296 



3.0 



2.0 



■ TOTAL 



THICKNESS 



MEAN 

 l.OU LOADING 



PROPELLER 4118 

 i= 16.0 IN 

 J = 0.83 



C/Rq = 0.25 

 IN EXPERIMENT 



_L 



0.0 



0.1 



0.2 

 C/R 



0.4 



FIGURE 15. Modulus of blade- frequency force on ellip- 

 soid as a function of propeller tip clearance [calculated 

 using method of Vorus (1974)]. 



as procedures for predicting transient blade cavity 

 geometry and the attendant pressure field become 

 available, this important feature can be incorporated 

 into the analytical representation of the propeller 

 and the analysis of induced forces. 



As with any theoretical development of this kind, 

 the usefulness and limitations can only be fully 

 ascertained by comparison with a sufficient number 

 of experimental measurements. The comparisons 

 presented in this paper for the simple case of a 

 body of revolution adjacent to a propeller in uniform 

 flow represent an encouraging first check. This 

 experimental technique can be extended to examine, 

 in a systematic manner, the effects of nonuniform 

 flow (unsteady blade loading and cavitation) and 

 more general body shapes. For example, wire screens 

 selected to produce certain wake harmonics can be 

 towed upstream of the propeller. At the same time, 

 the need is evident to undertake calculations for 

 comparison with results of the many experiments 

 reported during the past several decades. 



rapidly, largely due to the thickness contribution. 



ACKNOV/LEDGMEIITS 



CONCLUDING RE.MARICS 



The analytical methods given in this paper can be 

 applied to a wide range of problems in which it is 

 desired to determine the unsteady pressures and 

 forces generated by a propeller on a nearby boundary. 

 The formulation is quite general, being applicable 

 to arbitrary hull (and appendage) geometries, and 

 propeller locations, geometry, and loading charac- 

 teristics. The assumption of high frequency 

 propeller excitation, which greatly simplifies the 

 treatment of the free surface, is not at all 

 restrictive in most cases of practical engineering 

 interest. A severe limitation, to be sure, is the 

 restriction to subcavitating propellers. However, 

 researchers are actively pursuing this subject and 



This work was jointly supported by the American 

 Bureau of Shipping (ABS) and the Maritime Adminis- 

 tration (MarAd) . The continued interest and 

 encouragement by ilr. S. Stiansen and Dr. H. H. Chen 

 (ABS) and Hr. R. Falls (MarAd) is greatly acknow- 

 ledged. Prior support of the Office of Naval 

 Research, Fluid Dynamics Division, enabled the 

 development of the velocity field program. The 

 authors are also indebted to Mr. D. Valentine and 

 Dr. S. Tsakonas of the Division Laboratory for their 

 painstaking effort in developing the programs and 

 to Messrs. K. Saulant and M. Jeffers (DTNSRDC) for 

 invaluable assistance in the design and conduct of 

 the experiments . 



REFERENCES 





0.0 0.25 0.50 0.75 1.0 



AXIAL POSITION OF PROPELLER, V( L/j) 



FIGURE 16. Modulus of lateral blade- frequency force 

 produced on an ellipsoid of revolution (L/B = 6.0) as 

 a function of propeller axial position (constant tip 



clearance, C/R 



0.25) -calculated for DTNSRDC pro- 



peller 4118 using method of Vorus (1974) . 



Breslin, J. P. (1962) . Review and Extension of 



Theory for Near-Field Propeller-Induced Vibratory 

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 Hydrodynamics, ACR-92, Office of Naval Research, 

 Washington, D. C. 



Breslin, J. P., and K. Eng (1965). A Method for 

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 2002. 



Cummins, W. E. (1957). The Force and Moment on a 

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Denny, S. B. (1967) . Comparisons of Experimentally 

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 Report 2349. 



Denny, S. B. (1968). Cavitation and Open-Water 

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Hess, J. L. , and A. M. O. Smith (1964). Calculation 

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