42 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62 



For very low speeds, the quantity A%o is often found to change sign ; 

 therefore, the two terms on the left may be of opposite sign and a 

 large value for Mq diminishes D^C-,^ and increases B-^E-^^. In a " stall- 

 ing " attitude the aeroplane should have Mq small, Mw large, and, if 

 possible, the radius of gyration in pitch Kb small. 



The attitude of a " stalled " aeroplane is not ordinarily considered 

 a "normal" attitude of flight, but, unfortunately, an aeroplane is 

 frequently " stalled " by an inexperienced pilot. The longitudinal 

 motion of an aeroplane if held in a " stall " would be, in general, 

 unstable, but vmder favorable circumstances with Zq, Z^, Kb small 

 and Mw large it is possible to have a stable motion. For example, 

 in an extreme case with Zw zero, if the aeroplane head up higher due 

 to large .Y,^ it slows down, loses lift and sinks. In sinking, M^, if 

 large, will head the machine down, speed \vill be gained on the dive 

 and the resultant gain in lift causes the aeroplane to rise again. The 

 oscillation will not increase in amplitude with time if the machine is 

 able to respond quickly to the righting moment Adw. The damping 

 Mq and radius of gyration Kb must not be too large. If Mq and 

 Kb are too large, the machine is dynamically unstable by having 



The question of safe flight at a stalling attitude is complicated by 

 the fact that the lateral controls become ineffective, but by manipula- 

 tion of the power delivered by the motor, combined with skilful use 

 of the rudder, an expert can land an aeroplane at surprisingly low 

 speed. 



The period is given by the imaginary part of the roots, or 



-,_ 27r 



I J 4^1.. / D,C,-B,E, y' 

 5 — ^ ^ ^ — 1 1 is usually small, we may write approximately, 



P 



= 27ry 



E. 



then 



\ -gZyAU, U 



'^y^H^-w- 



At low speed, U as well as Z^ and Mq are reduced and the period 

 becomes short. A stiflf machine with large Mw would have a rapid 

 period. For given speed, if we make Mq large in order to provide 

 heavy damping, care must be taken that Mw shall be small in order to 



