NO. 5 STABILITY OF AEROPLANES HUNSAKER AND OTHERS 67 



This is a pair of imaginary roots indicating an oscillation of natural 

 period p= =5-9 seconds, which is damped to half the initial 



amplitude in t= -^ =14 second. The motion is so heavily damped 



as to be of no consequence. The period is fairly rapid, and if the 

 damping were not great, the oscillation might become uncomfortable. 

 For the high-speed case, it appears that the lateral motion is quite 

 stable. 



Intermediate Speed. 



At the intermediate speed, where j = 6°, we have for the first factor : 



D=-.2S2, 



a subsidence which damps to half amplitude in 



t= ' ^ =2.72 seconds. 

 •254 

 This motion is very strongly damped, even more than at the high 



speed. 



Similarly, the second factor gives an enormously damped sub- 

 sidence. 



D=-12.l, 



/= ■ " =.oS7 second. 

 12. 1 ^^ 



The oscillation corresponding to the third factor is of fairly slow 



period, but so strongly damped that it is of slight importance. Thus : 



, D^ + .iiD + . 346 = 0, 



D=-:5S±.5S6i, 



p= —^^ =10.7 seconds' period, 



t= °^ =1.25 second to damp 50 per cent. 



Slow Speed. 



For the slow-speed condition, 1=12°, we observed that the coeffi- 

 cient Eo is negative indicating instability of motion. Mathematically, 

 that is to say, the real root corresponding to the first factor of Bair- 

 stow's approximate method, 



D=- ^jy = .096, 



is now no longer a subsidence, but a divergence which doubles itself 



in f= °^^ =7.2 seconds. This is not an alarming rate of increase, 



.096 

 since 7 seconds should be ample time for a pilot to observe a devia- 



