Computing Hearing and Pitching Motions 521 
encouraged to continue the theoretical work for the three-dimensional or any other more com- 
plicated cases. [ am very pleased with this contribution. 
P. Kaplan (Technical Research Group, Syosset, N.Y.) 
We have received in this rendition by Dr. Grim, quite an outstanding piece of work in 
the sense that it covers many problems that have been considered in the past 10 years from 
the point of view of ship motion analysis. Dr. Grim, in the past, has provided the largest 
amount of available data for use in the predictions of motions of ships in waves. This 
latest work is an improvement in the sense that three dimensionality is rather important, 
since there are not many three-dimensional solutions for determining the coefficients and 
the resulting motions of ships in waves. One of the main points which I see here, from my 
point of view, leads me to a question which I would like to place before Dr. Grim. The very 
fine thing that you have found is a creation of a distortion in the wave pattern, even in the 
case of a ship which is restrained in waves. This means you have taken account of the in- 
fluence of the free surface in computing the excitation. Now, this has never been done in 
all the latest work used for computing the motions of ships and also it has not been taken 
into account in determining the bending moments which act upon ship forms. Therefore, I 
would like to know if you can tell me if you have made a comparison of the magnitudes of 
the exciting forces on a restrained ship with your theory and compared it to the simple slen- 
der body theory which just replaces the effect of the interaction by a dipole and does not 
take into account the influence of the free surface. Secondly, I would also like to make a 
point here concerning Fig. 27 in the paper. I gather here that what has been found is an ex- 
pression for the magnitude of the virtual mass coefficient and also the damping coefficient 
at the particular section. Two dimensionally, one finds the value at a section all the time, 
but now you have a three-dimensional effect which shows the inclusion of interactions. The 
point I would like to make is that the appearance of close values for the damping terms in 
both the two-dimensional and three-dimensional cases is not necessarily to be taken as say- 
ing that there appears to be only a small difference between two-dimensional and three- 
dimensional values when you look at a section. It happens to be so for this particular case. 
I can report, and will some time in the future, the fact that there are large differences in the 
local values of damping; that is, the distribution along the hull is quite different, yet the 
total values are about the same. So [ think it important for this one case to see this close- 
ness yet realize local values must be looked at with care. That, of course, is most true for 
bending analysis, which is of vital importance for the structure of ships. 
O. Grim 
Dr. Kaplan has put two questions: At first he asks how large the differences are between 
the normal strip method of computing the forces and the bending moments without any defor- 
mation of the wave and the other computations with the deformation of the wave. I have not 
made such a comparison, but I think the last figure in which the reduced wave amplitude is 
represented will enable us to make a judgment about this comparison. It may be that the 
forces and the bending moments will be reduced in about the same magnitude as the wave 
amplitudes. Dr. Kaplan’s second question is whether the added mass and the damping force, 
mentioned in Fig. 27, are typical. I think that this is so and that the differences between 
the two-dimensional and the three-dimensional results for heaving and pitching motion are 
only important for the range where the frequency is near to zero, while in the other range 
these differences are not so important. More important are the differences for the ship in 
waves, and the reason for this is the following: For the ship which undergoes a heaving 
