Schmiechen 



introduced? Apparently only the overall propeller efficiency may be determined 

 as a function of an arbitrary advance ratio, of some reference length is intro- 

 duced. This situation changes when either the maximum cross section A^ or 

 the outlet cross section Aj of the propeller is introduced, which ever may be 

 typical for the dynamically equivalent ideal propeller. Now, the load factor 



Cti = 2T/(pV2Ai) (53) 



may be defined and consequently the universal advance ratio 



^IDEAL= 2/(1 + V 1 + CtJ (54) 



or ■ . . , = s ■: — s\:fn 



! i I ■■ 



^IDEAL = 4/(3 + /TT^) . (55) 



This again is a conventional procedure circumventing the difficult measurement 

 of the mass flow. In the case of unducted propellers it appears to be the only 

 possible procedure. 



From the propeller efficiency and the ideal efficiency so determined, the 

 basic performance characteristic, the hydraulic efficiency, may be derived, i.e., 

 actually from the data usually at hand; Schmiechen, 1966.2. In case these are 

 provided in terms of the nondimensional parameters (11)-(13) the load factor 

 may be determined according to the formula 



C^ = 2K^ /J2 . (56) 



i i 



Although the whole procedure appears to be rather straightforward its ap- 

 plication is often hampered by the ambiguity in the choice of the appropriate 

 cross section. While the selection of the maximum cross section may (e.g., for 

 shrouded propellers) at least for the larger area ratios 



a = A/Aq (57) 



result in hydraulic efficiencies exceeding unity this difficulty does not arise, if 

 the outlet cross section is selected as reference. 



The reason for this effect is simply, that in the first case the geometrically 

 equivalent ideal propeller is referred to, while in the second case the dynami- 

 cally equivalent reference propeller is chosen. Unless no appropriate criterion 

 for the space requirement of a propeller has been defined the usual, over- 

 simplified comparison of shrouded and unshrouded propellers does not make 

 much sense; Saunders, 1957, and predecessors. 



4.2 Further Analysis 



The analysis may be carried on following the lines indicated, if further in- 

 formation is provided, e.g., the mass flow through a ducted system. From the 

 momentum principle, the momentum outflow 



1094 



