Davis and Zarnick 



are required to characterize a model in regular waves. Assuming that the func- 

 tions involved can be suitably approximated by tests at 10 wave lengths, 30- 

 degree increments in direction from ahead to astern, and 5 speeds, 350 separate 

 model tests are required, with measurement and analysis of a number of dy- 

 namic variables on each test. A program such as this requires a major invest- 

 ment of time and money, and any techniques which can be developed to abbrevi- 

 ate the test time without technical compromise will reap high dividends. 



It is clear that relative wave direction and model speed must remain fixed 

 for any one test. However, under these constant conditions, a series of experi- 

 ments in varying wave lengths is nothing more than a frequency response de- 

 termination of a linear dynamic system, a common experiment in systems in- 

 vestigations for many engineering disciplines. 



The frequency response characteristics of linear systems may be measured 

 in three fundamental ways, that is, using sinusoidal, random, or transient exci- 

 tations. The first two techniques are commonly employed in testing ship mod- 

 els. The latter technique, using a transient water wave, is the subject of this 

 report. 



A transient wave will contain energy which, in general, is distributed over 

 a range of wave lengths. Thus, a single motion test can yield information about 

 the response of the ship at all wave lengths of interest. In the representative 

 example just quoted, the number of tests required to characterize a ship design 

 can be reduced from 350 to 35. 



In the following sections, the theoretical and practical aspects of transient 

 wave testing are presented. First, the basic mathematics of linear systems 

 analysis are outlined. Then, the analytic peculiarities of the ship-wave system 

 are discussed, stressing the fact that a wave is not properly an "input" as the 

 term is usually understood. Next, the complex subject of unidirectional water- 

 wave transients is treated in a simplified fashion by developing an expression 

 which relates various wave height time histories that might be recorded at var- 

 ious points along the path of the wave. 



A particular wave which arises quite naturally from this analysis is the one 

 which would, in theory, produce an impulse of infinite height and zero duration 

 at some measurement point. An approximation to this theoretical waveform is 

 quite easy to generate in a seakeeping facility; it has been extensively used at 

 DTMB for model testing because of its several attractive analytical properties. 



Three sets of model tests are reported herein to support the theory and to 

 illustrate some of the practical problems, especially associated with the meas- 

 urement of wave height, that can be anticipated in using transient waves to ex- 

 cite ship motion. 



PRELIMINARY THEORY 

 Mathematics of Transient Testing 



Suppose that a linear dynamic system (such as shown in Fig. 1) is under 

 investigation, with an "input" x(t) as the independent excitation, and an "output" 



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