Lindgren, Johnsson and Dyne 



(1) Morgan and Lerbs use the pitch distribution for an equivalent pro- 

 peller as input data and calculate the circulation distribution. In our scheme the 

 circulation distribution for the equivalent propeller is used as input data. 



(2) Morgan and Lerbs use Lerbs' induction -factor method when calcu- 

 lating the relation between the circulation and the induced velocities. In our 

 scheme the modified induction factor method proposed in (11) is used. The pitch 

 angles assumed for the free vortices, when determining the induction factors, 

 are those of an equivalent propeller, as defined in (10). 



(3) The interference velocities between the propellers are defined in 

 (9) and (10) as 



, , "ail = ""as! ^a2 i^ - ^ al') ' 



"ai2 = "asl ^al (1+^al) ' 

 "ti2 = 2Uf3i ftl (1 + ^tl) ' 



where u^^ and Uf^ are axial and tangential self-induced velocities, f^ and f^ 

 are factors for obtaining circumferential average of interference velocities, and 

 g^ and if are factors for obtaining effect of axial distance on interference ve- 

 locities. 



By using Stokes' law, Lerbs derived 



t\ ' 





and introduced the following approximation: 



fax = fa2 = ^l 



In our scheme the additional approximation 



fn =W (^. ^i) . 



where H = Goldstein factor has been used in order to facilitate the procedure of 

 convergence. U Eq. (1) is used instead, very large values are obtained for 

 small values of u^ , which tends to upset the calculation procedure. 



For gg, Lerbs obtained values by replacing each propeller by a uniformly 

 loaded sink disk. Tachmindji (12) later derived new values by replacing the 

 propellers by a succession of ring vortices, whose strength varies with propeller 



1270 



