Lindgren, Johnsson and Dyne 



velocity, however, errors can arise due to the simplified representation of the 

 propeller. Since corresponding disadvantages have not been found in the calcu- 

 lations of the axial velocity, the continuity -law method is preferred when the 

 shape of the duct is determined. 



A method is presented which makes it possible to adjust the shape of the 

 duct, if the first calculations give a shape that is not satisfactory from a practi- 

 cal point of view. The corrections applied do not influence the velocities at the 

 propeller disk directly, and the first calculations need therefore hardly be re- 

 peated. 



In the propeller calculations the number of blades is assumed to be finite. 

 Starting from the propeller thrust as obtained above, the velocities induced by 

 the propeller are determined by a conventional lifting line method. The pitch of 

 the helical vortices is assumed to be determined by the velocities in the ulti- 

 mate wake. Due to the finite number of blades, the velocities induced by the 

 duct and the hub at the blades deviate from the circumferential mean values, 

 especially near the blade tips. No allowance is so far made for this fact when 

 the pitch of the propeller blades is determined. 



Due to the relatively great blade widths generally used for ship propellers, 

 the axial variation of the induced velocities makes camber and pitch corrections 

 necessary. Besides the ordinary corrections, calculated by some lifting-surface 

 method, additional corrections have to be introduced, primarily due to the vor- 

 ticity of the duct. 



Pitch corrections due to viscosity and blade thickness are calculated in the 

 same way as for a conventional propeller. 



4.2. Experimental Verification 



In order to obtain an experimental verification of the design method, a se- 

 ries of open-water tests with four heavily loaded, ducted propellers has been 

 carried out in the SSPA cavitation tunnel. The design value of the total thrust 

 was in all cases the same, while the theoretical thrust of the duct was varied 

 systematically. 



The important design and test data of the ducted propellers are given in 

 Table 3. The blade form and distribution of blade circulation were the same as 

 for a conventional propeller. The shapes of the ducts are given in Fig. 9. 



The experimental results are described in (17). A comparison between 

 computed and measured ducted propeller characteristics is also given in Table 4 

 and in Figs. 7 and 10. As long as no flow separation occurred, the agreement 

 between the theoretical and experimental values of total thrust at the design ad- 

 vance ratio was very good. The duct thrust was found to be slightly too large for 

 small duct vorticity, while the opposite condition was valid when the theoretical 

 vorticity of the duct was large. The efficiency of the ducted propellers was 

 somewhat lower than that predicted by the theory (see Fig. 10). 



1278 



