Vassilopoulos and Mandel 



The second part of the current correlation which is concerned with the ef- 

 fect of weight distribution is illustrated in Figs. 58-65. For small radii of gy- 

 ration, theoretical heaving motion amplitudes are slightly less than the experi- 

 mental ones, but the situation is reversed and slightly worsened as k^ is 

 increased. Agreement in pitching motion appears to be similar and the tendency 

 here is for the experimental data to be 15-20% higher, particularly at high wave- 

 lengths. 



All figures for ahead seas indicate that for wavelengths less than about half 

 the length of the model, both pitching and heaving motions are negligible while 

 for wavelengths higher than about twice the model length, heaving becomes equal 

 to the wave amplitude and pitching corresponds to the maximum wave slope. 

 The rar^e 0.9L < X < 1.5L excites the models the most. On the contrary, astern 

 seas do not induce large responses in heave or pitch and amplitudes tend to in- 

 crease in a linear fashion with wavelength. These findings are in accord with 

 those of earlier investigations [24] which showed that for all wavelengths and 

 speeds, conventional ships suffer only small responses in astern seas in con- 

 trast to the more severe resonant responses that do occur in ahead seas. 



It was noted in the introduction that both experiment and strip theory, as 

 they were utilized for the purposes of this paper, are replete with errors. The 

 inadequacies of the strip theory as it was employed so far in this paper will be 

 discussed in the next section. Some of the shortcomings of the experimental 

 approach, particularly as they relate to a comparison with theory (not to a com- 

 parison with a full scale ship responding to hypothetical regular waves) are as 

 follows: 



1. The models used by Vossers et al. [18], were free to move in all six 

 degrees of freedom. Theory treats motion in the longitudinal plane of symmetry 

 only and furthermore presumes the absence of surge. 



2. All models tested at NSMB were equipped with bilge keels and were 

 furthermore self-propelled. Bilge keel damping and propeller thrust fluctua- 

 tions are ignored by theory. 



3. Errors in measurement of wave heights. 



4. Wall effects especially at low speeds and small wavelengths. 



THE EQUATIONS OF MOTION FOR A SURFACE SHIP 

 MOVING IN WAVES 



General Remarks 



A constructive appraisal of a given theory is best accomplished by examin- 

 ing the issue from different points of view. In this case, many such different 

 points of view exist. We will therefore examine the validity of the linearized 

 theory of ship motions as developed by Korvin-Kroukovsky by using a different 

 approach which is backed by physical reasonii^. The approach will involve two 

 cardinal steps: 



324 



