Brard 



Equations (2) to (7) show that the "apparent" coefficients are constant if, 

 and only if, the effects of the wake are negligible. When this is not the case, 

 they depend upon the "reduced frequency." 



According to the quasi-steady theory, the harmonic forced motions should 

 yield the coefficients which are found in the (?-)-set of forces. In fact, they 

 may yield the effects of the wake and allow to check whether these effects shall 

 be taken into account for practical purposes. 



15.3. The Behaviour of the "Apparent Coefficients" 



Let us consider again the functions f, f, fj, fjg, g, g', gj, gg. 



We have admitted (par. 5) that an unique set of functions 4>,^,4>' is sufficient 

 in order to define the wake due to the body. We admit, here, for the same rea- 

 son, that the functions 4>^^, 4>^^ (and cp^^) are identical. 



Such an assumption is presently not essential, since, in principle, the in- 

 terest of tests on a body in harmonic forced motions is to supply these func- 

 tions. But, the discussion which follows will be easier. 



Firstly, we may observe that, for instance: 



f(0) = [ ^(T')dr' = 0(co) - 0(0) = -0(0) . 



Consequently, any "apparent" coefficient involved in an "out phase" force 

 or moment has, when wL/U -> 0, a limit equal to its "true" value. For instance 

 [see (2)]: 



wL/U -» 



and so on. On the contrary: 





ojL 



Therefore, when wL/U is small, if we neglect the wake effects, we have a 

 small error about the apparent coefficients involved in the out phase force and 

 moment; on the contrary, the error may be great if we deal with those involved 

 in the in-phase force and moment. When wL/U is great, the errors concerning 

 this second family of coefficients are small (provided the reduced frequency is 

 not high enough to change the nature of the flow around the body). 



Because <l^ is increasing from zero to 1, 4> is decreasing from a positive 

 value to zero, and 



892 



