Brard 



Let us consider again f , f ' , f j . We know that ^(O) < l. In the case of an 

 airfoil of infinite span, 0(0) = 1/2. If, here, we have also o <0(O) < l, </> is de- 

 creasing and probably f increases. Therefore agpp decreases when ojL/u in- 

 creases (Fig. 9b). If, on the contrary, 0(O) < 0, ^ is increasing, f decreasing 

 and a^pp is increasing (Fig. 9c). 



We note that functions f and fg are not necessarily monotonic. In its 

 present state, the theory yields only the general behaviour of these functions. 

 The real behaviour should be supplied by experiments. Nevertheless, on Fig. 

 9a, b, c, f and fg are assumed to be monotonic. 



Functions g are null when ojL/u = 0, and when coL/U- co; but 



(coL\ IcoL 



^ U J/ir 



may be monotonic. We may consider that probably the general behaviour of 



U//1 U 



is rather similar to that of f (ojL/U) . However, the possibility for one or sev- 

 eral functions g/(wL/U) to be increasing at first, and then decreasing, or vice- 

 versa cannot be excluded a priori. 



Lastly we will observe that, in certain terms, the variations of the appar- 

 ent coefficient may be damped because they are the sums of a constant term of 

 a great value and of a variable term. That is, for instance, the case for Msapp? 

 a' , b , X.2 but not for a . Moreover, some terms are probably small 



app' app ' ^app app ' m. ^ 



(i^35,b') and their variations are probably of a little importance. 



15.4. Calculation of 4>,^,(p' ,(p 



From the considerations above, it results that, when an "apparent" coeffi- 

 cient varies in a wide range, that is due mainly to a function f . Consequently, 

 it is necessary to take into account the variation of the functions (t>, >A, 0' or cp 

 related to this coefficient when writing and solving the equation of the free 

 quasi -rectilinear motion. 



In principle, such a function may be obtained by starting from the experi- 

 mental values of f or g. However, it is easily seen that the f-functions are 

 known with a better accuracy than the g -functions (except when the variation of 

 the coefficient are small, but, in this case, the knowledge of the 0-function in- 

 volved is of no practical interest). 



Finally, we consider that must be given by 



«''>^lf'(t 



-rr T d 



u / \ u 



894 



