Ship Domain in Open Sea Areas and Restricted Waters: an Analysis of Influence of the Available Maneuvering Area

A ship domain is nowadays an important navigational safety assessment criterion. Its shape and size depend on many factors. The available maneuvering area seems to be one of the most important of them. This article examines the influence of the available manoeuvring area on the shape and size of ship domain in the open sea and restricted waters. The research was conducted using a simulation method. Expert navigators participated in simulations using the ECDIS system. The domains of ship passages in open sea area and restricted area have been compared.

section_content: Sea navigators of today face several important tasks in their work. One of the most important navigatorʹs tasks is to ensure shipʹs safety during its passage at sea. There are several criteria currently used for ship safety assessment. 

An intensifying debate has been held for the past five decades on the use of the ship domain for analysis and evaluation of the navigational situation (i. e. Fuji & Tanaka 1971, Coldwell 1975, Śmierzchalski & Weintrit 1999, Pietrzykowski & Uriasz 2009, Wielgosz 2016). 

The problem of ship domain determination is still up-to-date due to a large number of factors affecting its shape and size, so great that for practical reasons in the actual domain determination method some of these factors are taken into account. In many expertsʹ opinion, the most important domain determinants include the size and speed of the vessel and the type of sea area -open or restricted. 

The ship domain as a criterion for assessing the safety of navigation is of great importance for navigation in waters with high traffic intensity, where the vessel has limited available manoeuvring area due to physical and legal limitations and in open sea areas, with less traffic and a large available manoeuvring area. 

The observed behaviour of marine navigators reveals large differences in distances kept to other vessels encountered and passed in either type of navigable area, which directly translate into differences in the size and shape of the domain. 

In this paper the ship domains in open sea area and restricted area have been compared. 

Ship Domain in Open Sea Areas and Restricted Waters: an Analysis of Influence of the Available Maneuvering Area
section_name: INTRODUCTION

section_content: Maritime University of Szczecin, Szczecin, Poland ABSTRACT: A ship domain is nowadays an important navigational safety assessment criterion. Its shape and size depend on many factors. The available maneuvering area seems to be one of the most important of them. This article examines the influence of the available manoeuvring area on the shape and size of ship domain in the open sea and restricted waters. The research was conducted using a simulation method. Expert navigators participated in simulations using the ECDIS system. The domains of ship passages in open sea area and restricted area have been compared. Five relevant scenarios for each size of ship were prepared and recorded, thus allowing later to repeat the initial situation with the possibility of individual maneuvers by attending experts -sea navigators. A detailed description of the research and analysis method is described in author's earlier publications). 

The main purpose of the conducted research was to determine the influence of the available maneuvering area conditions on the ship domain.
section_name: M. Wielgosz

section_content: The problem and models of ship domain in the restricted area have been described in many publications lately (Hansen et al. 2013, Wielgosz & Pietrzykowski 2012, Wielgosz 2015). Most of the domains have an elliptical shape. 

In this paper the author implements a model of anti-collision domain developed through his research (Wielgosz 2015). The adopted model is an ellipse with an offset centre, described by parametric equations (1 to 6), which takes into account the size and speed of the vessel. 

where: a1L, b1L, c1L, a2L, b2L, c2L -length influence coefficients; a1v, b1v, c1v, a2v, b2v -speed influence coefficients; t -relative bearing; px, qx, rx -X-axis centre displacement coefficient; py, qy, ry -Y-axis centre displacement coefficient.
section_name: The ship domain in a restricted area

section_content: Implementing the same method as for restricted areas (Wielgosz 2015), three types of domain were studied for the analyzed ships. In order to determine the shape and size of a domain in the open sea area, the author continued the research described above, using the same ship models of different size, considered to be representative for today's shipping. 

Selected parameters of the ship models are presented in Table 1.
section_name: The ship domain in an open sea area

section_content: As expected, the domain shape in the open sea remains elliptical, as presented in Figures 2, 3 and 4. 

These figures are drawn in the ship coordinate system, with the vertical X axis (X axis is commonly used in navigation as the longitudinal axis of symmetry) and the horizontal Y axis. Approximated data for "small", "medium" and "large" ship are visualised in Figures 2, 3 and 4, respectively.
section_name: The domain shape

section_name: Length of the semi-axes

section_content: Detailed data concerning the length of semi-major and semi-minor axis for 3 types of the examined domains in the restricted area are presented in Table 2. The lengths of elliptical domain semi-axes in the open seas are presented in Table 3.
section_name: Restricted area

section_content: The research results are also presented in a graphical form in Figures 5 and 6 for semi-major and semi-minor axis, respectively.
section_name: _______________________________________________

section_content: The domain area can also be analysed as a criterion of navigational safety assessment, so the area of the domains (here counted as an area of an ellipse with known length of the semi-axes) was also analysed. The results are presented in Figure 7.
section_name: The domain area

section_content: The resulting length of semi-axes in both sea areas concerned are shown in Figures 8 and 9 for the major and minor ellipse semi-axes, respectively. Another approach to analyzing the obtained data is to calculate the coefficient of change (ratio) of the examined parameter values from the two sea areasthe relative magnitudes of two quantities. 

The ratio of length to surface area of the analysed domain parameters in the waters under consideration is presented in Figure 10. It follows from Figure 11 that the change of the analysed ratio is of linear character, which allows using a linear function ( 7 ) for approximation and mathematical description. Described by function ( 7 ), the change in the ellipse parameters while a ship transits from the restricted to the open sea area can be used to modify a domain model adopted for the restricted area (1, 2, 3, 4, 5, 6) for application in the open sea area.
section_name: Comparison of the results for examined sea areas

section_content: The result of ratio increase approximation referring to the semi-major axis is presented in Figure 12 and described by equation ( 8 ). 

Figure 12. The ratio increase -the result of approximation for semi-major axis. 

The linear model:

where:

x -ship size factor (to be calculated, see Table 4 ), m1, n1 -function coefficients. 

The coefficients (with 95% confidence bounds): The linear model:

where:

x -ship size factor (to be calculated, see Table 4 ), m2, n2 -function coefficients. 

The coefficients (with 95% confidence bounds): m2 = -0. 235 (-0. 345, -0. 125), n2 = 3. 22 (2. 982, 3. 458). 

The goodness of fit:  SSE: 0. 00015  R-square: 0. 9986  adjusted R-square: 0. 9973  RMSE: 0. 01225.
section_name: The semi-major axis length increase

section_content: The values for "very small" and "very large" ship are suggested only -for extrapolation -and to be verified in the future research, as preliminary research has been conducted only for such size of ships. Intermediate values from 1 to 3 are to be interpolated for a specific ship length. 

In conclusion, the length of elliptical domain semiaxes in the open sea area can be presented as (10, 11): In particular, the following changes have been observed for navigation in the open sea: 1 increase in length of semi-major axis; 2 increase in length of semi-minor axis; 3 increase in the size of the domain area; 4 changed displacement of ellipse centre (x0, y0) is proportional to length increase of the relevant semi-axis. 

Another important observation is that the proportions of domain axes changes -domains in the open sea are relatively wider and more oval than those relatively slim in restricted areas. 

Regularity is observed in the increase of semi-axis length in relation to ship size. It is possible to describe it by equations (10 and 11 or 12 and 13). 

Is seems purposeful to verify the results with real data from AIS based research as proposed by Hansen et al. (2013) for a restricted area.
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