Abstract
Objectives. The movement of a ship in shallow water at both constant and variable depths of a navigation area is considered in the article. With the deterioration of the navigation conditions, the ship's handling is reduced; this is explained in terms of the influence of disturbing factors, among which shallow water has the strongest impact. Based on the analysis of existing mathematical models of ship movement in deep and shallow water – and taking into account their shortcomings – the task is to develop a mathematical model of ship movement in shallow water at a constant and variable navigation area depth, as well as its implementation in software. Methods. One way to improve the accuracy of a manoeuvre is to obtain a mathematical model, taking into account the analytical dependencies of the shallow water effect on the hydrodynamic coefficients on the hydrodynamic equations of the ship, defined as a function of the ratio of the ship draft to the depth of the water area. Results. Mathematical models of ship movement in shallow water at variable navigation depths, which differ from the existing ones, are developed: the coefficients of variable hydrodynamic equations are not constant values, but variables obtained by approximating the shallow water impact curves onto hydrodynamic coefficients in the form of third-order polynomials. Conclusions. The developed mathematical models and their implementation present a number of advantages, which consist in the conducted studies contribution to the development of a new approach in modelling ship movements in shallow water when operating at variable navigation area depths, as well as when simulating ship movements in shallow waters at variable navigation area depth according to a given curvilinear trajectory. The software implementation of mathematical models and algorithms for ship movement in shallow waters with variable depth of the navigation area can be used for further studies on the dynamic characteristics of ships in shallow waters having variable depths, as well as for the analysis and assessment of skipper-induced accidents in maritime transport.
Highlights
Based on the analysis of existing mathematical models of ship movement in deep and shallow water – and taking into account their shortcomings – the task is to develop a mathematical model of ship movement in shallow water at a constant and variable navigation area depth, as well as its implementation in software
One way to improve the accuracy of a manoeuvre is to obtain a mathematical model, taking into account the analytical dependencies of the shallow water effect on the hydrodynamic coefficients on the hydrodynamic equations of the ship, defined as a function of the ratio of the ship draft to the depth of the water area
Mathematical models of ship movement in shallow water at variable navigation depths, which differ from the existing ones, are developed: the coefficients of variable hydrodynamic equations are not constant values, but variables obtained by approximating the shallow water impact curves onto hydrodynamic coefficients in the form of third-order polynomials
Summary
МОДЕЛИРОВАНИЕ ДВИЖЕНИЯ СУДНА НА МЕЛКОВОДЬЕ ПО ЗАДАННОЙ ТРАЕКТОРИИ ПРИ ПЕРЕМЕННОЙ ГЛУБИНЕ. В статье рассматриваются вопросы движения судна на мелководье при постоянной и переменной глубине района плавания. На основе анализа существующих математических моделей движения судна на глубокой воде и мелководье с учетом их недостатков поставлена задача разработки математической модели движения судна на мелководье при постоянной и переменной глубине района плавания и ее программной реализацией. Разработаны математические модели движения судна на мелководье с переменной глубиной района плавания, которые отличаются от существующих тем, что коэффициенты при переменных уравнений гидродинамики являются не постоянными, а переменными, полученными аппроксимацией кривых влияния мелководья на гидродинамические коэффициенты в виде полиномов третьего порядка. Разработанные математические модели и их реализация обладают рядом достоинств, которые заключается в том, что проведенные исследования вносят вклад в развитие нового подхода при моделировании движения судна на мелководье при циркуляции с переменной глубиной района плавания, и при моделировании движение судна на мелководье с переменной глубиной района плавания по заданной криволинейной траектории. MODELING OF SHIP MOVEMENT IN SHALLOW WATER ACCORDING TO A SPECIFIC TRAJECTORY AT VARIABLE DEPTH
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