Lehman and Kaplan 



DISCUSSION 



J. p. Breslin 



Davidson Laboratory , Stevens Institute of Technology 



Hoboken, New York 



Figure 51 reveals that the two-dimensional cascade representation of a pro- 

 peller leads to forces on the appendage some 8 to 10 times that measured. The 

 velocity and pressure fields of a propeller are roughly three-dimensional. Their 

 blade frequency components are strongly three-dimensional, having very rapid 

 decays in all directions. Thus it is not surprising that the two-dimensional 

 theory provides gross overestimates in magnitude and errors in phase. 



Mr. Lehman's data provides one of the first opportunities to make compari- 

 sons with a three-dimensional propeller- rudder interaction theory recently de- 

 veloped by Dr. Tsakonas and Miss Jacobs at the Stevens Institute of Technology. 

 To obtain results for the experimental configuration it will be necessary to 

 modify the computer program in a straightforward manner. Hopefully when 

 support is found for such calculations, much closer agreement between meas- 

 urement and theory may be expected. More importantly the character of the 

 force decay with increase of axial clearance should be well predicted. 



REPLY TO DISCUSSION 



August F. Lehman and Paul Kaplan 



We appreciate the interest in our work and the comments made. With re- 

 gard to the comment by Dr. Wereldsma, we are definitely interested in the in- 

 fluence of cavitation on propeller- induced forces, although we did state that our 

 conclusions were applicable only to the case where no cavitation occurred in the 

 system. We recognize that fluctuating cavitation on a propeller will contain a 

 broad spectrum of pressure disturbances, since such a force on the appendage 

 will occur at frequencies other than those corresponding to the blade rate and its 

 harmonics, but we still also expect to have large discernible blade rate force 

 signals. The problem of the influence of a cavitating propeller is certainly one 

 in which we have definite interest, and for which we can obtain measurements of 

 induced forces by the same basic techniques described in our paper. Thus we 

 would welcome the opportunity of extending our work to such conditions. 



The comment by Dr. Milgram can be answered by recognizing that the 

 mathematical model used in our work was based on an infinite cascade, and the 

 exponential rate of spatial decay directly follows from the analysis, similar to 

 the treatment of aerodynamic compressor blades in the work of Kemp and Sears. 



232 



