^2 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62 



that of the longitudinal motion and unless strongly damped, the 



motion may become so violent as to be uncomfortable. Note that 



since A^;, Lv, Np, Lp, N,-, Lr are involved, the motion must consist of 



a combination of side slipping, rolling, and yawing. 



The motion is stable and the oscillation tends to damp out in time 



C E . 

 and the aeroplane to return to her course if ^ — jy^ is positive. To 



damp to half amplitude requires t= ., p x seconds. 

 Substituting approximate expressions we have 



B, D, Kc'Kl, l; 



Since L,- is positive, in order for the damping" to be real, —Nv/Ev 

 must be greater than Np/Lp and positive. 



Stability of this motion is, therefore, assisted by : 



1. Large negative yawing moment due to side slip (" weather 

 cock " stability) A\-. This is incompatible with stability against a 

 " spiral dive." 



2. Large damping of the rolling due to rolling Lp. 



3. Small positive rolling moment due to side slip Lv. This is also 

 incompatible with stability against the " spiral dive." 



4. Small yawing moment due to rolling A',^. 



5. Large rolling moment due to yawing velocity L,-; another re- 

 quirement incompatible with " spiral " stability. 



6. Small radius of gyration Kc in yaw. 



It does not appear practicable to make A'^ small on account of the 

 steepness of the drift curve at high angles of incidence. The drift of 

 the downward moving wing when the aeroplane rolls is increased 

 while the drift of the rising wing is decreased. The resultant yaw- 

 ing moment tends to swing the aeroplane away from her course. Note 

 that at slow speed, near stalling angles, A'^, becomes large. This is not 

 desirable, but is unavoidable. 



The rolling is heavily damped by the wings and Lp will always be 

 large and negative. This assists stability. 



To avoid " spiral " instability, we saw above that it was necessary 

 to make the weather cock or " directional stability " small. That is, 

 A,; was to be small and the preponderance of vertical fin surface aft 

 slight. In the motion now under discussion, we wish to make Nv 

 large. The two conditions imposed are unfortunately conflicting. 

 We must compromise and make A^ numerically not too great, but 

 still essentially negative. 



