Theory of the Ducted Propeller — A Review 



11 

 10 

 0.9 

 0.8 



0.7 

 0.6 

 5 

 0.4 

 0.3 

 0.2 



-0 1 



0.1 0.2 0.3 0.4 0.5 



0.6 

 9m 



7 0.8 9 

 ^max/R 



10 



Fig. 8 - (See (106)) The lift ratio L^^,^.3/L^^,, 

 i.e., of (wing + body) to wing without body 

 for a cylindrical wing (a = 0.5) and an el- 



lipsoidal body [/ 



1 3/( 2R) = 2] in sev- 



eral axial positions, plotted against ^^ 

 r„„„/R 



edge of the duct. At this surface a jump in 

 the tangential velocity v^ must exist in order 

 to cancel the jump Ap in total pressure such 

 that the static pressure as determined from 

 the Bernoulli equation is continuous. If the 

 velocity jump is represented by a distribu- 

 tion 7f of ring vortices on the free surface, 

 and if the mean tangential velocity is de- 

 noted by v^ this condition is expressed in 

 the form 



pv^y^ = Ap {p - density) 



(3.1) 



Obviously, the resulting velocity field does 

 not depend on the location of the disk in the 

 duct. 



In the linear theory, the duct is repre- 

 sented by a distribution of vortex rings and 



^L^ 



0.2s 



0.25 



05 



0.75 

 9m 



Fig. 9 - (See (106)) The 

 lift ratio L^ + g/L^j, for cy- 

 lindrical wings and cyl- 

 inder bodies plotted over 

 the diameter ratio p^ 



1225 



