JO SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62 



Note that Lr is greatest at low speed and high angle of incidence. It 

 should be unaffected by dihedral angle of wings. 



The instability corresponding to £0 negative is, therefore, a ten- 

 dency on side slip to the right, for example, to head to the right 

 toward the relative wind on account of much fin surface aft. At the 

 same time, due to the spin in yaw, the machine tends to overbank on 

 account of the greater lift on the left wing. The increased bank, 

 increases the side slip, the yaw becomes more rapid and in turn the 

 overbanking tendency is magnified. The aeroplane starts off on a 

 spiral dive and will spin with greater and greater angular velocity. 

 The term " spiral instabiUty " has been given to this motion. 



Spiral instability appears to be the most probable form of insta- 

 bility present in an ordinary aeroplane. It appears to be readily 

 corrected by modification of fin surface and there appears to be no 

 excuse for leaving it uncorrected. It is true that an alert pilot should 

 have no trouble in keeping an aeroplane out of a spiral dive, but in 

 case of breaking of a control wire disaster would be certain if the 

 machine were spirally unstable. 



§12. "ROLLING" 

 The second approximate factor 



when A^C^ is small compared with B^, is seen to reduce to : 

 or 



Now Yv, Lp, and Nr may be expected to be always negative in 

 ordinary machines, and the radii of gyration Ka and Kb are essen- 

 tially positive. Hence this root D will always be negative and the 

 motion a damped subsidence. It will be observed that Yv expresses 

 resistance to side slip, Lp damping of an angular velocity in roll due 

 to the wings, and Nr damping of an angular spin in yaw. In magni- 

 tude Lp is usually so great that Yv and Nr may be neglected, giving 

 roughly 



A/ 27 ^ 



at low speed, or a subsidence damped 50 per cent in ?=.o8 second. 



