Hydrodynamic Problems Solved by Rheoelectric Analogies 



of the saturated vapor pressure; optimal span circulation distribution, (b) Me- 

 chanical — span thickness distribution that ensured everywhere a sufficient me- 

 chanical resistance. These conditions can be ensured independently, because 

 it is possible, as in the case of wings, to divide the problem into two parts; one 

 referring to the determination of the lifting effect of an infinitely thin surface, 

 and the other to the calculation of the thickness effect while entirely free of 

 lifting. 



For the first part, the load distribution, a constant on eight-tenths of the 

 chord and decreasing to zero at the leading and trailing edges, together with 

 optimal span circulation distribution are chosen. The shape of each section and 

 the distribution of velocities on the lower and upper surfaces are then deter- 

 mined. If the depression created by the velocities is considered significant, it 

 is possible to change the load distribution until acceptable levels are reached. 

 For the thickness effect, the calculation process is similar. The form of the 

 lower and upper surfaces corresponding to a nonlifting foil in a helicoidal flow 

 and the distribution of velocities on them, are determined. Once these two op- 

 erations are completed, the blade sections are deduced by comparison of the lift- 

 ing and thickness effects. Figure 24 shows the forms of different blade sections 

 according to the parameters just described. Table 1 gives the expected values 

 of the drag and torque coefficient and the values obtained in a test in free water 

 carried out at the Bassin des Carenes, Paris. 



Table 1 .. - 



Expected Values of the Drag and Torque 

 Coefficient and the Values Obtained in 

 a Test in Free Water at the Bassin des 

 Carenes, Paris 



It will be seen that the agreement between these values is satisfactory except 

 for the propeller efficiency, which is lower than estimated. The difference 

 seems due to an underestimation of the friction resistance in consideration of 

 the Reynolds number imposed by the test conditions. The experiments in a cav- 

 itation tunnel show, as was expected, that for the design value of k the propellers 

 function without cavitation on the upper surface of the blades, except very near 

 the blade tip (0.95 < f < 1) where the end vortex is attached. 



These satisfactory observations seem to prove that two important objectives 

 have been attained— control of pressure and a condition of adaptation - and that 

 analog calculation is likely to provide an effective solution to the theory of the 

 lifting surface of propellers. 



401 



