2.1. Transas 5000 Simulator Description
The School of Nautical and Marine Engineering (E.T.S Náutica y Máquinas) of the University of A Coruña (UDC) has, among others, the “Navi-Trainer Professional 5000”, a full mission bridge and navigation simulator to be used by the deck students as future officers and masters. It was manufactured by the Norwegian company Transas. It enables the training and certification of watch officers, chief officers, masters and pilots serving on commercial and fishing ships with a gross tonnage of 500 tons and more in compliance with the requirements of IMO STCW 78/95 during training sessions on specialized courses. Furthermore, the simulator is capable of re-constructing and analyzing complex navigational situations, including emergencies in the actual seamanship.
The NTPRO 5000 simulator, shown in
Figure 1, is a hard and software system consisting of dedicated and hands-on equipment of full mission navigation bridges operating under the instructor station control deployed on the basis of standard personal computers connected to a local computer network.
The software includes the program modules such as network operation manager; module for calculating mathematical models of ownships, target vessels, drifting objects, tugboats, model of 3D wind-induced waves, mooring lines, and fenders; the instructor’s main display; a conning display; visual channels; and an interface with a real ship’s equipment.
The simulator uses ready-to-use databases, which are permanently extended and updated: the library of visual 3D scenes of specific gaming areas, the library of radar scenes of the same areas, and the library of vessels’ mathematical models.
Among others, this simulator has Statement of Compliance with Class A Standard for Certification of Maritime Simulators No. 2.14, October 2007, based on requirements of the STCW Convention, Regulation I/12, issued by DNV [
8,
9].
According to the specific needs and requirements, the software database allows the instructor to customize different scenarios considering different models of ships, navigational areas, weather and hydrological conditions, at any time of the day, reaching a final aspect from a visual and acoustic point of view highly realistic. The correctly adjusted mathematical ship models ensure the required realism of their behavior during navigation, mooring, towing, and other port operations in any adverse conditions.
2.2. Description of the Mathematical Models
The set of mathematical models for a maneuver simulator consists of mathematical models of ships, hardware models and environment element models. The motion of all the objects is modeled, including the mechanic and hydrodynamic interaction between objects and the environment (if necessary).
The ship motion mathematical model is based on a set of nonlinear differential equations. The set of equations’ solutions was used to define the ship motion kinematics parameters, i.e., the ship center of gravity coordinates (xg, yg, zg), the inclination angles (roll, trim, and course), and the corresponding values of velocity and acceleration. Two coordinate systems are used: the fixed axes (XgOgZg)—a right-hand orthogonal system nominally fixed to the Earth—and the body axes (XOZ)—a right-hand orthogonal system nominally fixed to the ship.
The fixed axes’ origin lies in the fixed point Og. The OgXg axis and OgYg axis lie in the plane parallel to the calm free water surface, while the OgZg axis is perpendicular to the plane. The direction of the OgXg axis is poleward, OgYg axis directs eastward and the OgZg axis directs downwards.
The body axes’ origin is in the ship center of gravity. The OX axis and OY axis are parallel to the base plane, while the OZ axis is perpendicular to it. The direction of the OX axis is forward, OY axis toward starboard, and OZ downwards. Therefore, the equations describing the ship motion, expressed as force components, are as follows:
where m
A is the ship mass, calculated as follows:
where ρ is the water density; L is the ship’s length; B is the ship’s beam; Dr is the ship’s draught at midship; and BC is the block coefficient, (see
Appendix A).
correspond to the total force components due to water and wind influence in the three axes.
represent the total mechanical force in the three axes.
λ11, λ22, … λ66 are the added masses.
λ11, λ22, … λ66 define the ship velocity components in the body axis.
V
X, V
Y, V
Z represent the ship angular velocity components in the body axis, which can be calculated as follows:
where θ is the roll angle; φ is the course angle; and ψ is the pitch angle.
The corresponding total mechanical moment components can be expressed as follows:
where
represent the total moment components due to water and wind influence in the three axes;
indicate the total mechanical moment components in the three axes; and J
X, J
Y, J
Z correspond to the moments of ship inertia in the body axis.
The ship path coordinates (x
g, y
g, z
g) at the center of gravity is calculated according to the following equations:
The total components of forces and moments on the ship are defined by a set of equations consisting of several summands, which include the forces and moments on bare hull, the influence of steering devices (rudders and propellers), and the influence of external forces and moments (aerodynamic, current, wave, shallow waters, channel geometry). However, for the present paper, the simulations were carried out with the ship sailing in calm deep waters and with no rudder angle (amidships). With this premise, moving in calm deep water, the ship is affected by the hydrodynamic forces at the bare hull, the buoyancy forces, the stability forces, the inertia forces, and the forces on the ship’s propellers and steering arrangement. Moreover, at the same time, the forces on the ship’s propellers and steering gears depend on the ship control system parameters.
The hydrodynamic forces and moments on the ship are usually defined as the result of ship model experiment, and the measurements are usually performed in the body axes at given values of kinematics parameters, such as drift angle and rudder angle.
On one hand, rudders of different shapes are the most commonly used as a ship steering device. The hydrodynamic force on the rudder depends on the ship motion kinematic parameters, the rudder geometry, its relative area, the rudder angle, the propeller operating conditions, etc. The ship hull and propeller influence the hydrodynamic force on the rudder. Furthermore, the rudder and propeller affect the hydrodynamic characteristics of the bare hull. Therefore, the ship mathematical models consider the interaction forces and moments of ships equipped with different rudder configurations. On the other hand, in the mathematical models, when geometric parameters are considered, two propeller types were used: fixed pitch propeller (FPP) and controllable pitch propeller (CPP). For the models in which two propellers are included, each propeller thrust is calculated, and the total thrust and moment are calculated as the sum of the corresponding values.
2.3. Testing Simulations: Data Collection
During the simulations, different ship models were tested (bulk carrier, tanker, VLCC, passenger ferry, container carrier, and LNG), each having very different ship’s particulars. Furthermore, in some of these models, different loading conditions were studied, resulting in a total of 12 studied cases, which can be considered representative enough of the most common ships in the merchant fleet.
Table 1 includes the main ship’s particulars affecting the maneuverability of the different used ship models.
To find the CLR position with the ships sailing ahead at any constant speed, the following premises were considered:
All simulations that started with the ship from a stationary position (zero speed).
The main engine(s) running at the five modes (RPM) of engine telegraph orders: stop (STP); dead slow ahead (DSA); slow ahead (SA); half ahead (HA); and full ahead (FA).
The rudder was set at amidships and in follow-up mode.
Calm conditions were selected, without the influence of waves and wind force.
Navigation was performed in deep and open waters, without the influence of other ships, shallow waters, channels, or bank effects.
After applying the transversal virtual force, the corresponding longitudinal position was set when no turning moment was observed (ROT = 0) once the ship reached a constant speed at the corresponding engine telegraph (RPM).
Different types of ships and, in some cases, different loading conditions, cause differences in the maximum and constant speeds according to the same engine telegraph order (RPM). For this reason,
Table 2 includes the speeds achieved corresponding to the five different engine telegraph orders (RPM).
To locate the position of the CLR, i.e., the neutral point from a maneuverability point of view, a virtual force of 20.0 tonnes was applied transversally to the ship’s centerline. It was necessary to carry out a large number of tests along the ship’s length until a stable condition is noted, where the ROT was equal to zero. In
Figure 2, the virtual force transversally applied from the starboard side of the LNG carrier can be observed from the instructor station, and in
Figure 3, the full vision of this model during the navigation is represented.
Although the conning display shows the value of instantaneous ROT (nil; + starboard side; − port side), in the simulator, there is a specific panel of ship speed indicators for the ship’s longitudinal and transverse speeds, both on the bow and on the stern. Therefore, despite noting a constant ROT = 0 in the stable condition, a detailed observation of the tendency of bow and stern speeds was carried out. Moreover, when the CLR position was located after applying the transversal virtual force to the centerline, the transverse speed of the bow and the stern had to be the same, and in the same direction.
In all simulations, the magnitude of the applied virtual force was 20.0 tonnes. Although the magnitude of this force could vary in different simulations, the only difference would be that the transverse speed of the bow and the stern would be different (higher or lower), but the CLR position would be the same. In the conning display in
Figure 4, a forward speed of 7.08 knots for an ROT = 0 can be observed.
Furthermore, the aim of applying the virtual force transversally to the ship’s centerline was to avoid creating a new forward/stern speed component.