01 



02 



03 



05 



0.7 



0.8 



Q9 



ID 



Figure 2 - Effect of Hub Diameter on Distribution of Circulation for 



fi = 4, p = 4 



Induction factors have also been used for the development of the theory for wake 

 adapted contrarotating propellers. Although considerable effort has been expended, par- 

 ticularly by Lieber, Yen and Spiegel, in trying to determine the potential function for 

 contrarotating systems, calculations cannot yet be performed by the theory. The use 

 of induction factors is presently the only method available without going into arbitrary 

 assumptions on the applicability of Goldstein's work for such propellers. It would be 

 interesting to hear Dr. Lerbs' opinion as to the magnitude of the time dependent 

 effects on contrarotating propellers and the need of theoretical work in this subject. 



A. Silverleaf 



I wish to add a few footnotes to Professor Lerbs' lecture rather than comment 

 directly on the theory he summarised. One of the duties of the propulsion and cavita- 

 tion group at Ship Division, N.P.L., is to design propellers which will be built and 

 fitted to ships, and we are therefore concerned with both propeller theory and its 

 practical consequences. The theoretical developments of the last ten years have undoubt- 

 edly been of very great value as a firm guide to practical design, and, as Mr. Tachmindji 

 mentioned, Prof. Lerbs' own part in this has been a major one. However, it is neces- 

 sary to check the consequences of using these theoretical design methods, and, whether 

 we like it or not, at present the only reasonably precise way of doing so is by experi- 

 ments with models. This produces some disconcerting features and also presents some 

 difficulties. For instance, propellers designed by modern theoretical methods quite 

 often have a knack of being slightly less efficient than those designed by what may 

 be called rather 'slap-happy' methods. Further, these 'empirical' propellers are often 

 less sensitive to variations from their designed operating conditions which, of course, 

 occur owing to changes in loading, and this adds to the difficulties of using theoretical 

 methods in designing propellers for ships which have to operate under widely varying 

 conditions. 



Many of the problems in the model experiment techniques can be grouped 

 together under the general heading of scale effects. Thus we have found at N.P.L. 

 that propeller models often suffer heavily from laminar boundary layer flow, affecting 

 their performance under both non-cavitating and cavitating conditions, while differences 

 in free stream turbulence levels between model and full-scale must also be taken into 

 account. Another problem is that of boundary wall interference effects in propeller 



167 



