harmonically in heave in calm water and have measured the heaving forces and pitch- 

 ing moments. This enabled us to determine the frequency, amplitude and speed 

 dependence of one-half of the coefficients in the commonly used pair of linear differ- 

 ential equations of motion. Subsequent pitching experiments later this year will 

 determine the missing coefficients. 



The principal results concerning the added mass and damping are as follows: 



1. The added mass and damping coefficients are independent of the amplitude 

 of motion. 



2. The added mass in heave shows a strong frequency dependence which closely 

 resembles in form the theoretical results of Ursell and Grim. 



3. The added mass is essentially independent of forward speed. 



4. The variation of damping coefficient with frequency shows the characteristic 

 peak at the frequency predicted by the Distributed Source technique and the Grim 

 solutions but the former greatly overestimates its magnitude while the Grim solutions 

 are an improvement. The Haskind-Riman experiments at zero speed were re-analyzed 

 and the same superiority of the Grim solutions was demonstrated. 



5. The speed effects on damping are not very great. The maximum value is 

 about the same for all speeds but the peak occurs at slightly different frequencies. 



6. The existence of quadratic damping is indicated by harmonic content in the 

 measured forces. It was then demonstrated that the neglect of these non-linear terms 

 would lead to a serious overestimate of the motions in the vicinity of resonance. 



In addition, significant cross-coupling moments were obtained for the sym- 

 metrical model which increased with increasing speed. 



1. The pitching moment due to heave velocity showed a very strong frequency 

 dependence that is not indicated by the theoretical work of Haskind and Havelock. 



2. A moment due to heaving acceleration was obtained which is sharply peaked 

 at low frequencies. This coupling moment is not indicated previously by theory or 

 experiment for a symmetrical model. 



E. V. Lewis 



I have enjoyed Professor Weinblum's interesting survey on the seaworthiness 

 problem very much, and appreciate the honor of being asked to comment on both 

 it and some of our experimental work at Stevens. 



It is of interest to note that Professor Weinblum now rates the importance of 

 the irregular seaway concept very high. But I certainly agree with him that the study 

 of the theory of motions in regular waves is no less important than before. In fact, 

 it is probably even more so, and the many interesting graphs and data that Professor 

 Weinblum has assembled from sources rather difficult to obtain in this country will be 

 of great value to us in this work. 



Professor Weinblum records definite progress in the overall problem of ships 

 in a seaway, but he does not expect revolutionary improvements, within practical limits 

 of ship form and proportions. My own feelings are somewhat more optimistic, because 

 besides the possibile use of fins, it does seem that the possibility of gains in speed by 

 careful consideration of ship proportions are quite large, even though perhaps not 

 "revolutionary." 



For example, within the scope of the Series 60 models that are now being 

 extended by Dr. Todd, there is the likelihood of an appreciable increase of sea speed. 

 In considering this matter, it is convenient to use the condition for synchronism with 

 a wave of ship length as a rough criterion of relative speed attainable in rough irregular 

 head seas. This is a useful reference because although the oceanographers feel that 

 most seas have a very wide range of different frequencies present, motion studies show 

 that wave components appreciably shorter than the ship's length are not serious, even if 

 synchronous conditions exist. So if we consider the speed for synchronism with the 

 shortest wave components that is apt to be significant, i.e. a wave of about the length 



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