Davis and Zarnick 



SUMMARY AND CONCLUSIONS 



The complete determination of the response of a ship in regular waves in- 

 volves a large and expensive testing program. When the transient wave tech- 

 nique is used properly, the total testing time can be reduced by an order of 

 magnitude. 



In a theoretical discussion of ship dynamics, it has been stated that the 

 usual systems representation of ship motion as an "output" and wave height as 

 an "input" is a misconception; both dynamic quantities are "output." Water 

 wave transients traveling in a single direction can be readily analyzed with the 

 use of Fourier transforms; the transforms of two measurements on a single 

 wave transient are related by the so-called "transfer function" of water, 

 g-jwu,. ix/k ^ where x is the distance separating the measurement points in the 

 direction of wave travel. 



The wave used at the Model Basin for transient testing has a continuously 

 increasing wave length which results in an intense concentration of wave energy 

 for a short period of its travel. Model transient tests are commenced in calm 

 water, then passed through a wave having energy in all frequencies of interest, 

 and eventually returned to the smooth water condition. The transfer function 

 for a particular motion variable is found for all frequencies by dividing the Fou- 

 rier transform of the motion transient by that of the wave height record, refer- 

 enced to the model center of gravity. With a suitably tailored wave transient, 

 mean square motion levels in a particular random seaway can be found immedi- 

 ately by squaring and integrating the motions during a transient test. 



Transient tests conducted on three models in ahead waves have verified the 

 theory presented. Close agreement between transient and regular wave tests 

 has been obtained for heave and pitch motions at zero and forward speed. The 

 major difficulty encountered has been in the generation and measurement of 

 waves, where further refinements and research are proposed. Digital programs 

 are being written for the bulk processing of transient records. 



Finally, the technique of using a transient excitation which is a linear fre- 

 quency sweep is an original contribution to general linear systems analysis; it 

 has virtues of linearity and noise- immunity, the capability of determining fre- 

 quency response of a system by visual inspection of the transient records. 



Appendix 

 WEIGHTING FUNCTION OR IMPULSE RESPONSE OF WATER 



It has been shown in this report that the operator e" J'^'"'"'/^ is the fre- 

 quency response function that relates wave height measured at two points sepa- 

 rated by a distance x in tlie direction of travel. The weighting function w(7) 

 can be determined by taking the inverse Fourier transform of the frequency re- 

 sponse function: 



538 



