analysis of the last achievements and publications is resulted in work, the decision of the considered problem and selection of parts unsolved before is begun in which. It is shown that binary coordination is the basic method of description of cooperation of pair of the dangerously drawn together vessels, urgent strategies of divergence are considered, the structure of which depends on the conduct of target in the process of divergence, the analysis of procedures of account of navigation dangers is also produced by an analytical method for different types of navigation dangers.

Procedure of transformation of the ship safe region set in space of relative motion is offered, in space of veritable motion, a virtual region is formed as a result.

It is indicated, that basic properties of virtual regions are: rapprochements of ship with a target dangerous, when the current area of programmatic trajectory of motion of ship gets in the virtual region of target;  distance of the shortest rapprochement of ship with a dangerous target will be equal to the set minimum-possible distance of rapprochement, if direction of current area of programmatic trajectory of motion of ship is tangent to the border of virtual region; equality of distance of the shortest rapprochement of ship with a target and set minimum-possible distance of rapprochement is saved at the following of ship on a virtual region tangent to the border to the moment of the shortest rapprochement.

It is shown in the publication, that by the computer program dependences of position and form of virtual region on the relation of speeds of ship and target were explored, from distance between a ship and target, and also from bearing on a target.

It is shown that depending on distance between a ship and target at the unchanging bearing a virtual region occupies unchanging position in relation to the line of programmatic way of ship, and position and sizes of virtual region depend on bearing on a target.

Keywords: safety of navigation, warning of collision of vessels, ship safe region, virtual region of target.

1. Пятаков Э.Н. Взаимодействие судов при расхождении для предупреждения столкновения / Пятаков Э.Н., Бужбецкий Р.Ю., Бурмака И.А., Булгаков А.Ю. – Херсон: Гринь Д.С., 2015. – 312 с.
2. Пятаков Э.Н. Оценка эффективности парных стратегий расходящихся судов / Э.Н. Пятаков., С.И. Заичко // Судовождение: Сб. научн. трудов. / ОНМА, – Вып.15. – Одесса: “ИздатИнформ”, 2008. – С. 166 – 171.
3. Volkov. Apprisal of the Coordinability of the Vessels for Collision Avoidance Maneuvers by Course Alternation / A. Volkov, E. Pyatarov & A. Yakushev// Activites in Navigation.-Adam Weintrit/ – 2015, P. 195 – 200.
4. Бурмака И.А. Экстренная стратегия расхождения при чрезмерном сближении судов / Бурмака И.А., Бурмака А. И., Бужбецкий Р.Ю. – LAP LAMBERT Academic Publishing, 2014. – 202 с.
5. Мальцев А. С. Маневрирование судов при расхождении / А.С. Мальцев, Е.Е. Тюпиков, И.И. Ворохобин – Одесса: Морской тренажерный центр, 2013. – 304 с.
6. Бурмака И.А. Управление судами в ситуации опасного сближения / И.А. Бурмака., Э.Н Пятаков., А.Ю. Булгаков – LAP LAMBERT Academic Publishing, – Саарбрюккен (Германия), – 2016. – 585 с.
7. Цымбал Н.Н. Гибкие стратегии расхождения судов / Н.Н. Цымбал, И.А. Бурмака, Е.Е. Тюпиков. – Одесса: КП ОГТ, 2007. – 424 с.
8. Волков А.Н. Применение судовой безопасной области для учета опасной цели и навигационного препятствия / Волков А.Н.// Водный транспорт. – 2014. №2 (20).– С. 29 – 35.
9. Волков А.Н. Формирование процесса расхождения судна в ситуации опасного сближения методом виртуальных областей / Волков А.Н., Булгаков А.Ю., Голиков А.А. //East European Scientific Journal, №11 (27), 2017, part– С. 4 – 13.

The paper indicates that navigation in narrow waters requires navigators to use means of passage safety assessment prior to choosing a route. It is pointed out that a relevant factor when assessing the safe passage probability is the cross-track error distribution law, whose impact is the subject of the research.

The article analyses recent developments and publications that have begun investigating this subject, and highlights previously unsolved parts of the general problem. The results revealed two equivalent approaches, as well as a navigational safety parameter, which are used to determine the probability of safe navigation in narrow waters on the chosen route.

The need to develop advanced predictive vessel motion models is noted, while many researchers study the design of an information system for vessel motion simulation with complex dynamic models and an intelligence system for vessel motion prediction that imitates the learning process of an autonomous control unit created with the use of the artificial neural network. Methods for identification of vessel manoeuvring models are shown. Based on the analysis of vessel hydrodynamics, a nonlinear model frame of vessel manoeuvring is established.

The available publications suggest using compound laws of the first and second types for describing random errors in navigation measurements as an alternative to the normal distribution law.

The article examines the dependence of the safe narrow waters passage probability on the cross-track error distribution law. The normal law and compound laws of the first and second types are considered as the cross-track error distribution laws. A formula for estimating the safe passage probability in the manoeuvring area is given, and expressions for the distribution function of the normal law and compound laws of both types are obtained. To assess the impact of the cross-track error distribution law for the same route, the safe passage probability for the normal distribution law, as well as compound laws of the first and second types, was calculated.

For the same route, the probability of safe passage was calculated with the use of one-dimensional and two-dimensional density models. It is shown that the average relative difference between the estimated safe passage probability for both models is 0.3%, which confirms the validity of using a one-dimensional cross-track error distribution density.

Keywords: safety of navigation, laws of distribution of random errors, safe passage probability, navigation in narrow waters.

1. Кондрашихин В.Т. Определение места судна / Кондрашихин В.Т. – М.: Транспорт, 1989. – 230 с.
2. Ворохобин И.И. Эквивалентность оценки вероятности безаварийного плавания судна в стесненном районе / Ворохобин И.И., Северин В.В., Казак Ю.В. // Судноводіння: Зб. наук. праць / ОНМА. Вип. 25. – Одеса: «ВидавІнформ», 2015 – С. 40 –
3. Мельник Е.Ф. Обоснование выбора критерия навигационной безопасности судовождения/ Мельник Е.Ф.// Судовождение. – 2002. – № 5. – С. 65 – 73.
4. K. Benedict. Manoeuvring Simulation on the Bridge for Predicting Motion of Real Ships and as Training Tool in Ship Handling Simulators/ K. Benedict, M. Kirchhoff, M. Gluch, S. Fischer, M. Baldauf // TransNav, International magazine on marine navigation and safety of marine transport, Vol. 3, № 1, page 25-30, 2009.
5. Benedict. Simulation Augmented Manoeuvring Design and Monitoring – a New Method for Advanced Ship Handling/ K. Benedict, M. Kirchhoff, M. Gluch, S. Fischer, M. Schaub, M. Baldauf, S. Klaes// TransNav, International magazine on marine navigation and safety of marine transport, Vol. 8, № 1, page 131-141, 2014.
6. Ljacki. Intelligent Prediction of Ship Maneuvering / M. Ljacki // International magazine on marine navigation and safety of marine transport, Vol. 10, № 3, page 511-516, 2016.
7. J. Shi. Identification of Ship Maneuvering Model Using Extended Kalman Filters/ C.J. Shi, D. Zhao, J. Peng, C. Shen// TransNav, International magazine on marine navigation and safety of marine transport, Vol. 3, № 1, page 105-110, 2009.
8. Астайкин Д.В. Идентификация законов распределения навигационных погрешностей смешанными законами двух типов / Астайкин Д.В., Алексейчук Б.М. // Автоматизация судовых технических средств: науч. -техн. сб. – 2014. – Вып. 20. Одесса: ОНМА. – С. 3 – 9.
9. Monteiro Luis. What is the accuracy of DGPS? / Sardinia. Monteiro Luis, Moore Terry, Hill Chris. // J. Navig. 58, № 2, p. 207-225.
10. Сикирин В.Е. Описание навигационных погрешностей с помощью обобщенного распределения Пуассона/ Сикирин В.Е.// Судовождение: Сб. научн. трудов / ОНМА, Вып. 26. – Одесса: «ИздатИнформ», 2016 – С. 152 – 156.
11. Астайкин Д.В. Оценка точности координат судна при избыточных измерениях / Астайкин Д.В., Сикирин В.Е., Ворохобин И.И., Алексейчук Б.М. – Saarbrucken, Deutschland / Германия: LAP LAMBERT Academic Publishing, 2017. – 274 с.
12. Вентцель Е.С. Теория вероятностей/ Е.С. Вентцель – М.: Государственное издательство физико-математической литературы, 1962. – 564 с.

Science and technology achievements in the 21st century have qualitatively changed the traditional methods and techniques of Earth’s surface research. Nowadays, remote methods have been used widely, when an observer or a measuring device is located at a certain distance from the study object in order to increase the observation area by several times. These materials can expand horizons of researchers, lead to increasing the flow of valuable information about already known objects and phenomena of the Earth.In presented research, there are some explanations about mechanisms of using natural processes to make forecast of changes in bottom topography in shallow water under navigation conditions. The key factor is the development of programs that can track changes in natural processes with displaying and fixation on electronic devices. Any research should preferably be carried out considering changes of the object over time and under the influence of various factors simultaneously and dynamically. In the article dynamic processes are divided into “significant” and “insignificant”.

This dependence is determined by the scale of space and time, where and when they occur. The concept of “scale factor” is introduced in order to determine significance of dynamic processes influence during research. Presented in the research dynamic map modelling method enables to make a forecast of siltation of the sea / river bottom for a given period of time. After comparing the forecast with the actual result, you can make corrections of the selected function, i.e. constantly improving the model.

As a result of the research, we came to the following conclusions:

1. The “scale factor” should be entered in dynamic navigation map research and compilation with using different-scale data of the water surface and bottom topography;
2. It is recommended to enter a dynamic component into the information block of the navigation cartographic systems ECDIS and Inland ECDIS, allowing the skipper to see the position of the vessel, considering the wave height relative to the bottom in real time;
3. Above methods of parallel bottom topography transferring are based only on the data of statistical observations with using iterations. These methods usually give proper results on sandy and silty soils, where the relief has distinct wave-like forms, as well as relatively often repeated external influences with following the general main direction.

Key words: RIS, dynamic processes, “scale factor”, “chart dynamic model “, ECDIS.

1. Юдин Ю.И., Сотников И.И. Математические модели плоскопараллельного движения судна. Классификация и критический анализ Вестник МГТУ, том 9, No2, 2016 г. стр.200-208
2. Самонов В. Е. Математическое моделирование движения тонкого слоя жидкости под действием поверхностных сил, дисс. К.т.н. СГУ,- Ставрополь 2013. – 145с.
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The design of ships or any other floating systems intended to operate on or close to the surface of the sea is controlled to a large extent by what is usually referred to as seakeeping, or, in more common terminology, safety at sea. This is a primary consideration and criteria, which has to be fully met. Safety of a ship naturally includes the crew, cargo and the hull itself. Seakeeping is, indeed, a generalized term and reflects the ship’s capability to survive all hazards at sea such as collision, grounding, fire, as well as heavy-weather effects related to the environment in general and waves in particular. The two most likely types of failure under these conditions are due to structural causes and capsizing resulting from insufficient stability under severe weather conditions.

Such criteria as economical navigation of the ship as related to speed-keeping abilities, fuel consumption, avoidance of damage to ship components and cargo, and comfort to crew or passengers, or both, are key items. The operational limits of electronic equipment, mechanical components and weapon systems on board warships are other aspects of sea keeping.

In this work it is highlighted that seakeeping is a generalized term that includes a wide variety of subjects such as ship motions (amplitudes, accelerations, phases), deck wetness, slamming, steering in waves, added resistance, hydrodynamic loadings (pressures, forces, moments) and transient loads. Since the ship environmental operability or its sea keeping characteristics are closely linked to the severity of the sea, the description of the seaway is usually considered as an integral part of sea keeping.

It is taken into consideration that the severity of the sea cannot be considered in absolute terms, since for each floating system, be it a ship, a platform or a buoy, the intensity of the sea state can only be determined in terms of the system’s responses. Hence, different thresholds apply to different problems, and sea state 4 may be just as severe for a small patrol craft as sea state 8 may be for a larger containership. Hence, the characteristics and frequency of occurrence of waves in specific sea zones are required if a possible reduction in the system environmental operability is expected.

It is demonstrated that most texts or papers, which deal with the overall question of sea keeping, devote some attention to the basic phenomena, that is, the seaway and the motions of the ship or other floating platforms as a result of the excitation imposed by the seaway. Ship motions, as such, do not always constitute the criteria for sea keeping, and much more often other responses directly related to the magnitude and phasing of the motions or the resulting velocities and accelerations constitute the prime cause for exhibiting good or bad sea keeping qualities. Such responses could be a function of the motion only, as in the case of added resistance or hydrodynamic pressures, or they could be a function of motion and other design parameters, such as freeboard in the case of deck wetness or the longitudinal weight distribution in the case of vertical bending moments.

In this work, latest methods of modeling and computation for body-wave interactions described and compared with data observed for container carrier. The foregoing calculation routine is fairly well accepted today among naval architects specializing in the sea keeping aspects of the ship design process. Differences between the results obtained by various techniques as presented by the available computer programs are insignificant. However, since the regular-wave results are of little or no value except as input for the more realistic long- and short-term response predictions in a real seaway environment, it is important to determine which wave data information and what statistical extrapolation techniques are used to obtain the latter.

The format used to describe the seaway in most ship response calculations is the wave spectrum. However, since measured spectrum for a specific sea zone or route are very rarely available, it is often necessary to use spectrum measured in one location for predictions in another location. In such a case, while the basic spectruml shape and scatter remain unchanged, the percentage of wave height distribution would vary to represent realistic conditions for the sea area in question. Such data usually are based on observations, and assuming the sample is large enough the distribution of expected wave heights should be quite reliable.

An alternative approach often used in ship design is to utilize one of several theoretical spectruml formulations [2, 3, 4] such as the Pierson-Moskowitz one-parameter spectrum, the ISSC spectrum, the JONSWAP spectrum, and other. In each of these cases, some input parameters are required usually in the form of wave height, period, peak frequency, fetch, etc. The reliability of the wave data depends in these cases both on the quality of the input parameter and the adequacy of the theoretical formulation.

Keywords: safety of navigation, seakeeping qualities, analytical modelling, stability assessment.

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8. Tsai, S. C., Hsu, S. H., Chien, H. L., Chou, C. M., Malenica, M. & Chen, X. B. 2013. Numerical study on seakeeping-sloshing coupling effect of container ship for sea trial purpose. In Proc. 12th Int. Symp. on Practical Design of Ships and Other Floating Structures PRADS, Changwon, Korea.
9. Kim, Y. & Park, S. G. 2014. Wet damping estimation of the scaled segmented hull model using the random dec-rement technique. Ocean Engineering 75, 71-80.
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12. Tadeusz Szelangiewicz, Bernard Wiśniewski, Katarzyna Żelazny, Maritime University of Szczecin, West Pomeranian University of Technology: POLISH MARITIME RESEARCH 3(83) 2014 Vol. 21; pp. 61-67

Development of modern ship’s automatic steering systems, navigation simulators, research of ship maneuvers stipulates the necessity of adequate mathematical models of the ship propulsion complex. The main components of the non-inertial forces of the ship propulsion complex are the hydrodynamic forces on the hull. Therefore, the improvement of mathematical models of these forces refers to important scientific and practical problems. This paper proposes a general approach to the construction of mathematical models of hydrodynamic forces on the hull. The approach is based on a multivariate quasilinear regression analysis, considering the values of the multiple correlation coefficient, the significance of the model, and the significance of each explanatory factor (regressor). In particular, the Fisher’s criterion was used to test the significance of the models, and the statistical significance of each regressor was checked with the help of the Student’s criterion. In addition, the standard error of each regressor was investigated. We also checked the absence of multicollinearity of the obtained models. The inadequacy of many existing mathematical models of hydrodynamic derivatives of longitudinal hydrodynamic forces on the hull is shown. In particular, it was found that one-factor correlation analysis cannot provide the construction of adequate models with high significance for all hydrodynamic derivatives. It has also been proven that applying only the AIC minimum criterion (Akaike Information Criterion) cannot ensure that all the regression analysis criteria are met. New adequate models of hydrodynamic derivatives have been constructed for longitudinal hydrodynamic forces on the hull with a high level of correlation, high indicators of significance of the models as a whole and of each regressor separately. The models are built for the whole range of variation of the block coefficient: (0.5; 0.9) and separately for the two ranges: (0.5; 0.7) and (0.7; 0.9). As regressors, we used the relations of the basic geometric parameters of the vessel, such as length, breadth on the current waterline, draught and the value of the block coefficient.

Keywords: longitudinal hydrodynamic forces, ship hull, mathematical models, multivariate regression analysis.

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It registers in the publication, that one of major is the problem of providing of safety of navigation, the successful decision of which conduces to the decline of harm of human life and environment.

Paid attention, that sailing of maritime vessels in the straitened districts is considerably complicated by the navigation obstacles and intensive navigation, which create pre-conditions for the origin of emergency situations, thus sailing in the straitened districts is characterized by the fleeting change of navigation situation, that requires development of operative methods of estimation of danger of rapprochement and choice of safe maneuver of divergence. The high level of the use on the ship of information technologies determines expedience of computer realization of the developed methods of prevention of collision of vessels.

It is specified, that in the conditions of intensive navigation there are the situations of dangerous rapprochement of ship with two targets at presence of navigation danger in the district of maneuvering.

The analysis of the last achievements and publications is resulted on the theme of prevention of collisions of vessels and it is shown that at the locally-independent management for this purpose offered method of forming of flexible strategies of divergence, methods of nonlinear integral invariance and theories of optimum discrete processes. Formalization is also produced cooperation of vessels in the situations of dangerous rapprochement and choice of strategy of divergence.

Strategy of urgent divergence is considered at rapprochement of vessels on small distances and description of process of divergence of vessels and choice of maneuver of divergence is produced in terms of differential antagonistic game.

It is shown that for the decision the problem set in the article it is necessary to choose the course of deviation the nearest to programmatic, and which does not belong to none of three impermissible great number of courses of deviation: with the first target, with the second target and with a navigation danger.

The condition of the safe passing by the ship of point danger, which foresees superiority of value of distance of the shortest rapprochement with her above the value of maximum possible distance of rapprochement, is resulted, and his analytical expression which allows to expect scope safe courses of deviation of ship. For estimation of danger of rapprochement of ship with a target equalizations of scopes of region of impermissible parameters of motion of ship are resulted.

The situation of rapprochement of ship is considered with two targets and the regions of impermissible values of parameters of motion of ship in relation to each of targets are formed. The condition of dangerous rapprochement is formulated.

The example of situation of rapprochement of ship with two targets is represented, when there is a point navigation danger in the district of sailing. The graphic reflection of regions of impermissible values of parameters of motion of ship in relation to each of targets is shown, on which the maximum courses of deviation on navigation limitations are also inflicted by the dotted lines. The optimum courses of deviation by the change of course to the right and to the left are certain.

Keywords: safety of navigation, warning of collision of vessels, divergence with two targets, navigation dangers

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The article deals with steering gears, used on marine and river ships, namely with ram-type steering gears. Article topicality due to the fact that ship controllability and sailing safety depends of steering gears reliability. Reliability could be increased through the refinement of processes, which took place during the perception and transfer of load.

Process of lateral force perception by plungers and guide beams is studied theoretically. It is shown that perception depends of gap size between plunger and sleeve and could pass in one, two or three stages. Those stages are characterized changing in the loading process plungers fixing conditions, and respectively plunger lateral load proposed to determinate by three design schemes.

Received expressions for calculation ultimate gaps of «plunger-sleeve» pare landing, that gives the limits of application each of three design schemes. Ratios for determination load of plunger and guide beam are received trough consideration their joint deformation for each design schemes. On the example of YOOWON–MITSUBISHI YDFT-335-2 ram-type steering gear is shown that in new gear, where landing gap is minimal and conditioned by tolerances of plunger and sleeve diameters, guide beam can take only 2.0…6.5% of lateral force, which applied to it and plunger from tiller. In steering gear with partially worn out plunger and sleeve in time of rudder feather shifting from diametric plane to board (when α = 5…35º), guide beam could take 4.7…6.8% of lateral force. The source of origin significant loads on plungers in ram-type steering gears is application of sinus-type mechanism for transformation progressive plunger motion to rotating tiller motion. Decreasing lateral loads on plunger through using unloading guide beams, with considering low unloading percent is ineffective. Guide beams availability complicates steering gear construction, increasing number of friction surfaces and trough this complicates steering gear maintenance.

Keywords: steering ram-type gear, plunger, guide beam, tiller, torque, lateral force, load, distribution, deformation, landing gap.

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4. Булюкина Н.А. Фрикционные автоколебания в судовых гидравлических рулевых машинах: автореф. дис. канд. техн. наук: спец.08.05 – судовые энергетические установки и их элементы (главные и вспомогательные); ФГБОУ ВПО «Санкт-Петербургский государственные морской технический университет».–СПб., 2013.–23с.
5. Месропян А.В. Методика идентификации струйно-золотниковой гидравлической рулевой машины / А.В. Месропян, К.А. Широкова, В.А. Целищев // Вестник УГАТУ. Серия «Машиностроение. Гидравлические машины, гидропневмоагрегаты». – Уфа: УГАТУ. – 2007. – Т.9, №6(24). – С. 44 – 55.
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   М.Я. Морозов. – М.: Транспорт, 1989. – 174 с.
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    В.В. Матвеев – К.: Наукова думка, 1988. – 736 с.
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15. Прикладна механіка / Д.М. Коновалюк, Р.М. Ковальчук, О.О. Фесенко, В.І. Шваб’юк, М.П. Ярошевич. – Луцьк: ЛДТУ, 2003. – 776 с.

During the movement of the vessel along the route there is a problem of observation of natural and man-made obstacles, which is solved by modernizing the management using e-navigation. Intensification of the movement process is provided by increasing the number and frequency of observations according to static criteria. In this case, the methods of graphical and analytical calculation of the path are the basis of navigation, forcing a return to the local criterion, which reflects the full physical nature of the process.

The calculation of the vessel’s path on the route is carried out according to the rule of the polygon, the sides of which are the vectors of the speed of the path, the vessel and perturbations (wind, waves, current). The main problem is the accuracy of determining the magnitude of the perturbation vector. The inaccuracy of the definition leads to the extension of the vessel’s path, which contributes to energy and financial losses for transport support and maintenance of the vessel.

The aim of the study is to create a reliable, fast and accurate (innovative) way to determine the characteristics of rectilinear gradual uniform motion of the vessel, which features three speed vectors: perturbation, relative and absolute velocities. The object of study was the process of ship movement, and the subject – the elements (parameters) of movement.

The article determines the forecast parameters with a minimum of a priori information at the beginning of the vessel: the sequence of determining the angles of the speed triangle is determined, the sides (modules) of the speed triangle are determined, the order of determining the coordinates of the vertices of the velocity triangle is established. This allows to solve more complex problems of graph-analytical and mechatronic calculus and observation of translational and rotational motion of the vessel along the route and to improve control to reduce risk on the course of disturbances in “big” real time, with variable intervals of observations, approaching invariant and robust control.

The advantage of the coordinate method is to solve the problem of determining the parameters of vectors by methods of analytical geometry more accurate, proven and simple in comparison with empirical dependencies, as well as geometric constructions.

Keywords: calculation, ship, vector, speed, movement, perturbation, speed triangle

1. Кривой А.Ф. Математические модели гидродинамических характеристик пропульсивного комплекса судна для произвольных углов дрейфа [текст] / А.Ф. Кривой, М.В. Миюсов // «Судовождение»: Сб. научн. трудов / НУ «ОМА», Вып. 28. — Одесса: «Издат Информ», 2018 — с. 88-102.
2. Баранов Г.Л. Ергатичні іноваційні технології управління рухом суден [текст] / Г.Л. Баранов, І.В. Тихонов // «Судоводіння»: Зб. наук. праць / НУ «ОМА», Вип. 26. — Одеса: «Видав Інформ», 2016 — с. 10-19.
3. Голиков В.В. Ситуационный подход к безопасному управлению судном [текст] / В.В. Голиков // «Судовождение»: Сб. научн. трудов / НУ «ОМА», Вып. 26. — Одесса: «Издат Информ», 2016 — с. 191-198.
4. Лысый А.А. Влияние факторов внешней среды на тип и главные размерения судов каравана при ледовых проверках в Азовском море [текст] / А.А. Лысый // «Судовождение»: Сб. научн. трудов / ОНМА, Вып. 25. — Одесса: «Издат Информ», 2015 — с. 121-128.
5. Пипченко А.Д. Создание упрощенной математической модели судна, управляемого рулем и винтом [текст] / А.Д. Пипченко // «Судовождение»: Сб. научн. трудов / ОНМА, Вып. 9. — Одесса: Феникс, 2005 — с. 75-81.
6. Бондарь В.В. Метод оценки и регулирования безопасности якорной стоянки судна при действии ветра, волнения и течения [текст] / В.В. Бондарь // «Судовождение»: Сб. научн. трудов / ОНМА, Вып. 15. — Одесса: «Издат Информ», 2008 — с. 11-19.
7. Мальцев А.С. Методологические основы маневрирования судов при сближении // А.С. Мальцев, В.В. Голиков, И.В. Сафин и др. — Одесса: ОНМА, 2013. — 218 с.
8. Голиков В.В. Анализ вектора смещения пути судна от ветра [текст] / В.В. Голиков, С.Э. Мальцев / Научный журнал — Херсон: ХГМА, 2015 №1(12), — с. 29-35.
9. Габрук Р.А. Врахування впливу течії на об’єкт управління системою динамічного позиціонування / Р. А. Габрук // Матеріали конференції «Морські перевезення та інформаційні технології в судноплавстві» 19-20 листопада 2015 року – с. 14-16.
10. Деревянко А.А. Инверсный метод планирования схемы маневрирования при швартовке VLCC к монобую/ А. А. Деревянко // Матеріали конференції «Морські перевезення та інформаційні технології в судноплавстві» 19-20 листопада 2015 року – с. 126-129.

Golikov V.A. A simple technique for identifying vessel model parameters / V.A. Golikov, V.V. Golikov, Ya. Volyanskaya, О. Mazur, О. Onishchenko // IOP Conference Series: Earth and Environmental Science. 4th International Scientific Conference SEA-CONF 2018, Published by IOP Publishing Ltd, 2018. – Vol. 172. – № 012010. – Р. 1-8. – Doi:10.1088/1755- 1315/172/1/012010.

The paper analyzes hydrometeorological phenomena in the port of Chornomorsk. Changes in climatic conditions over the past 5 years have been identified. The most dangerous directions and speeds of winds, waves, which affect the operation of the port, have been determined. Analyzed the precipitation and the frequency of occurrence of various meteorological phenomena (thunderstorms, fogs, blizzards) in recent years. Conclusions were made on the unfavorable conditions of the port.

Ensuring the safety of navigation during entry and exit from the port is one of the most pressing problems. Analysis of hydrometeorological conditions helps to reduce the number of accidents that occur due to ships grounding and bulkheads on the berth. Knowing the weather conditions in the port water area, you can ensure the safety of navigation.

To compile a statistical analysis of the hydrometeorological characteristics in the port, a study of the logs of meteorological observations for every day over the past 10 years, as well as the cadastres of the seaports of Ukraine was carried out.

The result of this analysis is the receipt of unfavorable factors that hinder the operation of the port in normal mode. It was also possible to establish the most unfavorable phenomena that limited the possibility of entering and leaving the port, as well as the months in which these phenomena are possible.

Analysis of the parameters of the hydrometeorological situation allows us to conclude that the industrial activity of the port largely depends on the state of the weather and the sea. unfavorable meteorological phenomena reduce the efficiency of work and can pose a threat to the safety of their conduct. Various weather and sea phenomena affect port operations in different ways.

The production activity of the port is largely dependent on the state of the weather and the sea, since unfavorable meteorological phenomena reduce the efficiency of work and can threaten the safety of their work. Various weather and sea phenomena affect port operations in different ways.

Keywords: port of Chornomorsk; meteorological conditions; water surface condition; ice mode; safety of navigation.

1. Ticiana G. Z. The effect of weather conditions on port technical efficiency / G. Z. Ticiana, G. Lorena. // Marine Policy. – 2020. – №113.
2. Kirkegaard J. Metocean forecasting for ports and terminals / J. Kirkegaard, P. Sloth. // Sciencederict. – 2018. – №110.
3. Asariotis R. Port industry survey on climate change impacts and adaptation / R. Asariotis, H. Benamara, V. Mohos-Naray. – United Kingdom: United Nations, 2018. – 66 с. – (UNCTAD Research paper). – (RP/2018/18/Rev.1; № 18).
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5. Журналы наблюдений за метеорологическими явлениями с 2011 по 2019 гг.
6. Кадастр морских портов Украины.

In the publication is specified, that providing of safe divergence of vessels at sailing in the straitened waters is one of most the issue of the day of accident-free of navigation. Therefore, straitened districts of sailing with especially intensive motion for the control of process of navigation by the stations of traffic control of vessels which for providing of safe divergence of vessels must dispose by modern facilities of warning of collision of vessels, reducing influencing of human factor of operator by the use of methods of automatic determination of strategy of divergence of vessels at their external management. Actuality of development of method of automatic determination of parameters of strategy of divergence of vessels by the change of their courses is determined to these.

The analysis of the last achievements and publications is resulted in work, the decision of the considered problem and selection of parts unsolved before is begun in which. It is shown that for the decision of problem of warning of collisions of vessels was used method of nonlinear integral invariance, methods of theory of optimum discrete processes, and also methods of differential game theory. The method of warning of collision of vessels by displacement on a line parallel of way of ship and method of flexible strategies of divergence of vessels got development, allowing to form optimum strategy of divergence of ship with a few dangerous targets taking into account substantial factors.

The publication contains analytical dependence of values of courses of deviation of vessels providing their divergence on minimum – possible distance of rapprochement, without taking into account inertia. It is specified, that for optimum of maneuver of divergence is needed, that increases of courses and were minimum, and as the criterion of optimum the sum of their squares is chosen.

It is shown that without taking into account inertia of ship at a turn distance of the shortest rapprochement appears less minimum-possible distance on a size which depends on the increase of relative coordinates of vessels in times of turn and relative course of their deviation.

Procedure of progressive approximations is offered for the calculation of courses of deviation of vessels taking into account their inertia and the algorithm of calculation of course of deviation is represented. Set by the values by the increases of courses from – 60° to 60°, the courses of deviation of the second ship settle accounts, which the courses of deviation of the first ship taking into account the dynamics of vessels and increase of his course are determined on. Every maneuver of divergence is characterized by the criterion of optimum, thus the maneuver of divergence gets out as optimum, at which the criterion of optimum is minimum.

A situation is resulted in the publication, for which the computer imitation program expected the optimum courses of deviation of vessels. By the computer program, playing of maneuver of divergence of vessels with the got courses of deviation was produced.

Keywords: safety of navigation, warning of collision of vessels, external process of divergence control, automatic determination of parameters of strategy of divergence.

1. Павлов В.В. Некоторые вопросы алгоритмизации выбора маневра в ситуациях расхождения судов/ В.В. Павлов, Н.И. Сеньшин // Кибернетика и вычислительная техника. – 1985. – № 68. – C. 43-45.
2. Куликов А. М. Оптимальное управление расхождением судов / А. М. Куликов, В. В. Поддубный // Судостроение. – 1984. – № 12. – С. 22-24.
3. Lisowski J. Dynamic games methods in navigation decision support system for safety navigation/ Lisowski J. // Advances in Safety and Reliability. – – Vol. 2. – London-Singapore, Balkema Publishers. – Р. 1285-1292.
4. Кудряшов В. Е. Синтез алгоритмов безопасного управления судном при расхождении с несколькими объектами / В. Е.  Кудряшов // Судостроение. – 1978.- №5. – С. 35-40.
5. Пятаков Э.Н. Взаимодействие судов при расхождении для предупреждения столкновения / Э.Н. Пятаков, Р.Ю. Бужбецкий, И.А. Бурмака, А.Ю. Булгаков – Херсон: Гринь Д.С., 2015.-312 с.
6. Вагущенко Л.Л. Расхождение с судами смещением на параллельную линию пути / Л.Л. Вагущенко. – Одесса: Фенікс, 2013. – 180 с.
7. Бурмака И.А. Маневр расхождения трех судов изменением курсов/ И.А. Бурмака, А.Ю. Булгаков // Автоматизация судовых технических средств: науч. -техн. сб. – 2014. – Вып. 20. Одесса: ОНМА. – С. 18 -23.
8. Цымбал Н.Н. Гибкие стратегии расхождения судов / Н.Н. Цымбал, И.А. Бурмака, Е.Е. Тюпиков. – Одесса: КП ОГТ, 2007. – 424 с.
9. Мальцев А. С. Маневрирование судов при расхождении / А.С. Мальцев, Е.Е. Тюпиков, И.И. Ворохобин – Одесса: Морской тренажерный центр, 2013. – 304 с.
10. Калиниченко Г. Е. Формирование области опасных курсов судов с учетом их динамических характеристик/ Калиниченко Г.Е., Пасечнюк С.С. // Автоматизация судовых технических средств. – 2017. – № 23 – С. 44-51.

The questions of drafting of cargo plan of containership on a voyage are considered in work, duting of which the reception and unloading of parties of containers is produced in a few ports.

Forming of loading of the ship «Sky Gemini », which can adopt containers in eight holds and on their lids is considered. Placing of containers can be produced in 16 cargo apartments, thus in each of cargo apartment it is possible to place 192 twenty foot container.

The voyage of ship with arrival in five ports is considered in the article, thus in the first port the complete loading of ship is produced 3072 containers, gross weight of which makes 45000 т. A load consists of three parties which are addressed accordingly in fifth, fourth and second ports. In the second port the second party and ship unloads with two remaining parties follows in the third port, where fourth party of containers for fourth port is loaded. Unloading of the third and fourth parties is produced in fourth port, and a ship with the unique first party accomplishes transition in the last fifth port.

As a result of every loading of parties of containers list of ship must be in limits from 0 to -2,0 м. List, which placing of containers, suiting longitudinal durability, corresponds to, gets out from the indicated interval. Therefore, for every party of loading it is necessary to find the scope values of static moments which provide list of ship accordingly 0 and -2,0 м.

The results of imitation design of four loads of ship are represented. As the conducted imitation design showed, the computer program formed the loads of ship, the feature of which there is their admission on the requirements of his landing, stability and general longitudinal durability. Minimization of forces of inertia at tossing of ship during transition is attained by the order of piling of containers in every tier: containers with greater mass are disposed nearer to the diametric plane of ship.

In the imitation program is present module of estimation of parameters of landing, stability and longitudinal durability of the ship «Sky Gemini», using his hydrostatical tables and information about durability. Taking into account distributing of weight of containers of parties of loading, the criteria of nautical safety of ship, which are represented as the diagram of static stability, shire forces and bending moments, settle accounts by the program.

Keywords: nautical safety, loading of containership, voyage plan of loading, imitation computer design.

1. Simonovich Milivoje. The correlation of ship hull form and her static stability diagram / Simonovich Milivoje, Sizov Victor G, Vorobjov Yuri L. // 21 Jugosloven. kongr. teor. i primenjene meh., Nis. 29 maj – 3 jun. – 1995. – Р. 167-173.
2. Сизов В.Г. Теория корабля. – Одесса: Феникс, 2003. – 282 с.
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4. Xia Jinzhu. A dynamic model for roll motion of ships due to flooding / Xia Jinzhu, Jensen Jorgen, Pedersen Preben Terndrup // Schiffstechnik. – 1999. – 46, № 4. –Р. 208-216.
5. Miller Lutz. Advan­ced calculation techniques for ship structural design / Miller Lutz.// Germ. Maritime Ind. J. – 19 – 8, Spec. Issue. – Р. 37 – 40.
6. Wan Zheng. Estimation of ultimate strength of ship`s hull girders / Wan Zheng, He Fu. // Ship Mech. – 2003. – 7, № 3. – Р. 58-67.
7. Васьков Ю.Ю. Некоторые вопросы оптимизации грузовых операций навалочных судов / Васьков Ю.Ю. // Судовождение. – № 6. – 2003. – С. 40 – 45.
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Цымбал М.Н. Планирование загрузки контейнеровоза в случае проведения грузовых операций в нескольких портах/ Цымбал М.Н. //Science and Education a New Dimension. Natural and Technical Sciences, VIII(27), Issue: 224, 2020.- С. 71 – 74.

Geodetic network, both virtual and real, is considered today as an important infrastructure similar to electrical networks or transport. Each country has its own national network, which is built so that it is as close as possible to the surface of the geoid of this country. But the geoid is not a correct geometric figure and that is why when meeting geodetic networks on the border of neighboring countries there is a so-called coordinate jump Δx; ;Y; Δz, which should be found and distributed in the form of corrections to geodetic points located near the border. With regard to the height reference system, the initial data of the reference level surfaces may also differ significantly. The reference system is implemented in the form of fixed geodetic points. For example, in Europe such reference systems as ETRS (European Terrestrial Reference System) and ERTF (European Reference Terrestria Framework), as well as EVRS (V-Vertical) and EVRF are used. In Ukraine, the ellipsoid WGS 84 with certain parameters and the Baltic altitude system are used for the planning coordinate system. The paper considers the possibility of bringing the coordinate systems at the border areas on the Danube River to the generally chosen reference system.

The aim of this study is to develop an algorithm that would bring all coordinate systems used by the Danube countries to a harmonized state by introducing permanent values at the border of these countries. The paper shows how this can be implemented on the example of border geodetic networks between Ukraine, Romania and Bulgaria.

The use of the DaWAT software product is proposed, which allows to automatically transform data from the vertical reference system of Romania (MN75) to the Ukrainian and Bulgarian (Baltic altitude system).

Keywords: coordinate systems, Danube countries, ETRS, ERTF.

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