Brard 



In many circumstances, the angles ^ and a are not small. Consequently, 

 the variations of u/u, w/u, Lq/u, v/u, Lr/u and Lp/u may be great. 



In such circumstances, the equations of the "quasi-steady motions" are the 

 same as above, at least when the steady effects of the wake are neglected. How- 

 ever, many coefficients which are found in the set of forces (J^) are unknown. 

 Generally, the theory is unable to yield them. It is necessary to resort to ex- 

 periments. But tests on models themselves require special and complicated 

 instrumentation because of the high number of degrees of freedom and, conse- 

 quently, because of the number of the coefficients which are to be determined. 



If we now consider the effects of the wake, we encounter difficulties which 

 we partly emphasized in par. 9. When the nuclei found in the integral equations 

 of the motions are functions of t'- r' only, they can be deduced, as we will see 

 in Section II of this paper, from measurements made with small harmonic forced 

 motions. But, when these nuclei are functions not only of t ' - r', but also of r', 

 the problem is much more intricate. 



The main difficulties are of two types. 



The first is due to the fact that, for certain forms of hull, there is no rea- 

 son why the free vortices should be shed along lines attached to the body (for 

 instance, that is the case of a submerged body of revolution, the complication, 

 in this case, being due to the fact that the axis of revolution is not always of 

 revolution for the distribution of the masses inside the body). 



The second is due to the curvature of the trajectory described by the origin 

 of the axis attached to the body, and also, to the roll motion. Obviously, the 

 velocities induced by the wake are no more given by the formulae above. 



That does not mean that there are no possibilities to investigate this prob- 

 lem with some chance of success, but, before undertaking such a research, it is 

 desirable to check whether the effects of the wake are or not of importance. 



That is why, in the next section, we study the effects of the wake in har- 

 monic forced motions in the (z,x)-plane. We will see that these effects are 

 not negligible, at least for some coefficients. That will give a lead for fruitful 

 researches. 



n. STEADY AND HARMONIC FORCED MOTIONS 

 PARALLEL TO THE (z,x) -PLANE 



14. Definition of These Motions — Set of Forces 

 Acting on the Body 



14.1. Steady Motions, Purely Heaving Motions, Purely 

 Pitching Motions 



The fixed axis O'z', O'x' are in the (z,x)-plane. The z' -axis is vertical 

 and positive downwards. The x'-axis is horizontal. The absolute coordinates 

 of the origin of the axis attached to the body are ^,^. 



882 



