Morgan and Caster 



Fig. IZ - Lift, drag, and moment coefficients for NSRDC duct II (33) 



The theoretical moment shown in Fig. 12 consists of two parts: one part 

 from the vertical forces (lift) and one part from the horizontal forces (drag). 

 The solid line is the theoretical moment including both of these parts, while the 

 dashed line is the moment due to the vertical forces only, which is the dominant 

 part. 



In summary, the linearized theory gives a satisfactory prediction of the lift, 

 induced drag, and moment for angles of incidence up to where separation influ- 

 ences the results. The first effect of laminar separation at the leading edge is 

 on the drag force. This separation does not have much of an influence on the lift 

 and moment when it first begins, but as the separation region increases in size, 

 stall of the annular airfoil will occur (see footnote in previous Sec). 



It appears that the profile drag (viscous) of the annular airfoil can be esti- 

 mated with some degree of confidence. However, if separation occurs on the 

 duct, this drag may be underestimated by a significant amount. Because of the 

 detrimental influence of separation, it would seem worthwhile to attempt to pre- 

 dict separation during the design stage of an annular airfoil. References (12) 

 and (34) indicate that this has been done with some success. 



Annular Airfoil Axial Induced Velocities 



Axial induced velocities were measured at a number of locations inside 

 several ducts tested at ARL (35). Figure 13 presents the axial induced veloci- 

 ties measured at the midchord for Ducts Al, A2, and A3 along with the theoreti- 

 cal predictions obtained using Ref. (35). Figure 14 presents similar results for 



1326 



