NAVAL HYDRODYNAMIC PROBLEMS 



SOLVED BY RHEOELECTRIC 



ANALOGIES 



L. Malavard 



Faculte des Sciences (Chair e d' Aviation) 



Universite de Paris 



Paris, France ■ •■ ^ 



INTRODUCTION 



For the past 10 years the Centre de Calcul Analogique of the Centre 

 National de la Recherche Scientifique has made various contributions to the 

 study and solution of a large number of naval hydrodynamic problems. These 

 contributions are significant, because they have been made by a small team of 

 research scientists using very simple computing equipment which would seem 

 inadequate to people who are accustomed to using large, sophisticated computers. 



It is not feasible to consider these studies of naval hydrodynamics in com- 

 plete isolation from the context of rheoelectric analogy which has made possible 

 important developments in the various fields of mathematical physics. In this 

 connection, it is convenient to recall that the first studies carried out in France 

 using electric analogy techniques for solving some hydrodynamic problems 

 (flows around bodies with or without circulation— Oseen flows (1,2), flows with 

 Jetstream lines (3), etc.), gave promise of future development. This develop- 

 ment has been realized intensively since 1958 because of the experience gained 

 by the Centre de Calcul Analogigue in the study of problems in incompressible 

 aerodynamics, thin foils, lifting lines, lifting surfaces, cascades, simple heli- 

 coidal machines, etc. (Refs. 4 through 6), and because of the introduction by 

 Tulin and Burkart (7) in 1955 of the linearized theory of cavitating flows. 



One of the assets which has assured the success of rheoelectric analogy 

 since its early beginnings has been its ability in solving Laplace field equations. 

 This computing capacity, together with the experimental character of the tech- 

 nique employed, makes rheoelectric analogy ideal for the practical worker, 

 engineer, or physicist, who remains in contact with a model on which his control- 

 ling action may be exercised without any restraint. Nevertheless, for an inten- 

 sive and complete use of the method, analog simulation often requires turning to 

 certain methods of theoretical formulation familiar to the mathematician. It is 

 in this way, for example, that the knowledge of elementary analytical solutions, 

 the use of conformal mapping, the analysis of singularities, etc., allow the solu- 

 tion of each problem in the most efficient way. 



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