moderately loaded propellers. Furthermore, it also allows the evaluation of such 

 effects as wake distribution and hull interaction on the loading distribution of the 

 propeller. 



The paper has given an excellent outline of the work conducted on propeller- 

 hull interaction, a problem which is of primary concern to the propeller designer. It 

 is by increasing development in such areas that a more fundamental understanding of 

 propeller action will be accomplished. 



The increasing use of propellers with relatively large hub diameters has 

 emphasized the need of a solution for the circulation distribution for these cases. 

 Such a circulation distribution may be considerably different than the one obtained 

 by considerations of zero hub diameter. Through the use of corrective induction factors, 

 Dr. Lerbs has investigated the effect of the presence of the hub. The problem has been 

 pursued further at the David Taylor Model Basin and it was possible to extend Gold- 

 stein's work and derive the potential for the optimum circulation distribution 1 to 

 include the effect of a finite hub. Similar work has also been conducted by McCormick 

 who, however, solved the problem for simplified boundary conditions at the hub 

 radius. Figure 1 shows a plot of the Goldstein factor K, which is defined as the ratio 



Figure 1 • Effect of Hub Diameter for p - 4, p - 4 



Determined by Induction Factors for — = 0.2 



R 



Figure 2 shows the actual circulation distribution for the same propeller and the same 

 cases. These calculations have been performed by using approximations to the solu- 

 tion but it is planned to calculate the exact solutions at DTMB. 



of the circulation for a propeller having a finite number of blades to the circulation 

 for one having an infinite number of blades, plotted against the propeller radius. 

 This has been obtained for a four bladed propeller operating at a A; = 0.25 and 

 shows the effect of hub diameters of 0.2, 0.3 and 0.4 as compared to a propeller 

 having zero hub. Points calculated by means of the induction factors are also shown. 



1 DTMB Report 1051 



166 



