where X'R〜N'Rare coefficients determined by rudder angle tests. αR is the effective attack angle of rudder and given by

　

　

 where yR is the decreasing ratio of inflow angle, and lR is the distance between application point of the rudder force and C.G. of the ship. We assumed this application point as the center of rudder blade area then lR =13.0m. The decreasing ratio of inflow angle yR is defined as follows:

　

　

 where δo is the rudder angle at the normal force to the rudder is zero when leeway angle is β. The relation between yR and β is shown in Figure 7. The coefficients Cxδ 〜 CNδ are shown in Table 2 and the comparison of coefficients between measured and calculated by Equation (7) are shown in Figure 8.

　

4.3 Angular Velocity Terms

　

 Hydrodynamic derivatives of the hull due to yawing motion such as XvΨ,YΨ,NΨ are calculated as follows assuming those are same as Xvr,Yr,Nr respectively.

　

 Xvr is evaluated by the following relation [4]

　

　

 where,welet Cm=0.3 then X'vr=-0.138.

　

 Yr and Nr are evaluated by the Inoue's formula [5] based on the linear wing theory. Let k be the aspect ratio of projected area of under water part of the hull including reflected image by the water line. Then Y'r and N'r are obtained as follows:

　

　

N'2=k²-0.54k (12)

　

 where,k=0.230 then,

　

 As for the derivatives due to rolling motion, we consider about Kφ using Takahashi's approximation [6] as follow:

　

　

 where Fn is Froude Number, Tφis natural oscillation period of rolling, N is extinction coefficient and φm is mean rolling angle. The measured oscillation period of rolling was T φ= 3.83sec, and we let N= 0.017 and φm= 10 deg, then