Lehman and Kaplan 



propeller configurations evaluated herein. Thus the ratio of the induced forces 

 to the thrust of the propeller, under these conditions, would be expected to be 

 the same for the particular case of the two-bladed and four-bladed propellers 

 referred to. Similarly the theory would then produce the same values of the 

 ratios of the forces to the propeller thrust for a single- bladed propeller, when 

 examining the output at the higher harmonics, i.e., for N = 1 and m = the cor- 

 responding harmonic number that will include the effect of the number of blades. 

 Thus some indication of the reasons for the predictive capability of single-bladed 

 propeller testing is provided by the present theory, although it is considered 

 under the constraint of requiring constant thrust characteristics. While no pre- 

 cise proof of this technique is provided by the present theory for arbitrary con- 

 ditions, and more conditions should be evaluated analytically with greater care 

 in determining the actual thrust characteristics of propeJllers with different 

 numbers of blades, there is indication that a theoretical basis does exist for the 

 method of single-bladed propeller testing described in the experimental section. 



As a result of the general agreement between the present theory and avail- 

 able experiments a number of possibilities exist for extending the present com- 

 putations to other cases to obtain further fundamental information on this phe- 

 nomenon of propeller- induced forces. The theoretical procedures can then be 

 applied to a number of varied operating conditions and thus used to provide use- 

 ful insight into the important factors that determine the blade- rate forces and 

 their harmonics. The. theoretical results will guide particular experimental 

 programs that seek ways of reducing the vibratory input excitation to naval ves- 

 sels from these propeller-induced effects. 



CONCLUSIONS 



The previously described experimental and theoretical studies have pro- 

 vided a number of significant results for the problem of propeller- induced forces 

 on nearby appendages. The emphasis in this work has been devoted to append- 

 ages upstream of the propeller, and most of the conclusions obtained from this 

 work are concerned with that particular arrangement. However certain conse- 

 quences due to other geometric and/or hydrodynamic influences were found, and 

 their features also provide signficant information. 



Considering the case of appendages parallel to an oncoming stream and up- 

 stream of the propeller, the main conclusions derived from this study are the 

 occurrence of a force in accordance with the number of propeller blades and 

 whether that number is odd or even, the importance of propeller thickness in de- 

 termining the magnitude of both transverse and axial appendage forces, and the 

 nature of the decay with distance between the propeller and the appendage. All 

 of these features have been illustrated by the experimental results, and the 

 theoretical model also predicts the same effects. 



An important experimental technique for this arrangement is the use of the 

 single-bladed propeller to determine induced appendage forces in terms of the 

 ratio of the induced force to the thrust of the tested propeller system, with pre- 

 dictions obtained for a multibladed propeller. The small dependence of the 

 ratios of the induced appendage forces to the propeller thrust on the advance 



228 



