Ogilvie 



The f.r. functions may be found by a straightforward set of experiments in 

 regular waves, by experiments in irregular waves (as by Dalzell (1962a,b) and 

 others), or by tests in transient waves (Davis and Zarnick (1964)). 



The regular wave tests are the simplest in principle, but there are objec- 

 tions against them: (1) A separate test must be run for each frequency of in- 

 terest, at each speed and at each heading. (2) With most wavemaking installa- 

 tions there is a question about the regularity of "regular waves." Harmonics 

 may be non-negligible, causing large errors if ignored. (3) The amplitudes 

 must be kept very small, to avoid nonlinear distortion of the f.r. functions. 



The irregular wave tests are better in each of these three respects. In 

 particular, the whole frequency spectrum is covered in a single well-designed 

 test. However, here there is another objection: The test rvin must be long 

 enough for the records to be analyzed statistically. In most tanks this is im- 

 possible, and so several test runs are made and the records are patched to- 

 gether. 



Tests in transient waves, that is, in wave pulses or wave packets, avoid the 

 difficulties of both regular and confused sea tests in that a single record of rea- 

 sonable length provides all of the information necessary for finding the f.r. func- 

 tions. The price one pays here is in meeting the stringent requirements on 

 measurement accuracy. 



Sometimes it is desirable to characterize the ship in a more detailed man- 

 ner than is possible with the 'Tjlack box" methods. A procedure has been de- 

 veloped for this purpose by several investigators, and, although it requires 

 more testing than any of the above mentioned procedures, it also provides more 

 information. In mathematical terms it may be described as follows: 



A sinusoidal wave system exerts on the ship a force and moment, which can 

 be represented by the expressions FjEeje^*-'^**^' ^}, j = 1, 2, . . . , 6. There may 

 be other external forces and moments as well, such as oscillatory propeller 

 thrust, control surface forces, and artificial constraint forces on the model. 

 Let these be represented by G Rele'^'^** ' ^} . Finally, there will be forces 

 which are induced by the motions of the ship itself. If the instantaneous dis- 

 placement in the k-th mode is represented by Xj^Reje^'^'^**^''^} , then we assume 

 that the motion -induced forces and moments are proportional to the amplitudes 

 x^, but of course they may have phases which are quite different from the mo- 

 tion phases, s^. This troup of forces includes inertial reactions. 



It must generally be accepted that all modes of motion interact with each 

 other and with all of the force and moment components. The simplest possible 

 relationship is a linear one, and so we assume that the excitations, external 

 constraints, inertial reactions, and hydrodynamic and hydrostatic motion- 

 induced forces are linearly related: 



i(^t + 8k) J i(a;t + ej) 



RHS AjwXue = Re F^e 



+ Re 



i(&)t + (9j ) 



where Aj^ is a complex matrix of coefficients. 



20 



