Nowaekt and Sharma 
APPENDIX C 
LIFTING LINE CALCULATIONS 
C.1. Problem Formulation 
The principal method for calculating thrust deduction and free- 
surface effects due to a propeller as described in Appendix B pre - 
supposes that a lifting line representation of the propeller , i.e. the 
distribution of bound circulation along the radius , is known . In order 
to be able to apply this method to a given propeller we need a scheme 
for determining the circulation distribution for any given operating 
condition of a propeller of predetermined geometry . This is essential- 
ly the classical "performance" problem in propeller theory ( as opposed 
to the design problem , in which a certain performance criterion is 
prescribed and the optimum propeller geometry is sought for ) . 
Physically , the problem can be formulated as a set of rela - 
tions which must be satisfied at every propeller radius between the hub 
and the tip . Using standard symbols , these relations are 
ct. = Cc, {@) CGT) 
=" = 6. (G2) 
tan b= P/2rR (C3) 
tan B, = (1-w)V+u,t/ jek - apt (C 4) 
ee aria dR! 
eget ee ae reo 
Re (C 5) 
Dae E: » 7) §at(R')|_ aR! 
Shi ah i -(R/Rp» 8B,» 2) ) aR (ROR 
: (c 6) 
r= Cyc {(1-w )V tugl /(2sinB (C 7) 
1906 
