Weissinger and Maass 



(4) An option in the computer program allows calculations of the ideal 

 angle of attack of the duct section in the presence of a propeller. 



In (132), a computer program and results are presented for the inverse problem, 

 where the duct shape is computed once the duct pressure distribution has been 

 specified. 



Perhaps the most comprehensive investigations of ducted propellers have 

 been made by VIDYA (Nielsen, Kriebel, Mendenhall, Sacks, Spangler). For ex- 

 ample, they include duct stall interference in tandem configurations or interfer- 

 ence with hulls and also experimental investigations. The price for the compre- 

 hensiveness is a simplification of the theoretical models. So, to some extent, 

 these theories may be placed into the first category of theories characterized 

 above. The basic model is shown in Fig. 1 (164). The propeller annulus is di- 

 vided into a number ( <10) of equal-area annuli in each of which blade element 

 theory is used to describe local propeller -blade performance. The bound pro- 

 peller circulation is constant within each annulus, and a cylinder of ring vortices 

 is assumed to be shed from each annulus and to extend downstream. Centerbody- 

 induced velocities are neglected. The duct may have both thickness and camber, 

 the chord/diameter ratio is not restricted to small values. The propeller is 

 specified by the number of blades and by the radial distribution of chord and 

 pitch. From the above model, relations are derived by which, at a specified ad- 

 vance ratio, duct loading and propeller loading can be calculated from a given 

 inflow profile. From the loading distributions an improved inflow profile is de- 

 termined. The iteration converges rapidly. A digital computer program, pre- 

 sented in (164), takes one minute on the IBM 7094. A second program (164) for 

 the design of uniformly loaded propellers takes the same time. A rough esti- 

 mate of the influence of the angle of attack is also possible. 



. A 



Fig. 1 - Flow model used in (164) 



Last but not least in this enumeration of institutes and major research 

 groups, the name of van Manen and the Netherlands Ship Model Basin should not 

 be omitted. Their work, though mainly experimental and therefore not pertain- 

 ing to the subject of this review, has also contributed to the theory and gives 

 very valuable advice for design, based on theory and the results of extensive, 

 systematic series of experiments. 



1212 



