L/indgren, Johnsson and Dyne 



with conventional and ducted propellers, calculated according to analogous 

 methods (see (14)). 



From Table 2 it is evident that for the contrarotating propellers the torque 

 balance and propeller efficiency is predicted with good accuracy by the calcula- 

 tions. Figure 7 shows, however, that the propellers designed for low values of 

 the advance ratio J are overpitched in comparison with the calculations. This 

 is in contrast to what is the case for conventional propellers, designed accord- 

 ing to an analogous method. One of the reasons for this discrepancy could be 

 that the use of the pitch of an equivalent propeller when determining the induc- 

 tion factors is not accurate enough. 



In Fig. 8 the efficiency t^^ at the design value K^. = 0.38 is shown on the 

 basis of the advance ratio J for the four sets of propellers, at the design pitch 

 ratio as well as at other pitch ratios tested. Also the torque balance is shown 

 in the diagram. From the diagram it is evident that the influence of pitch dis- 

 tribution and torque balance on efficiency is very small. 



4. DUCTED PROPELLERS: THEORETICAL BACKGROUND 

 AND EXPERIMENTAL VERIFICATION 



4.1. Design Method 



The ducted propellers are designed in accordance with a method which has 

 been developed at SSPA (15). This method is an improvement of the theory of 

 Dickmann and Weissinger (16). Thus, the distribution of blade circulation is 

 arbitrary, the number of propeller blades is finite, and the thickness of the duct 

 is considered. The method is analogous to the design method for conventional 

 propellers in use at SSPA. This implies that also cavitation and strength calcu- 

 lations are included. 



The calculations start from known values of total thrust, number of revolu- 

 tions, propeller diameter, number of blades and blade form, distribution of 

 blade circulation, duct vorticity, minimum cavitation margin, etc. The method 

 determines blade area, propeller efficiency, duct thrust, shape of duct, and 

 pitch, camber, and thickness of the propeller blade sections. 



When calculating the shape of the duct and the thrust of the propeller and the 

 duct, the actual propeller is replaced by an equivalent infinite -bladed propeller, 

 represented by continuous radial distributions of ring vortices and rectilinear 

 vortices. The strength of the vortices is determined by the conditions in the 

 ultimate wake. The duct is replaced by systems of ring vortices and ring 

 sources, which simulate the acceleration (deceleration) and the thickness of the 

 duct, respectively. The hub is replaced by a source distribution along the axis. 

 If the hub is cylindrical and the thickness distribution of the duct is prescribed, 

 the source distributions of the hub and the duct, respectively, are determined by 

 the local axial velocity. The definite strength of the vortex systems of the pro- 

 peller and the duct and the hub is determined by an iteration process in such a 

 way that the desired total thrust is obtained. The total thrust is calculated ac- 

 cording to the momentum theorem and the thrust of the propeller according to. 



1276 



