Schmiechen 



As a consequence, the general relation 



1 _ t = l^J^^^^ (78) 



cp(l/M- 1) 

 for the thrust deduction may be derived, where 



1 - w 



denotes the wake ratio. The additional condition for the determination of the 

 momentum ratio of the equivalent propeller may be rendered in the simplified 

 form 



if the condition 



and the approximation 



are introduced. 



1/Mo = cp2(l/M^ - 77outf) - "^OUTF (80) 



(■^INf)o = ■^INF = 1 (81) 



(''^OUTF^O - ''^OUTF (82) 



In terms of the load factor, the inverse momentum ratio of the propeller it- 

 self is either 



1/^2 = 1 + Ct^ (83) 



or 



i/m^ = 1 + Ct + V 1 + 2Ct- , (84) 



which ever applies. Accordingly, the thrust deduction may be determined as a 

 function of the wake ratio, the load factor, and the outflow efficiency. Apart 

 from the generalization the basic concepts as well as the details of the present 

 reasoning differ considerably from those proposed by Dickmann, 1939. 



The notion that the thrust deduction does not affect the power balance may 

 be illustrated by the consideration of a ducted system, only the intake of the duct 

 taking part in the interaction; Fig. 6. The suction at the hull and the thrust of 

 the duct, being effected by the same pressure, vary in the same way for various 

 configurations without any overall effect. The higher nozzle thrust results ap- 

 parently only in higher frictional losses and the necessity of a stronger support. 



5.2 Nonuniform Inflow 



We have dealt so far with essentially free-running propulsion devices, the 

 evaluation of performance criteria being based on measured integral values, no 

 problems arising in the appropriate choice of the boundaries of the propulsion 



1098 



