323 



Authors' Reply 



BRUCE D. COX, WILLIAM S. VORUS , JOHN P. BRESLIN, 

 and EDWIN P. ROOD 



Our thanks to the discussers for their interest 

 and encouraging remarks. On Mr. Rutgersson's 

 question of calculating solid boundary factors, we 

 do believe it would be useful to perform computa- 

 tions for a series of hull afterbody forms and pro- 

 pellers. The results would illustrate sensitivity 

 to the various physical parameters and could pro- 

 vide guidance during the early stages of a ship 

 design. However, for realistic predictions of pro- 

 peller exciting forces, the complete calculation 

 should be carried out using the actual wake , hull 

 geometry, and propeller design under consideration. 



As noted in the paper and by Mr. Rutgersson, 

 only the non-cavitating propeller case is consid- 

 ered which is a severe limitation in many pratical 

 applications. The principal purpose of the paper 

 was to present analytical methods and simple form- 

 ilae for predicting hull surface forces for a given 

 representation of the propeller and show compar- 

 isons with experiments . Future improvements in the 

 propeller theory, in particular, the allowance for 

 transient cavitation, can be incorporated quite 

 readily into the surface force analysis. It can 

 be shown [Breslin (1977)] that the time rate of 

 change of the cavity volume plays a crucial role 

 in generating the propeller pressure field. We 

 are familiar with a number of proposed methods for 

 predicting blade cavity geometry including those 

 cited by Mr. Rutgersson. These approaches for the 

 most part are empirical. An alternative procedure, 

 described in Mr. Huse's discussion, consists of 

 finding an "equivalent" singularity distribution 

 so as to produce agreement between calculated and 

 measured values of pressure at selected locations 

 near the propeller. The problem of analytically 



predicting the proper singularity distribution to 

 represent the cavity volume dynamics is now the 

 subject of active research. 



We agree with Mr. Rutgersson that compress- 

 ibility effects should be examined when considering 

 the far field pressures generated by a propeller. 

 A 5-bladed propeller operating at 100 rpm produces 

 a blade rate frequency disturbance with a acoustic 

 wavelength on the order of 600 feet. The relative 

 phase of the distrubances generated far ahead of 

 the propeller may be important in the integrated 

 pressure force amplitude and phase. 



The theory presented in this paper assumes a 

 rigid hull boundary, intended to provide a first 

 estimate of propeller exciting forces acting on 

 the hull girder. Certainly for detailed stress and 

 vibration analyses , the interplay between fluid 

 loading and hull structural deformation would have 

 to be accounted for. In principle, the present 

 theory can be extended to satisfy the bo\indary 

 condition on a deformable body. The complete 

 analysis would then involve coupled equations des- 

 cribing the fluid loading and structural response, 

 and could be solved by finite methods. 



REFERENCE 



Breslin, J. P., (1977). A Theory for the Vibra- 

 tory Forces on a Flat Plate Arising from Inter- 

 mi ttant Propeller Blade Cavitation. Symposium on 

 Hydrodynamias of Ship and Offshore Propulsion 

 Systems J Oslo, Norway 



