Abstract: Approximate formulae for estimating coefficient of hydrodynamic forces acting on ship are proposed. The formulae were obtained by analyzing model test data, which consist of 1 5 kinds of ships and their 48 loading conditions, and by theoretical investigation. Comparison between measured hydrodynamic forces and predicted forces using the approximate formulae are made, and close agreement is obtained. Numerical simulations of turning motion and zigzag manoeuvre for ships, which are not included in the database, are also carried out. Simulated results of ship manoeuvring agree well with model test results.

　

 The Interim Standards of Ship Manoeuvrability A.751(18) was adopted finally as IMO Resolution MSC.137(76) Standards for Ship Manoeuvrability in 76^th MSC of IMO in December 2002. Consequently it is required to predict ship manoeuvring performance at design stage. In general, there are three methods for predicting ship manoeuvring performance. One is the method due to database, the second one is due to free running model test and third one is due to the numerical simulation of manoeuvring motion. In these methods, most useful one will be the numerical simulation.

　

 At the design stage, we have to estimate the highly accurate hydrodynamic forces acting on ship for predicting ship manoeuvring characteristics by means of numerical simulation. The hydrodynamic force required in simulation will be obtained by model test or theoretical calculation such as slender body theory or CFD. But at design stage, a quick application will be needed to access the manoeuvring performance. From these points of view, it will be expected to express some simple formulae for hydrodynamic coefficients.

　

 In this paper, we propose the practical method for predicting ship manoeuvrability at design stage, including the approximate formulae for estimating the coefficients of hydrodynamic forces acting on ship.

　

2.1 Equations of Ship Manoeuvring Motion

　

 The equations for surging, swaying and yawing motion of ship can be written in following form using coordinate systems in Figure 1:

　

　

　

 The superscript "'" in the equations refers to the non-dimensional quantities defined by:

　

　

where

　

 The non-dimensional external forces X'&Y' and moments N' can be expressed assuming that they consist of hull, propeller and rudder components noted with subscripts "H", "P", and "R".

　

　

2.2 Equations of Ship Manoeuvring Motion

　

 For the longitudinal component of hydrodynamic force acting on ship hull X'H, the authors adopted the form:

　

　

 The lateral force Y'H and yaw moment N'H acting on ship hull are expressed as follows:

　

　

where Y'β, Y'r・・・N'β/βr are hydrodynamic derivatives.

　

 Recently Mori [3] proposed prediction formulae for four parameters such as ea, e'a, σa and K to express characteristics of aft hull shape. The coefficients ea & e'a express fullness of aft run and σa is aft sections fullness metric respectively. K is the form factor. The parameters are defined by principal particulars with water plane area coefficient Cwa and prismatic coefficient Cpa of aft hull between A.P. and s.s.5:

　

　

 We analyzed model test results database again which was used to construct the original approximate formulae for hydrodynamic derivatives using these four coefficients. We also added new six model test data to the database. The database totally involves 15 kinds of ship (container ship, bulk carrier, tanker, cargo ship and so on) and their 48 loading conditions. The approximate formulae are shown as follows.