222 SCIENCE PROGRESS 



General Conclusions 



We shall see later that X„, etc., can be found and therefore 

 P s , P' s , P" 8 , for approximately ideal and at the same time prac- 

 tical cases, in terms of a — the angle of incidence of the air on 

 the planes — and the forward velocity U of the aeroplane. 



If for certain ranges of U and a the aeroplane is so con- 

 structed that there are no multiple roots of A(X) = o, and also 

 because the values of X will be of the type — a s ± i/3 s or 

 — n s ± ip s , there being resistances, the forced oscillations will 

 not in general become large, since the disturbing forces are in 

 general permanent, and the terms which stand for them will 

 have no real exponential. 



In a few cases we see that, the disturbing forces being 

 evanescent, there is danger of an indefinitely large increase of 

 the forced oscillations whether the roots are multiple or not. 

 Again, where for certain ranges of the velocity U and the angle 

 of incidence a there are multiple roots of A(X) = o, the free 

 vibrations once set up by an impulsive gust are magnified. 

 Such a machine would be unstable for those ranges of U and a. 



In the case of indefinitely increasing disturbed motion much 

 depends on the aviator's skill. The vibration increases inde- 

 finitely about some axis, and excessive pitching and canting will 

 occur. The moments of inertia, entering into the equations of 

 motion, will affect this oscillation. The aviator then elevates 

 or depresses, and turns his steering planes until stability is 

 restored. Instinctively he has caused the aeroplane to strike 

 the air so that the oscillation now takes place about a new axis 

 relative to the machine. The moments of inertia, etc., about 

 this axis not being the same as those about the old will alter 

 the equations of stability and give new values for \ in the free 

 vibrations. These values of X may not then be multiple, nor be 

 equal to the " m " of the disturbing force. The increasing dis- 

 turbances are thus damped by a skilled aviator who possesses 

 developed instinctive steering capabilities. 



The Resistance Derivatives 



The following is a brief summary of and reference to certain 

 chapters in Prof. Bryan's Stability in Aviation 1 : 



1 See pp. 38-56. 



