Some Hydrodynamic Aspects of Ship Maneuverability 



external force and moment contributions to the left side of the equations arising 

 from their associated towing constraints, and in special cases, e.g., ships 

 equipped with a flume stabilizer system, significant internal changes of the mass 

 distribution will exist. 



COMMENTS 



M. Gertler 



David Taylor Model Basin 



Washington, B.C. 



Although I have not had time to study this paper in any great detail, I would 

 like to make a few comments with respect to the problem of "frequency effects." 



The author divides the frequency effects into two categories: those that 

 stem from vorticity shed from the oscillating hull and those that stem from the 

 unsteady motion of the hull at the free surface. The characteristic nondimen- 

 sional frequencies governing these two phenomena are given as L/V and - V/g, 

 respectively. By comparing the two frequency parameters, he concludes that 

 the unsteady viscous effects will become significant before the unsteady free- 

 surface effects, especially for slower ships. This interesting finding suggests 

 that if we examine the case of a deeply submerged submarine where frequency 

 effects, if any, can only be of viscous origin, then we can determine whether 

 such frequency effects are apt to be important in the surface ship case. 



Since 1958, the David Taylor Model Basin has carried out carefully con- 

 ducted planar-motion-mechanism tests on well over a hundred models of sub- 

 marines and other types of submerged bodies. In general, the experiments 

 were carried out over a range of .^jL/v values at least up to about 4, which is 

 well beyond the realm of practical interest for most submarine and submerged 

 body applications. Except for a few isolated cases involving forms which were 

 extremely poor from a hydrodynamic standpoint, the data from the oscillation 

 tests showed no significant evidence which could be interpreted as a variation of 

 the pertinent hydrodynamic force or moment coefficients with frequency within 

 the range mentioned. This was true of both the out-of-phase quantities (rotary 

 derivatives) and in-phase quantities (acceleration derivatives). Furthermore, 

 the coefficients derived from planar-motion-mechanism tests have been used in 

 conjunction with quasi steady-state equations of motion to make predictions of 

 the trajectories of submarines in various types of maneuvers such as spirals, 

 zigzags, and turns. These predictions, in a number of cases, have been com- 

 pared with the results of free-running model tests and full-scale trials and the 

 correlation has usually been excellent. Thus, we are firmly convinced that, in 

 the case of deeply submerged submarines, frequency effects can be neglected 

 both in predicting motions and in stability and control analyses. 



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