SOME STUDIES ON THE PREDICTION FOR SHIP MANOEUVRABILITY
Katsuro Kijima (Kyushu University, Japan)
Abstract: In December 2002, International Maritime Organization (IMO) has adopted the Resolution MSC.137(76) Standards for Ship Manoeuvrability. For applying the standards, we have to estimate and evaluate the manoeuvrability of a ship at the design stage as accurate as possible. Numerical simulations due to mathematical models for describing a ship manoeuvring motion will be a very useful method for predicting ship manoeuvrability. It is indispensable to estimate or obtain the hydrodynamic derivatives in a manoeuvring motion for the numerical simulations. In this paper, some studies on a prediction method for ship manoeuvrability with high accuracy are shown.
At the design stage, it is of importance to know ship manoeuvring characteristics from the view points of ship performance and also of the safety of navigation. In December 2002, International Maritime Organization (IMO) has adopted the Resolution MSC.137(76) Standards for Ship Manoeuvrability. For applying the standards, we have to estimate and evaluate the manoeuvrability of a ship at the design stage as accurate as possible.
For evaluating the ship manoeuvrability at the design stage, the following items as shown in Figure 1 will be picked up as the most important factors. On the manoeuvring performance, we have to investigate the inherent performance of a ship, human factor and environmental condition such as wind and waves . The relationship between inherent ship manoeuvrability and human factor corresponds to evaluation for performance. Finally we have to consider total evaluation including the above items. Therefore, of course it is indispensable that we have to take both environmental condition and human factor into consideration in the inherent ship manoeuvrability at the design stage for the safety of navigation and marine safety.
Figure 1 Total evaluation of ship manoeuvrability
In general for the design of a new ship, it will be requested to satisfy several kinds of conditions such as the owner's requirement, rules and regulations. From the view points of ship manoeuvrability, when we check the ship manoeuvrability to apply the manoeuvring standards, we will be able to picked the following methods up as shown in Figure 2,
1) The method based on data base,
2) The method based on model test,
3) The method based on numerical simulation by using mathematical model.
In the first, the method based on data base will be very useful, but demerits are to be limited within the mother group of the data, i.e., when we make a design of a new ship having the dimensions which are not included in such data, we have to estimate it by some extrapolation. This is the weakest point in this method.
In the second method, we will be able to estimate the manoeuvrability of a new designed ship by a free running model test. But this has also some demerits, because the model ship takes much cost and the time, then this will be not practical method. As shown in Figure 2, a captive model test for obtaining the hydrodynamic forces that needed to numerical simulation is also on the same situation.
The third method, numerical simulation due to the mathematical model for describing a ship manoeuvring motion will be very useful method for predicting ship manoeuvrability. In this method, it is indispensable to estimate or obtain hydrodynamic derivatives in a manoeuvring motion for numerical simulation. If we can estimate the accurate hydrodynamic derivatives in manoeuvring motion, we may predict the ship manoeuvring characteristics in any condition and also in any motion. Therefore obtaining the derivatives becomes a key point in this method. However, it will be difficult to estimate accurately all the derivatives in a mathematical model by pure theoretical methods from the practical points of view. In the method based on numerical simulation, we will be actually able to use approximate formulae for estimating the hydrodynamic derivatives in a mathematical model, which was produced by the way combined with a data base and results of theoretical calculation.
Figure 2 Flowchart for evaluation of ship manoeuvrability
As shown in the above, prediction of ship manoeuvrability must be taken at the design stage by some method and also the accuracy of its prediction is requested in recent years for application for ship manoeuvring standards.
In this paper, some studies on prediction method for ship manoeuvrability with high accuracy are shown.
2 MATHEMATICAL MODEL FOR SHIP MANOEUVRlNG MOTION
The equations for surging, swaying and yawing motions of a ship can be written in the following form  using coordinate systems shown in Figure 3, Superscript " ' " in equation (1) refer to the non-dimensional quantities defined by,
Figure 3 Coordinate systems
L,d : ship length and draft
m, mx, my : the mass and the x & y-axis components of the added mass of a ship,
Izz, izz : the moment and added moment of inertia of a ship,
U, β : ship speed and drift angle,
γ : yaw rate,
X, Y : the x & y-axis components of external force acting on a ship,
N : yaw moment acting on a ship,
ρ : the density of fluid.
The non-dimensional external forces X' , Y' and moment N' can be expressed as follows assuming that they consist of hull, propeller and rudder components noted with subscripts "H", "P" and "R".
There are many kinds of mathematical models for each component in equation (3) and it is difficult to discuss which expression is the best because each model is composed based on different concepts and back-grounds. If one could adopt suitable model for each component in equation (3) and could identify appropriate values for coefficients in the component, the manoeuvring motion of a ship can be predicted with high accuracy. Then the most important problem is how to define values of coefficients included in the mathematical models.
As shown in Figure 2, there are mainly three ways to identify the hydrodynamic coefficients, such as :
1) The method based on data base,
2) The method based on captive model test results,
3) The method based on theoretical calculation.
When we evaluate the manoeuvrability of a ship at the design stage, predicting the coefficients using data base or approximate formulae with a few parameters such as principal particulars must be practical way. However, it is well known that the shape of the frame lines of aft half hull has much influence upon the ship manoeuvrability. Then the hydrodynamic characteristics should be evaluated with not only principal particulars also parameters which represent the shape of aft half hull.