Newman 



So I think that it is necessary to study carefully the various components of 

 the force and moment due respectively to: added mass, circulation, free- 

 surface effect, separation, propeller. As for the personal views of the author 

 about the free-surface effect, I think that emphasis must be put on them, since 

 they are of very great interest. 



The last part of Dr. Newman's paper is devoted to a discussion of the fre- 

 quency effects, or to the "memory" effects. He explains why initially the vis- 

 cous effects rather than the free-surface effects come into play. 



My own paper read in Bergen in 1964 was aimed at drawing the attention to 

 these viscous effects. The experiments which were carried out at the Bassin 

 d'Essais des Carenes at the time, using a planar motion mechanism, showed 

 that these effects could be of importance in certain cases. Since then, new ex- 

 periments have been undertaken. They have shown that it is necessary to en- 

 sure a very accurate angular setting of the sine-cosine potentiometer used for 

 the integration, with respect to the driving shaft of the struts, or else significant 

 errors would affect the calculation of the out-and-in force and moment. This 

 has been a problem for sometime, but it is now solved. And now when experi- 

 ments are repeated with identical conditions, the results obtained are quite con- 

 sistent. This was not the case before. The curves given as examples in my 

 1964 paper must be considered as erroneous. Now, as is correct, the curves 

 giving the coefficients of the so-called quasi steady motion versus the reduced 

 frequency always show a horizontal asymptotic line. For instance in the case of 

 motions parallel to the horizontal plane, we have found that the asymptotic value 

 of the derivative dCy/3/3 may be 50% greater than the value corresponding to the 

 steady motion. For ^iy/^ the variations are insignificant and this is in agree- 

 ment with the fact that 3^y/Bi/^ is very small in steady conditions. The variations 

 of ^Cn/^/S are small but B^j^/30 decreases when the reduced frequency increases. 



The techniques to be used in experiments whose purpose is to study the ef- 

 fect of the frequency in the case of a submerged body are rather critical because 

 the small values of the reduced frequency are obtained for high speed values. 

 The effects of the free surface may interfere with those of the viscosity. How- 

 ever, the experiments indicate that the influence of the free surface is small 

 even for wL/u less than unity, the submergence of the model being about 2 me- 

 ters and the greatest period being 5.69 sec. 



The asymptotic values of the coefficients which are sensitive to the reduced 

 frequency are reached for practical purposes at a reduced frequency of about 

 ten. That leads to the feeling that the history of the motion may be of impor- 

 tance in the case of rapid transient motions. However the problem of determin- 

 ing the magnitude of the error when the effect of the history of the motion is 

 neglected is not yet solved in a satisfactory manner. In any case, it is to be 

 noted that, when a planar motion mechanism is used for obtaining the added 

 mass, the exact values of the corresponding coefficients are the asymptotic val- 

 ues and not the limit values for f^L u -• 0. 



Concluding my comments on Dr. Newman's paper, I should like to express 

 the opinion that the author has reached his goal. Not only has he made a very 



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