Weissinger and Maass 



aircrafts. In a pump- jet propeller, cavitation is delayed or compressibility ef- 

 fects are decreased. Noise can also be influenced by shrouding the propeller. 



We can discern two trends in the development of theories, one aiming at 

 most simple results and formulas which can be used in design without much ad- 

 ditional computation, the other trying to predict the whole field under most gen- 

 eral assumptions. The price to be paid in the first case is a loss in numerical 

 accuracy and a restriction in general applicability, because special assumptions 

 such as small chord/diameter ratio or special singularity distributions are in- 

 troduced. Aside from the fact that theories of the second kind require an expert 

 to understand them, their main disadvantage is the need of a big computer to 

 perform the numerical evaluations. Naturally, theories of the first kind were 

 developed first. So, we may distinguish two periods, one (ca. 1940-1955) in 

 which the first trend dominates, while after 1955 more efforts were exerted in 

 developing theories of the second kind. A "pioneer" period (ca. 1927-1940) pre- 

 ceded both during which the idea was born and first applications, experiments 

 and theoretical considerations were made. 



First Period: It seems that L. Stipa (84) in 1927 was the first to propose the 

 shrouding of the propeller by using the fuselage of an airplane as a duct. There 

 is also a Russian paper (82) claiming the concept for the Russian scientist CA. 

 Bracks back to 1887. In 1934 Kort proposed the "Kort-nozzle" for heavily 

 loaded marine propellers. 



Second Period: During World War n a group of Gottingen (Kuchemann, Weber, 

 Kriiger) began a systematic theoretical and experimental investigation of the 

 ducted propeller. Here, some of the basic ideas were conceived for all further 

 theoretical work. After the war, a group in Berlin (Horn, Dickmann, Amtsberg) 

 improved the theory and developed a design procedure based on representing the 

 duct by a vortex distribution and the propeller by a sink distribution. A similar 

 concept was applied by Lerbs (46). Stewart (83) and Ribner (75) developed a 

 theory for ring airfoils with small chord/diameter ratio based on a lifting line 

 theory. The papers of Helmbold (28, 29), which are not so well known because of 

 their restricted distribution, also contain some fundamental ideas. Unfortu- 

 nately, a limited distribution is the rule rather than the exception for most re- 

 ports on ducted propellers. 



Third Period: The paper of Dickmann and Weissinger (101) was the starting 

 point for the investigations of a group working at Karlsruhe (Dickmann, Weis- 

 singer, Wiedemer, BoUheimer, Brakhage, Maass, Rautmann). In (101) the shape 

 of the (thin) duct represented by the sum of a constant and an elliptic distribu- 

 tion of ring vortices was determined by a linearized theory under the assump- 

 tion of a constant pressure jump at the propeller plane. Dickmann also pro- 

 posed the use of semiempirical knowledge from turbomachines and pumps for 

 the propeller design, a line of thinking also followed by Bussler (8) and van 

 Manen. The theory was confirmed by experiments of Finkeldei (116). Using the 

 vortex model of (101) completed by ring sources, Weissinger developed a theory 

 for ring airfoils (without duct) of a given shape in axial flow, including effects of 

 profile thickness, struts, and central bodies. This theory was generalized for 

 ducted propellers with constant pressure jump in axial flow by Bollheimer, who 

 included some effects of profile thickness neglected in other theories. 



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