NO. 5 STABILITY OF AEROPLANES HUNSAKER AND OTHERS Jl 



The more exact calculation made in §ii showed t=.0'/6 second. 

 In a machine of very short span and great moment of inertia in roll, 



we might expect ^'^-^ to become small, but never positive so long as 



forward speed is maintained. 



When an aeroplane is at such an attitude that further increase in 

 angle of incidence produces no more lift (" stalled "), the damping of 

 a roll by the wings Lp may vanish. Then the downward moving wing, 

 although its angle of incidence be increased, has no additional lift 

 over the other and, hence, there is no resistance to rolling. In this 

 critical attitude, pilots have reported that the lateral control by 

 ailerons has no effect and the aeroplane is unmanageable. 



In any reasonable attitude short of stalling, there appears to be no 

 reason to fear instability in " rolling " corresponding to this second 

 factor of the equation. 



§13. THE " DUTCH ROLL " 

 In the approximate solution of the biquadratic, the third factor, 



for most machines will have A^C^ small compared with B^^, and we 

 may write : 



Considering the usual magnitudes of the derivatives entering in 

 Bo, Co, Do, E2, we may write very approximately : 

 ^2= —Kc'Lp, 



C^=(NrLp-LrNp), 



E, = g(NrLr-L,Nr). 



C E • 

 The motion is damped and stable, provided ' — ,v^ is positive, and 



the period 



27r 



W 



4^0 _ /C2 _ ^. 

 ^ \Bo_ D, 



or approximately = /' = 27r ^ ^- . 



Since ^ "^^ jg ordinarily of the order of i or 2 the period may be 

 of the order of 6 or 12 seconds. This period is rapid compared with 



