Morgan and Caster 



Fig. 10 - Pressure distribution on ARL duct B3 at 

 zero angle of attack (a^ = 0) 



misleading if extreme shapes were used. On the other hand, separation might 

 occur on extreme shapes which would void the comparisons anyway. The main 

 shortcoming of the theory is the inability to predict the pressure distribution 

 when separation occurs. 



Annular Airfoil Forces 



When annular airfoils are at a zero angle of incidence to the flow, the only 

 net force is that due to viscous drag. Each section of the duct will be subject to 

 forces and moments, however, which balance out. At an angle of incidence, the 

 forces and moments do not balance out, and there are lift, moment, and induced 

 drag forces acting on the duct in addition to the viscous drag. These forces and 

 moments, except for a moment arising from horizontal forces, are independent 

 of the section shape in linearized theory, and depend only on the chord-diameter 

 ratio of the annular airfoil. Figure 11 shows the theoretical lift -curve slope for 

 a range of chord-diameter ratios. Also plotted on this curve are the test spots 

 from Ducts I and II, BTZ duct, and results obtained by Fletcher (37). The ducts 

 tested by Fletcher had Clark-Y sections with a thickness -chord ratio of 0.117. 

 As can be seen from this figure, the theory gives a satisfactory prediction even 



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