322 



not been considered? These methods have been used 

 in Europe for several years and the agreement with 

 experiments is usually good. 



I agree that it is important that the integra- 

 tion of hull forces and moments is carried out over 

 a not too small part of the hull surface. This is 

 even more important when the forces from a cavita- 

 ting propeller are considered, as those pressures 

 have a slower decay than those induced by a non- 

 cavitating propeller [Lindgren and Johnsson (1977) ] . 



Assuming that the hull forces should be used 

 for an estimation of the vibration level for a 

 certain ship project, I think that the problem is 

 far more complicated than just a matter of integra- 

 tion area. First, the described method is a near 

 field theory where the influence of the propagation 

 velocity of the pressure wave has been neglected. 

 When calculating forces far from the propeller this 

 could cause some difficulties. Secondly, the ship 

 hull is not a rigid body. The vibration response 

 will therefore be dependent not only on the hull 

 forces but also on their location relative to the 

 nodes of the vibration mode. Forces located close 

 to the nodes will contribute very little and those 

 located on different sides of a node will more or 

 less cancel each other. Calculations with the Fi- 

 nite Element Method have shown that hull forces aft 

 of the aftermost node are particularly efficient 

 in exciting high vibration levels. This could be 

 the explanation for rather good results often being 

 achieved in vibration calculations in spite of the 

 fact that the excitation forces have been obtained 

 by integration over a rather small area. 



The correct treatment of the problem will, of 

 course, include vibration calculations, with a very 

 detailed Finite Element model with the complete ex- 



citation forces and moments. Since this is very 

 complicated and expensive it is seldom done. In- 

 stead, different approximate procedures have been 

 developed by different institutions. Referring to 

 the integration problems the authors claim that 

 "the current practice in European model basins is 

 highly suspect." I very much doubt that this is 

 current practice. At SSPA for example, we use the 

 pressure fluctuations in a reference point above 

 the propeller as a basis for estimation of the risk 

 of vibration. On the basis of full-scale measure- 

 ments we have established an approximate relation 

 between excitation at this point and the vibrations 

 at another reference point [ (Lindgren and Johnsson 

 (1977)]. 



REFERENCES 



Huse, E.,(1972). Pressure Fluctuation on the Hull 

 Induced by Cavitating Propellers. Norwegian Ship 

 Model Experiment Tank Pubt. No. III. 

 Johnsson, C. A., and T. SjzSndvedt, (1972). Propel- 

 ler Excitation and Response of 230,000 TDW Tankers. 

 SSPA Publ. No. 70. 



Oossanen, P. van, (1974). Calculation of Perform- 

 ance and Cavitation Characteristics of Propellers 

 Including Effects of Non-Uniform Flow and Viscosity. 

 NSm Publ. No. 457. 



Lindgren, H. , and C. A. Johnsson, (1977). On the 

 Influence of Cavitation on Propeller Excited Vibra- 

 tory Forces and Some Means of Reducing its Effect. 

 PRADS- International Symp. Tokyo. 



