Understanding and Prediction of Ship Motions 



The above set of equations can be solved for the quantities x^e'^k, provided 

 that the matrix, A-^., and the forcing functions are known. Such a solution then 

 effectively expresses a set of six f.r. fvinctions, and so it is entirely equivalent 

 to the previous approaches. Of course, this method requires knowledge of the 

 matrix, Aj^ , and of the forcing fvinctions. These can be obtained by a straight- 

 forward but tedious set of experiments, as suggested by Haskind and Riman 

 (1946) and as carried out partially or completely with specific models by Golo- 

 vato (1957), Gerritsma (1960), and others. Such experiments are in effect set 

 up to correspond to special cases of the above equations, as follows: 



1. If the model is completely restrained, then Xj^ = for all k, and so 



G.e ' = -F-e ' . 



Such an experiment provides measurements of the wave excitation force and 

 moment; the quantities G^e^^J are obtained from dynamometers in the struc- 

 ture which restrains the model. 



2. If there are no incident waves, then F. = for all k, and so 



6 



A.,X,e ^ = G.e ' , j . 1, . . . , 6. 



k= 1 



The model can be forced to oscillate in selected modes only, so that the Aj,^ can 

 be determined. For example, if k = 3 corresponds to the vertical velocity or 

 force component, and if the model is forced to oscillate in heave only, the set of 

 equations reduces to 



AjsXse ' = G.e ^ j = 1, ..., 6. 



which allows the determination of A^^, . . . , A^^. 



3. If the model is completely free to respond to incident wave excitations, 

 and if there are no extraneous sinusoidal forces (such as oscillatory propeller 

 thrust), then Gj^ = for all k, and 



Ei St i e ■ 



AjkXke ' = F. e ^ j = 1, 



This experiment is redundant if performed with (1) and (2) above, and so it can 

 be taken as a check on the validity of the whole approach. This was done in the 

 experiments of Gerritsma (1960) described in the preceding chapter. 



This method is similar to the method of finding f.r. functions by direct 

 measurement in regular waves, in that the ship behavior is determined at dis- 

 crete frequencies and the data are then smoothed to provide continuous curves 

 of the frequency dependence on all variables. In particular, the forcing functions, 



21 



