Newman 



It is therefore important to determine the values of these parameters at 

 which frequency effects become important and the characteristic frequencies 

 which are significant in practical ship maneuvers. Here the assumption of calm 

 water is important since it is well known from the field of seakeeping that sig- 

 nificant frequency dependence exists in the practical range of ship speeds and 

 frequencies of wave encounter, corresponding to values of the parameter c^v/g 

 of order one-half to one. But it is also known that conventional ships are rela- 

 tively slow in their maneuvers, so that in this case frequency effects may be 

 relatively unimportant. 



In discussing this question we shall lump together both of the sources of 

 frequency effects, viz., viscosity and the free surface, and examine the experi- 

 mental and theoretical evidence available. This includes the oscillator tests at 

 various establishments, both with surface ships and submerged bodies, the the- 

 oretical predictions which exist for unsteady forces as functions of the frequency, 

 and full-scale data from ships' maneuvers which delineates the practical range 

 of frequencies which are involved. 



First we note that the two frequency parameters differ by the ratio of the 

 square of the Froude number, or 



g " V Ul 



so that for fast ships 



and for slow ships 



^.O.lf^ 



— ^ 0.03 ( — 



Thus a tentative conclusion is that the reduced frequency will be the controlling 

 factor, or that unsteady viscous effects will become significant before those as- 

 sociated with the free surface, especially for slower vessels. The experimental 

 results which have been obtained with oscillator techniques have been limited 

 primarily to one Froude number in each case, or at best to a narrow range of 

 Froude numbers; it would be of interest to vary the Froude number sufficiently 

 in a given experiment to determine whether the frequency effects which are in 

 fact noted therein will collapse with respect to one or the other of the two non- 

 dimensional frequency parameters, thus giving a direct measure of the relative 

 importance of the two physical mechanisms involved. To a limited extent this 

 comparison can be made from the data of van Leeuwen (1964) which includes 

 results for the Froude numbers 0.2 and 0,3, and from Motora and Fujino (1965) 

 which includes results for 0.1 and 0.2. The preliminary conclusion is that such 

 a collapse of the data takes place, if at all, only in the initial stages of frequency 

 dependence. This is consistent with the conclusions that initially the viscous 

 effects come into play rather than the free surface effects. 



224 



