NO. 5 STABILITY OF AEROPLANES HUNSAKER AND OTHERS 53 



The fraction ^^is the slope of the curve of N plotted on angle of yaw 



xp as absciss?e. 



Similarly : _ _ 57.3 aL 



and 



V -- ^7-3 . ^> 



Taking- the slopes of the curves of L, N, Y at t/' = o from figure 15, 

 we obtain the following " resistance derivatives " needed in the 

 lateral equations of motion. 

 High speed : 



f Yv=-.204, 



i=o°J Lv=+3.o6, 



[A^,= -.449. 



Intermediate speed : 



fYv=-.oS78, 



i=6°J Lv=+3.44, 

 [a^=--35I- 

 Slow speed : 



i=i2°J Lv= +1.91, 

 [Nv=-.53- 



Note that these derivatives do not change greatly with speed. In 

 the longitudinal motion the effect of change of speed (attitude) was 

 more marked. 



§3. ROLLING MOMENT DUE TO YAWING, Lr 



It is obvious that if an aeroplane yaws quickly, the outer wing tip 

 moves through the air more rapidly than the inner wing tip and, 

 hence, due to the spin, the lift on the outer wing is the greater. The 

 resultant rolling moment tends to bank the aeroplane suitably for the 

 turn. The magnitude of this rolling moment was in dispute in the 

 recent Curtiss- Wright patent litigation. The following calculation 

 leads to a simple formula to determine the roll due to angular velocity 

 in yaw. 



In our notation, a rolling moment L is expressed in pounds-feet 

 per unit mass. In pounds-feet on the aeroplane, the moment is niL. 

 where m is the mass IV/g in slugs. 



