Combination Analysis;

 The resultant quasi-stationary hydrodynamic forces analyzed for harmonic captive tests of a single mode mentioned above are in good agreement with stationary hydrodynamic forces within the exerted kinematic variables, and the results predicted by the extrapolation may be in fairly good agreement with the stationary hydrodynamic forces. Then in order to reduce the differences between the predicted and the experimental results in the extrapolation range, the combination of the analysis for harmonic pure-sway, pure-yaw and combined motion was adopted for determining the stationary hydrodynamic-force characteristic constants that occur in the component-type mathematical maneuvering model to make good use of the features of each mode.

　

 In Fig. 7, the results of the combination analysis (symbol: solid and dotted lines) with the quasi-stationary hydrodynamic forces that occurred in harmonic pure-sway, pure-yaw and combined motions are shown and are in very good agreement with the stationary hydrodynamic forces (symbol:○) for a broad range of kinematic variables.

　

Characteristic constants;

 Table 3 shows the hydrodynamic-force characteristic constants that occur in the component-type mathematical maneuvering model for the three kinds of harmonic captive tests and the stationary straight-line and circular tests.

　

 The results show that the quasi-stationary hydro-dynamic forces in the harmonic PMM test were in low frequency and equivalent to the stationary hydro-dynamic forces in the stationary tests, and therefore the PMM test can be used in place of the troublesome stationary tests.

　

　

 In order to predict ship maneuvering motion, it is necessary to get information about hydrodynamic characteristics of the ship hull, propeller, rudder and etc. In this section, first methods to predict the hydrodynamic forces acting on a ship hull in maneuvering motion are described, and second, a mathematical maneuvering model for simulation and the examples of the simulation are described.

　

5.1 Predictions of ship hydrodynamic Forces

　

 In predictions of ship maneuvering motion under ship-design stage, no detailed information about ship hydrodynamic forces in maneuvering motion with a large drift angle is available. For the purpose of easily getting general information about ship hydrodynamic forces, the hydrodynamic-force characteristic constants which derived from stationary straight-line and circular tests, have been gathered for 8 kinds of ship models, including fishing boats with trim conditions, and formulated by regression analysis. In this section, the prediction methods [3] are described for hydrodynamic-force characteristic constants in the component-type mathematical maneuvering model.

　

Added mass and added moment of inertia;

 It is well known that the added masses mx and my and added moment of inertia JZZ are necessary to predict the acceleration components of hydrodynamic forces. To predict the stationary hydrodynamic forces in the component-type mathematical maneuvering model, the added masses mx and my are important to determine the idealforce because of Munk moment in yaw. The added masses mx and my and moment of inertia JZZ of conventional ships are predicted precisely by Motora's chart and other formulas[5][6][7].

　

Hydrodynamic-force characteristic constants of liner component;

 Hydrodynamic coefficients Yv (or Yβ), Nv(or Nβ), Yr and Nr that occur in the conventional mathematical maneuvering model are strongly related to the hydrodynamic-force characteristic constants C'Lf, C'La, Cev, and αL that occur in the component-type mathematical maneuvering model. This relation is shown as follows.

　

C'Lf=(x'f・Y'β+N'β-m'y+m'x)/(2・x'f・df/dm)

C'La=(x'f・Y'β-N'β+m'y-m'x)/(2・x'f・da/dm)

and

Cev≒2/3

αL≒1 　(3)

　

 where the last two constants are derived from the data base (see Fig. 8) of (N'r+m'y・x't)/(Y'v/4)=Cev and Y'r/(N'v+m'y-m'x)=(1+αL)・Cev, and first two constants C'Lf and C'La are predicted by the Kijima formula of Y'β and N'β under even keel conditions[9], because there is no difference in the two constants due to trim conditions of the target ships[4].

　

　

　

　

　

Hydrodynamic-force characteristic constants of the non-liner component;

 Hydrodynamic-force characteristic constants other than C'Lf, C'La Cev and αL in the component-type mathematical maneuvering model are related to non-liner components as follows.

　

 The prediction formulas[3] are as follows (see Fig. 9)

　

CDLc・C'C²=-0.027・(Cb・L/d)+1.166

p=0.027・(Cb・L/d)+0.571

CDLf=-0.003・(Cb・L/d)+0.106

CDLfc・C'C=0.021・(Cb・L/d)+0.051

αC≒8

Cevc=-0.001・(Cb・L/d)+0.172　(4)

　

Application;

 Fig. 10 and Table 4 show an example of this prediction method applied to the VLCC "Esso Osaka" for the stationary hydrodynamic forces X'H, Y'H and N'H(symbol:lines), and contain the experimental results of the stationary hydrodynamic forces [11](symbol:○) derived from the stationary straight-line and circular tests compared with the predicted results. Fig. 10 shows that there is little difference between the predicted and experimental results.