A Vortex Theory for the Maneuvering Ship 



REPLY TO THE DISCUSSION BY VOSPER 



Roger Brard 



Bassin d'Essais cles Carenes de la Marine 



Paris, France 



From a practical point of view, the use of quasi-static derivatives is prob- 

 ably justified for solving the problems concerning the stability of steady mo- 

 tions. Of course, as indicated in Section 5.2 of the paper, the "equation in s" is 

 different, at least in principle, whether the history of the past motion is taken 

 into account or not. But the stability of the motion depends mainly upon the 

 signs of the real parts of the roots of the equation which are in the vicinity of 

 zero, and the signs seem to be very little affected by the history of the motion. 



In some cases, it is possible to observe motions of surface ships, such as 

 harmonic variation of the heading, the rudder angle being constant and equal to 

 zero, for which complete explanation seemingly requires consideration of the 

 history of the past motion. 



In the case of a surface ship, I believe that we generally do not need a very 

 accurate theory to predict the motion of the ship, and, therefore, to introduce in 

 the calculation the effects of the history of the motion. But, I am not sure that 

 these effects are not of importance in the case of a submerged body. You state 

 that in submerged body work a good correlation has been achieved between prac- 

 tice and theory (that is the classical theory, without correction for taking into 

 account the vortex wake generated by the body). I personally have no knowledge 

 of results of comparisons between theory and experiments on models or on full- 

 scale submerged bodies, which permit to conclude in a way or in the other. That 

 is why I should be very grateful to you if you could give me more precise infor- 

 mations about this point. 



I was surprised to find that our experiments carried out with the Planar 

 Motion Mechanism show a great influence of the reduced frequency. Before 

 getting these results, I considered the phenomenon as possible, but I did not be- 

 lieve that it could be of such great importance. However, I should like to re- 

 mind you of the fact that the coefficients are not equally affected. It would be 

 interesting to compare calculated motions with constant coefficients and with 

 variable coefficients. But I have had no time to do it yet. 



I have also some doubts about the possibility to deduce the time forces and 

 moments acting on a ship or on a submarine from the forces measured in har- 

 monic motion by use of a planar motion mechanism. But, perhaps the reasons 

 behind our lines of thought are not identical. You seem to consider that your 

 doubts are justified by the fact that the actual motion of a surface ship or a sub- 

 marine is seldom harmonic; I rather consider that the actual motions of a ship 

 or a submarine are often outside the linear field, and therefore, that the inver- 

 sion of the Fourier integral becomes either impossible or meaningless. 



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