512 O. Grim 
The index M indicates that in both cases the mean value over the time is to be taken. 
The first part can be looked at as caused by the reflexion of the wave on the ship body 
and the second part by the phase shift between the motions of the ship and the wave. This 
representation of the resistance is known [1,8] and it now appears possible to compute both 
parts of the resistance. 
Example 
The results for an example which have been computed from the method discussed be- 
fore will now be given in detail. The ship body chosen is as follows: 
L/B = 6.4; B/T = 2.8; T = constant for all sections; B = 0.9, constant for all sections; 
section 
weer (for 10 sections) = 0.33, 0.70, 0.90, 0.99, 1.0, 1.0, 0.99, 0.90, 0.70, 0.33. 
max 
This ship body is symmetrical about x = 0. The 10 given sections lie in the midst of 
10 equally long intervals. 
Each integral equation (34) or (45), respectively, has been transformed into a system 
of linear equations and has then been solved. The 10 given sections were chosen as sup- 
porting points for this system of equations. Each system of equations contains, therefore, 
the 10 complex values U_, or Up or G, respectively, of these sections as unknowns and, 
therefore, three times a system of 20 equations for 20 real unknowns had to be solved. 
Figures 25-31 show the results in a nondimensional representation. 
Figure 25 shows the deformation of the smooth water surface caused by the heaving and 
pitching motions. This deformation would not exist for an infinitely long body. The veloc- 
ity of the deformation represented on the diagram is made nondimensional by the velocity U | 
of the motion and the velocity of the bow is chosen for the pitching motion, i.e., U, at 
x =L/2. Further X/L is chosen a parameter. The ratio \/L is defined by the relation 
since the wavelength A has in this case no physical meaning. 
Figure 26 gives the deformation at the point x = 0 which arises from the heaving motion, 
plotted against the frequency. This diagram is presented to show the course of U,,/U, for 
«0. From this course it follows that the virtual mass does not go to infinity for w > 0, 
as it does with the common strip method. For the virtual mass, the virtual moment, the 
damping force, and the damping moment about the same values are obtained for w > 0 as 
given in Ref. 11. 
Figure 27 shows for the section x = 0 the coefficient C of the virtual mass and the hy- 
drodynamic damping force both for the two-dimensional and for the three-dimensional case. 
The latter is computed on the basis of the former by means of the additional velocity. 
