Comparison of Theory and Experiment on Ducted Propellers 



2.0 3.( 



5.0 6.0 7.0 



Fig. 11 - Lift curve slope as function of chord-diameter ratio (33) 



though some of the ducts had laminar separation, 

 tion would not be satisfactory. 



When stall occurs, the predic- 



The theoretical lift coefficient C^ , drag coefficient C/, , and moment coeffi- 

 cient c^, along with measured values are plotted in Fig. 12 for Duct II (33). This 

 figure shows that the theoretical predictions are generally satisfactory. Results 

 for the other ducts mentioned previously show similar trends. 



The drag coefficient shown in this figure is the sum of the profile drag, i.e., 

 drag at zero incidence, and the induced drag calculated theoretically (33). The 

 profile drag can be approximated, for instance, by the method discussed by 

 Granville (38) for predicting the drag of axisymmetric bodies. This procedure 

 gives reasonable drag predictions when no separation occurs on the duct, e.g., 

 the measured drag coefficient for Duct n at zero incidence was 0.07, while the 

 drag predicted by the Granville method was 0.077. However, for Duct I, on 

 which separation occurred, the measured drag coefficient was 0.48 at zero inci- 

 dence, while the drag predicted by the Granville method was 0.413. At the 

 higher angles of attack (positive or negative) where separation begins, the drag 

 prediction starts to deviate from the measured value, Fig. 12. Ryall et al. (35) 

 indicated in their investigation that the profile drag of one of their ducts in- 

 creased by a factor of about 1.8 when the angle of incidence was changed from 

 to 10°. 



1325 



