64 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62 



air, follow its trajectory without the aid of the pilot. In gusty air, it 

 would roll and pitch and yaw as well as side shp and rise and sink, 

 but, if the altitude be great, there should be no danger. The machine 

 would not follow a fixed course, if controls were abandoned, but 

 would adjust its trajectory constantly to the changing conditions of 

 the air in an efifort to maintain the same relative velocity through the 

 air and the same angle of incidence. 



On the other hand, if the lateral motion be unstable and the angle 

 of yaw become as great as io°, the curves of figure i6 show that the 

 head resistance X is not greatly changed for slow-speed attitudes and 

 increases but lO per cent at high speed. This should tend to slow 

 down the aeroplane very little. 



The change in Z, or lift, is insignificant. 



However, the change in M is most interesting. For i=i2° no 

 change in M is produced by yaw, but for j = 6° a small diving moment 

 is induced. For an angle of yaw of 15° or more, this diving moment 

 is enormously increased. For i = 6° , 1/^=15°, Wilf = 37x50=1,850 

 pounds-feet, corresponding to a force on the elevator of nearly 100 

 pounds. 



If the pilot attempt to turn without banking he may side slip so 

 rapidly that he has the relative wind making an angle of 15° to the 

 longitudinal axis of the aeroplane. The aeroplane will then tend to 

 dive sharply. Similarly, an excessive bank may induce a side slip 

 inwards and the same tendency to nose dive. The cause of this 

 tendency to nose dive showm here is not understood, but it is signifi- 

 cant that many accidents have occurred to inexperienced pilots in 

 turning. 



§9. LATERAL STABILITY, DYNAMICAL 



The combined asymmetrical motion in roll, yaw, and side slip will 

 be called " lateral." For simplicity we will consider horizontal flight 

 in a straight line in still air, and for this condition investigate the 

 character of the disturbed motion. 



From the detail plans, the radii of gyration Ka and Kc have been 

 calculated. It is assumed that these values are not appreciably 

 changed by change of axes corresponding to the changed attitudes 

 proper for different speeds. Ka and Kc as given are referred to the 

 axes used at high speed. The products of inertia are neglected as 

 unimportant. 



From Part I, §9, we obtain the following simplified formute for 

 the coeflficients of the biquadratic equation which is characteristic of 



