Davis and Zarnick 



frequency analysis. To showjiow this can be done, consider the equation which 

 relates mean square motion m^ to the wave power spectral density at the fre- 

 quency of encounter ^(co) and to the applicable transfer function G(w): 



CO 



m^ = ^ j dco ^(co) \G( CO) \^ . (22) 



- 00 



In a transient test, the integral square motion is given by 



CO 00 



r dt m2(t) = ^ I do) |N(a;) I ^ |G(aj)| ^ (23) 



- 00 - 00 



where N(w) is the Fourier transform of the measured wave height, using a well- 

 known relation from linear systems theory. Thus, if N(aj)2 is programmed to 

 be equal to the wave height spectrum $( w) , we have 



Random Transient 



I (24) 



J 



dt m^(t). 



Simple analog data processing, conducted during the model test, would 

 square and integrate the motions of interest and yield, at the end of the run, 

 voltages proportional to motion variances in the defined random seaway. 



Although such a simplified scheme of data processing would not extract 

 much of the significant information available from a transient test, it is con- 

 ceivable that there might be occasions when a very fast answer to the seaworthi- 

 ness characteristics of a ship form in a given seaway would be required. One 

 example would be a search for the worst combination of speed and heading. 



GENERAL APPLICATIONS OF THE TRANSIENT 

 TECHNIQUE 



The method for producing a transient water wave described in this report 

 was developed in order to take account of the behavior of waves on a free sur- 

 face. The form of this wave, however, would appear to have considerable prom- 

 ise for applications in many linear systems investigations. 



Conventionally, a pulse- like transient is used for system excitation. The 

 frequency range of the excitation is determined primarily by the concentration 

 of the transient about a single point in time, and the amount of signal needed to 

 produce measurable response is a function of the amplitude levels of the pulse. 

 As a consequence, to faithfully reproduce a rapidly changing signal, measure- 

 ment requirements are severe and the probability of nonlinear behavior of the 

 system under test is high because of the large inputs often required to override 

 the effects of measurement noise in the recorded output signal. 



536 



