Computing Hearing and Pitching Motions 523 
determined by measurement or by someone solving it. Thus, it is possible, by solving a 
relatively simple problem, to get results that should be useful for a relatively complicated 
one. I would like to conclude by saying that the same ideas can be applied to calculating 
the waves produced by the motion of the ship in pitching or heaving or other periodic mo- 
tion. Again, in each case it is necessary to find the corresponding waves produced by the 
motion of a circular cylinder with the same radius of curvature and slope as the ship has at 
the point of interest and that problem hasn’t been completely solved. 
O. Grim 
I can imagine that this is a good idea as a way to compute the wave propagation for 
any large frequency. However, for a prediction of the motions of a ship a more complete 
solution than only for the wave propagation is needed. It could be helpful to obtain by 
Prof. Keller’s proposed simple method results which confirm those obtained from a more 
complete solution. 
Owen H. Oakley (U.S. Bureau of Ships) 
I am sure that if my colleagues, that is, my practical naval architectural-type colleagues, 
could see me standing here with the temerity to discuss Dr. Grim’s paper they would be 
amazed, and I assure you I am too. I have two points to make, one trivial and one more on 
the serious side. First of all, in 1957 I was a shipmate of Dr. Grim on an icebreaker in the 
Sea of Bothnia. We were concerned with vertical movements of the ship, because, installed 
in the bow of this ship was an eccentric weight device known as the Stampflanage which, 
when properly tuned at the remote control station in the pilot house, created a pitching mo- 
tion in the bow of the ship and thus helped to break ice. Dr. Grim was at the controls and 
occasionally he would turn the knobs the wrong way and a fore and aft surging motion would 
result which was a bit disturbing to say the least. I wonder whether Dr. Grim has consid- 
ered the matter of surge in this present analysis; I should think it would be something he 
would be very much aware of. Now a more serious comment. As a general rule practical 
naval architects do not have occasion to give serious thought to this sort of theoretical 
work. However, occasionally one encounters problem where such mathematical assistance 
would be most welcome. Such an experience was the design of the escort research ship. 
We would have liked very much to have been able to calculate the response of this ship to 
waves, but since we could not, we had to build models and go to the trouble of testing them, 
finding where we were wrong, correcting it, and trying again. The theoretical and empirical 
development of this subject has been going on for a number of years; many excellent minds 
have worked on it and produced a prodigious quantity of papers on the various aspects of 
the problem. I hope that some day all of this work to which Dr. Grim has contributed so 
greatly will bear fruit and we will be able to sit down with pencil and paper or with computer 
or what have you and predict quantitatively the amplitudes of response of arbitrary ship- 
forms. I am sure that the contribution which Dr. Grim has told us about today is another 
significant step in that direction. 
O. Grim 
I am glad to hear that Mr. Oakley likes to remember the time we spent together on the 
icebreaker in the Sea of Bothnia and I hope he forgives me for the wrong way in which I 
