Schmiechen 



Vi = Q/Ai , (24) 



A- denoting some cross section. The situation is very similar to that encoun- 

 tered in boundary -layer theory, where displacement, momentum and energy 

 thicknesses have to be distinguished. In this case the definition of the different 

 velocities, rather than cross -sections, has proved to be more promising. 



3.2 External Efficiency 



The external efficiency itself may be considered as the product 



■^EXT = ^'IDEAL ■^'JET (^^^ 



of the ideal and jet efficiencies 



- - t; - 



■^IDEAL = 2mi/(m2 + m j ) iOi\-ji'}n'v i (26) 



and '! ■ - 



VjET = ("^2 - '^?)/2(e2 - e,) ■ ' ■• (27) 



respectively. The ambiguity in the definition of the ideal efficiency, i.e., the ef- 

 ficiency of dynamically equivalent ideal propellers, due to the propeller advance 

 speed (undefined up to now), has been removed by the convention 



'■ -- ■ ' ''--'■ •' V = mj (28) 



SO that the efficiency is exactly the same as that of an actuator disk,, with the 

 important qualification, that all relevant velocities are momentum velocities. 

 Later on it will be seen that this choice is actually not the only and best one; see 

 Sec. 5.2. 



With the momentum ratio 



u = M1/M2 = m/m2 , (29) 



the ideal efficiency becomes 



^IDEAL = 2/(1 + 1/m) • (30) 



Either the momentum ratio or the ideal efficiency itseK may serve as universal 

 propeller advance criteria. Actually, any function rising with increasing values 

 of these criteria may serve the same purpose, while functions falling may be 

 considered as loading criteria, e.g., the load factor 



Cto = 4/r;jDEAL (1/^IDEAL "1) (31) 



based on the maximum propeller cross -section. 



1090 



