40 



SMITHSONIAN MISCELLANEOUS COLLECTIONS 



VOL. 62 



of the pilot's losing control, yet it is clear that he cannot fly at this 

 speed unless he is alert. 



Taking Roiith's discriminant as a measure of dynamical stability 

 we have its value +117x10" at high speed and —0.12x10'' at low 

 speed. Compared with the high-speed value, the latter is insignificant 

 and we may conclude that the instability at low speeds is of relatively 

 slight danger. Indeed, we may say that the aeroplane is stable at high 

 speed and about neutral at low speed. 



The progressive change in Routh's discriminant with speed is more 

 clearly shown on figure 14. On the same plot, we give a similar curve 

 for a Curtiss type tractor. The " critical velocity " for the Clark type 

 is about 40 miles per hour and 47 miles per hour for the Curtiss type. 



All aeroplanes of normal type are probably longitudinally stable at 

 high speeds but lose this stability for all speeds below a certain critical 

 speed where Routh's discriminant becomes zero or changes sign. 



The examination of the longitudinal stabiHty of the Bleriot men- 

 tioned above applied only to high speed. The importance of investi- 

 gating stability at low speeds has, it is l)elieved, never before been 

 shown. 



The reason the stability of the longitudinal motion vanishes at a 

 critical velocity must be found in the approximate factor representing 

 the long oscillation. 



D, _ B,E{ 



D-' + 



Cr'\ 



D+^' =0. 



Stabihty vanishes where D^/C^=EJi^lC\. or where D^C^ — E^B^. In 

 other words, stability is reduced as EJi^ is made large or D^C^ small. 

 At high speed we have 266 X I492> 59.2x317, but at low speed 

 22.1 X I49.8< 54x85.1. It appears that B^ is smaller at low speeds, 

 which is desired, but Z), and C, are reduced to a greater degree, which 

 is not desired. 



The cause of the reduction in the magnitude of Z), from 266 to 

 22.1 can be shown in the elifect of change in resistance derivatives in : 



D,= 



M„, sin 6*0 

 Mk, cos 6,^ 



For^, 



jIIm, iliw, Mq 



o, Xq = Zq = Mu = o, we have 



D^=- XuZ^Mq + XuUMlo + Z,,Xr„AIq- 



The first term is reduced at low speed because Z,, is less than }, and 

 Mq 7^ of their values at high speed. Since [■ and M „: are smaller, the 



