Some Hydrodynamic Aspects of Ship Maneuverability 



The maximum frequency at which these effects are unimportant can be in- 

 ferred quantitatively from the above referenced oscillator tests, as well as from 

 those of Paulling and Wood (1962), Brard (1964), and others. Such results are 

 outlined in Table 2. 



Table 2 

 Limiting Values of the Frequency Parameters Below 

 Which Frequency Effects are of Secondary Importance 



While the results of Table 2 are not entirely consistent with each other, it 

 is clear that the general order of magnitude of the limiting reduced frequency is 

 in the range between one and four, and for conventional Froude numbers the 

 corresponding limiting values of the frequency parameter wV/g are in the range 

 between 0.1 and 0.2. Moreover there is some evidence to suggest that the fre- 

 quency effects play a more important role in the out-of-phase (i.e., damping) 

 components of the force and moment than in the corresponding in-phase or 

 added-mass components. This is to be expected since in an ideal unbounded 

 fluid the force is entirely in phase with the acceleration. 



It remains to estimate the range of frequencies which are encountered in 

 practical ship maneuvers. This is somewhat less certain since in general ship 

 maneuvers are transient rather than sinusoidal processes and will include har- 

 monic content at all frequencies. If we arbitrarily select a 20° -20° zig-zag test 

 as a "typical" ship maneuver, then the reduced frequency follows directly in 

 terms of the period of time required for the maneuver, or simply 



225 



