A Vortex Theory for the Maneuvering Ship 



2') The problem connected with the stability of course of a submerged body 

 in the horizontal plane are more complicated than those related to the surface 

 ship because of the particular influence of the heel. 



3*) We have not studied the stability of the steady motions in the case when 

 the history of the previous motions is not negligible. That should be done; per- 

 haps the effective stability is not so high as predicted by the quasi-steady mo- 

 tion approximation. 



18. The Response to the Control Devices 



This problem is difficult because of the effect of the wake generated by the 

 body itself on the rudders and planes. 



We showed that at the beginning of a maneuver, the efficiency of a rudder 

 or of a diving stern plane is higher than that deduced from tests in a steady 

 motion. That comes from the fact that, at the beginning of the maneuver, the 

 wake which should reduce the effective angle of attack on the rudder, is not fully 

 developed. 



Moreover, when, for one or several functions ^, one has 7t(0) '' 0, the effect 

 of pressures p{ is so high that the lift (or the moment) following immediately a 

 perturbation is greater than at t ' = +«. Consequently, it may happen that the re- 

 sponse of the body is quite different from that suggested by the word "deficiency." 

 This point shall be emphasized, because the set of forces ? in the quasi-steady 

 motion and the real set of forces ?-A? don't act along a same line. For in- 

 stance, at the beginning of a gyration, the heel could be greater than in the 

 steady turning motion, even when the rudders are located so as to avoid an £- 

 moment of their lifts in a steady turning motion. 



19. The "True" Equations of the Motion 



19.1. Motions in the (z,x)-Plane 



The question examined here is as follows: In the case of a planar motion 

 in the (z,x)-plane, how is it possible to deduce the "true" equations of the free 

 motions from the forces and moment measured in a harmonic forced motion? 



These "true" equations are those we have to substitute for the equations of 

 the quasi-steady motions. 



When they are reduced to the linear terms, the three equations of the mo- 

 tion are obtained by writing that 



Z = 0, X = 0, )K = 0, 



Z,X,\[ being the forces and moment given in par. 8. 



As explained in par. 15.1, tests carried out in steady forced motions give 

 the numerical values of 



899 



