a three-dimensional type, has been simplified to a great extent by assuming 



the frequency high enough. As a numerical example, the model of Series 60 



and C = 0.7 is employed. Here we consider three kinds of calculation 

 B 



methods in carrying out the numerical work. 



Method 1 : Assume U = 0(1) and u) = 0(1). 



The added resistance is calculated by a three-dimensional formula. 

 The boundary condition at the free surface in near field is 



3(j) 9 2 4> 



■5^ + U c —^ =0 at z = (297) 



dz w . 2 

 9z 



The density of the source distribution in head sea waves takes /the form 



m(x) = - ^ (iw+U j^j {B(x) (z g -x^-C w )} (298) 



Making use of this source distribution in Equation (265) or (268) to calcu- 

 late the Kochin function, a consistent approximation in the present case is 

 obtained. However, the result of numerical computation yields enormous 

 values of added resistance which is hardly compatible with measured 

 results. The present formulation assumes that the disturbance by the ship 

 hull is represented by a distribution of singularities along the axis of 

 the ship which is taken on the undisturbed free surface. However, the 

 above mentioned results indicate that the singularities on the free surface 

 generate too strong disturbance. In order to avoid this difficulty, we 

 assume the singularity distribution a little below the free surface. As a 

 mean depth of the singularities, let us take the mean depth of disturbance 

 given by yT where y i- s tne vertical prismatic coefficient and T is the 

 draft of the ship. Then the Kochin function is expressed as 



H*(m) = e- mYT J"m(x) e**" dx (299) 



101 



