Weissinger and Maass 

 shroud trailing 



edge 



S, ^' />^- 



cone-frustum semi-infinite 

 segments cylinder 



i. 



Fig. IZ - (See (130)) Approximation of the 

 vortex distribution on a shroud and its slip- 

 stream by a vortex distribution on a system 

 of cone-frustum segments 



has been checked numerically that this gives an adequate representation. The 

 contraction ratio is not determined from the resulting value r^+M of the cylin- 

 der, but, in a more accurate way, from the constant boundary value v^y. One 

 general result of all numerical examples (cylindrical, conical, and parabolically 

 cambered ducts, < ^ < 1) is that the value of v^y and therefore of $ and of 

 other net characteristics does not change much during the iteration (see Fig. 13). 

 That is a strong indication that the linear theory affords good results for these 

 characteristics. 



The number of segments chosen for the computations is N = 24 on the duct, 

 M = 41 on the slipstream. A check has shown that smaller numbers will also 

 give sufficient accuracy (see Fig. 14). 



Unfortunately, the report does not present enough results to deduce general 

 conclusions about the accuracy of pressure distribution, etc., computed from 

 the linear theory. The only example presented extensively is the cylindrical 

 duct with chord/diameter ratio k = 0.1 in the static case. Fig. 15 shows that 

 the vortex distributions computed by both linear and nonlinear theories agree 

 rather well. Probably, with increasing \ and/or v (for noncylindrical ducts) 

 the agreement would even be better. 



Two other attempts to take into account nonlinear effects may be mentioned. 

 Bollheimer (116) developed a theory in which the ring vortices representing the 



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