Malavard 



plan (30) and by transposing the analog simulation used in the principle of the 

 "lifting-line computer" (31). Finally, in order to compare analog results and 

 experiments in a small high-speed hydrodynamic channel, a special simulation 

 device permitted the design of supercavitating wings with strut and wall effects 

 (32,33), and calculation of the hydrodynamic characteristics oiflat supercavitat- 

 ing wings. 



Screw Propellers — On the same principle as the "lifting-line computer," 

 Siestrunck had conceived, in 1944, an "analog propellers computer" for large- 

 aspect ratio blades. This realization was taken up again in 1959 by Sulmont, 

 who improved it by introducing a resistance network, thus making it easier to 

 use. He also adapted it to simulate hub effects easily (34). 



Because of the small span ratio of their blades, naval propellers can be cal- 

 culated from aeronautical theories only by introducing more or less justified 

 empirical correction coefficients. It was only in 1959 that our first efforts were 

 made to apply the theory of lifting surface to helical flows. The many difficulties 

 in solving this problem by analytical and numerical methods are well known; they 

 are caused mostly by the complexity of the flow field to be considered. 



The rheoelectric method allows the representation of this flow field, and thus 

 the design of small- span ratio blades becomes possible by means of techniques 

 similar to those perfected for wings of arbitrary shapes (35). The boundary con- 

 ditions corresponding to supercavitating blades can also be imposed without 

 major difficulty and lead to a correct definition of the lower surface for the im- 

 posed pressure distribution (34, 36). This problem has not yet received any 

 numerical treatment, and accordingly the studies being made at present at the 

 Centre de Calcul Analogique are attempting to transpose the analog method into 

 a program that could be used on large computers. 



In the same framework, Sulmont has studied the problem of ducted propel- 

 lers; by making some assumptions of the propeller's nature (infinite number of 

 blades), he has been able to define adapted duct forms which seem to promise 

 high propulsion efficiency. 



To complete this account we must mention the studies being carried out at 

 the Centre de Calcul Analogique. At present, our attention is directed towards 

 the solution of the problem of immersed or semi- immersed bodies which may 

 be so thick that the linearized boundary conditions relative to the obstacle are 

 no longer applicable, although the linearized free surface is preserved. A two- 

 dimensional study (37) has permitted us to test the validity of a new theoretical 

 scheme (38), and in forthcoming studies results in the three-dimensional area 

 should be obtained very soon. At that point, the calculation of the wave resist- 

 ance of a thick hull will be undertaken. 



It would be difficult to sum up completely here all the publications which 

 have been referenced above. We can only present some of the most significant 

 examples of the rheoelectric method and the most outstanding results of its use. 



370 



