these limitations, a more complete representation of the propeller based 



on lifting surface theory is required. 



A number of propeller lifting surface theories have been developed 



and programmed for computer-aided design calculations. The method of 



Is ^ ft 

 Kerwin ' is representative of the state-of-the-art and was selected for 



the present application because the theory and numerical techniques have 

 been extended to calculate induced velocities at arbitrary field points. 

 Free space pressure predictions based on this method show excellent agree- 

 ment with experimental measurements. Both the theory and numerical 

 analysis are conveniently divided into a lifting-line analysis and lifting- 

 surface corrections arising from blade thickness, blade location (skew and 

 rake), and chordwise variation in loading. Therefore, it is possible to 

 examine the separate contributions of various propeller characteristics to 

 the thrust deduction. 



LIFTING-LINE THEORY 



The basis of analytical propeller design methods is the moderately 

 loaded lifting line theory. ' The analysis considers the flow field 

 associated with the steady loading on a propeller with symmetrically spaced 

 blades. In accordance with circulation theory, the pressure loading on 

 the blades arising from camber and incidence can be represented by 

 distributions of bound and free vorticity. In the lifting line approxima- 

 tion, each blade is replaced by a single concentrated vortex line with 



Kerwin, J.E. and R. Leopold, "A Design Theory for Subcavitating 



Propellers," Transactions SNAME, Vol. 72 (1964). 

 1 c 



Kerwin, J.E. , "Computer Technique for Propeller Blade Section Design," 

 International Shipbuilding Progress, Vol. 20, No. 227 (Jul 1973). 



Denny, S.B., "Comparisons of Experimentally Determined and Theoreti- 

 cally Predicted Pressures in the Vicinity of a Marine Propeller," Naval 

 Ship Research and Development Center Report 2349 (May 1967). 



18 



Lerbs, H.W. , "Moderately Loaded Propellers with Finite Numbers of 



Blades and an Arbitrary Distribution of Circulation," Transactions SNAME, 



Vol. 60 (1952). 



19 



Morgan, W.B. and J.W. Wrench, "Some Computational Aspects of Propeller 



Design," Methods in Computational Physics, Vol. 4, Academic Press Inc., New 



York, N.Y. (1965). 



11 



