74 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62 



machine which tended to swing down into a " spiral dive "if left to 

 itself because there is no oscillation of rapid period involved. 



The production of a laterally stable aeroplane is attendant with 

 many compromises, and it cannot be too strongly insisted upon that a 

 freak type designed to be " very stable " is likely to be rapid and 

 violent in its motion, and even if stable against a " spiral dive " to be 

 frankly unstable against the " Dutch roll." 



One may inquire whether a machine made directionally neutral can 

 be made stable. In the notation here used Nv would be approximately 

 zero. The condition that " spiral " instability be not present is: 



Lv/Nv>Lr/Nr. 



But for Nv zero, we need only make Lv slightly positive to insure 

 stability in this motion. Lv may be made positive by a very slight 

 preponderance of fin surface above the center of gravity, raised wing 

 tips, etc. 



However, in the approximate criterion for stabiHty in the " Dutch 

 roll," we have 



-N^^/Lv>Np/Lp, 

 and for A^• zero, the motion is clearly unstable unless the magnitude 

 of the neglected terms is greater than Np/Lp, which is unlikely. 



Replacing neglected terms in C„, we obtain as a more nearly exact 

 expression : 



(C, _ £A _ L, /N, _NA_y_Kl N, .. 



[b, dJ-KcALp lJ ^ KIL, ■ 



If we make A^„ very small as in the case under analysis, the last 



term vanishes as well as the second, and we have as a condition for 



C E 



r,"" -^ positive : 





Substituting numerical values for the derivatives, for the slow-speed 

 condition, we find 



and 



L^Np__ 160x57 ^ _ Q.6 

 Kc^Lp 48.6x224 . ^^ • 



The slow-speed motion would, therefore, be very unstable if Nv were 

 zero. Consideration of the magnitude of the derivatives leads us to 

 the conclusion that in any aeroplane, if A''^ be made very small, the 



