Breslin, Savitsky, and Tsakonas 



DISCUSSION 



John F. Dalzell 



Southivest Research Institute 

 San Antonio, Texas 



Since this discusser was associated with the initial work on the techniques 

 discussed in the paper he cannot take serious technical exceptions, and must 

 admit responsibility for the lack of initial lucidity referred to in the Introduc- 

 tion. "Translations" from the mathematical developments of other branches of 

 technology, which the theoretical part of this paper is in large part, are made 

 necessary by the bewildering array of names for the same thing so often found 

 in the literature. The initial development of the techniques described in the 

 paper was characterized by expediency rather than elegance and consequently 

 the quite general notions of the impulsive response and the convolution integral 

 combined with a digital computer yielded plenty of numbers but no equations. 



The writer should comment that practical computer evaluation of the Fou- 

 rier transform and the convolution integral is dependent on the integrands going 

 to zero within practical ranges of co ov r . Fortunately, this almost happens in 

 all the modes of motion discussed in the paper and the errors incurred by inte- 

 gration over less than an infinite interval are not serious. One would have quite 

 a difficult time using the kernel function for wave motion "induced" by horizon- 

 tal separation (Fig. 1) unless the frequency content of the wave record was 

 known in advance (the highest wave frequency containing appreciable energy 

 dictates how many of the oscillations toward positive r must be retained). 



The attitude of some of those committed to the statistical approach is that 

 deterministic calculations of random phenomena can only ultimately result in a 

 set of statistics which are easier obtained by power spectrum (frequency do- 

 main) calculations. This is probably true. On the other hand, there were those 

 5 years ago who said that the power spectrum methods were all well and good 

 but that they did not take account of the occasional motion extremes observed in 

 most samples except for very low sea states, and that marine vehicle motions 

 became nonlinear in the mathematical sense very soon after wave heights 

 reached visible proportions. The present gambit was initiated as an aid in the 

 investigation of how far linear systems concepts could apply in severe seas. It 

 was intended as a complementing demonstration of how adequate or inadequate 

 linear systems concepts were. Figure 14 of the paper is the least significant of 

 the 3 similar plots from Ref. 4. Figure 14 of Ref. 4 shows almost as good 

 agreement between time domain predictions and observations for a wave whose 

 significant height was 4 times greater than that shown in Fig. 14 of the paper, a 

 result indicated by frequency domain analysis. 



The foregoing remarks were offered to illustrate that the methods discussed 

 in the paper were originally intended as, and used for, investigations comple- 

 mentary to frequency domain analyses. It is the writer's opinion that the par- 

 ticular analysis technique discussed in the paper may be viewed as a useful 

 special purpose tool which can be very beneficial but which may not necessarily 

 yield directly usable information. 



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