Gerritsma and Beukelman 



DISCUSSION 



J. N. Newman 



David Taylor Model Basin 



Washington, D.C. 



First of all let me congratulate the authors on yet another in the series of 

 excellent papers which we have come to expect from Delft. 



Certainly one of the most valuable results obtained recently is the very 

 simple forward speed correction to the strip theory, as outlined in the strip 

 theory paragraph, and the correlation of this theory with experiments. It would 

 seem that all important speed effects are taken into account simply by replacing 

 the time derivative in a fixed coordinate system by that for a moving coordinate 

 system, or 



A ^ ^ - Y — ' 



dt Bt Bx ' 



As a result, the added mass coefficient contributes both to the acceleration and 

 velocity terms of the equations of motion, since 



dt ^ o"^ ° dx ° 



However this process seems rather arbitrary; why not repeat it for the second 

 time derivative, so that 



1 2 J 



^" " ' dt2 '"'^° ~ dt ^'^° ~ 2pgyz„ 



' •• /m' rm dm'\ • /_ , „2 d^m' „ dN' 



= -mz„-(^N -2V^j z^-|^2pgy + V2— - V^ 



It is clear from the experimental results that too much cross- coupling would 

 result, and thus that the last equation is ridiculous both in appearance and in 

 practical utility, but I am left wondering why the equation used in the paper is 

 so much better. Is it possible to give any rational explanation for this? 



Finally, since Professor Vossers is not here to defend himself, let me 

 point out that, in general, forward speed will have an effect on the distribution 

 of hydrodynamic forces along an oscillating slender body. Vossers reached the 

 opposite conclusion only for the special case of high frequencies of encounter 

 and very slow speeds. 



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