52 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62 



that the aileron control shall be very powerful compared with the 

 natural banking tendency. Excessively stable aeroplanes may be 

 really dangerous to land in gusty air. In any aeroplane design, the 

 relative magnitudes of the natural rolling moment and the aileron 

 control available should be carefully considered. 



If the aeroplane side slip with a lateral velocity v, the resultant 

 velocity of the center of gravity of the aeroplane is obtained by com- 

 bining z; as a vector with the forward speed U. The apparent wind 

 in still air is then inclined to the axis of the aeroplane as it would be 

 w^ere the aeroplane yawed from her course by an angle 



A side slip to the left is equivalent aerodynamically to a positive or 

 right-hand yaw. The sign of the lateral force Y is negative for a 

 plus yaw and hence resists the side slip, as is desired. 



The asymmetrical motion is a combination of rolling, yawing, and 

 side slipping as is indicated by the qualitative discussion given above 

 and by the equations of motion in Part I, §9. In order that, under 

 the influence of A^, L, and Y, acting in concert, the disturbed motion 

 shall be stable, the aeroplane must tend to return in time to its original 

 attitude. It is impossible to determine whether the aeroplane is thus 

 stable from a consideration of A'^, L, and 1' separately. -The term 

 " directional stability," frequently used, means very little with regard 

 to the probable motion of the aeroplane. 



The quantitative determination of the stability of the motion can be 

 made only after we have found the numerical values of the coeffi- 

 cients needed in the equations of motion in Part I, §9. 



§2. RESISTANCE DERIVATIVES 



The rates of change of N, L, and Y with velocity of side slip v are 

 the partial derivatives Nv, Lv, Yv The side slip velocity v is equiva- 

 lent to an angle of yaw ij/ given by : 



tan i/' = jT . 



i U 



If (// is small and measured in degrees, the tangent is equal approxi- 

 mately to the circular measure of the angle, or 



and 



M - ^N -_ 57-3 ^K 

 ^ dv C Aip ' 



