NO. 5 STABILITY OF AEROPLANES IIUNSAKER AND OTHERS 55 



Hence the rolling" moment on one plane is —2UKIr, and substitut- 

 .ing for K its expression above, 



" AU 



For two identical wings of rectangular form, we have for our com- 

 plete aeroplane a total rolling moment in pounds-feet per unit mass : 



L= - ^- -^" r, making Z^ = g, 



Lr— — ^,T for horizontal flight. 

 6(7 



It appears that L,- can be made small by short span and high speed. 

 The sign of L,- is such that the bank is proper for the turn. 



Numerically, we have, making the mean span 6' = 40.2 feet and 

 6 = 5.62 feet, 



Lr= - 8660/ U, 



— '^77-^> l^i?4h speed, i = o° , 



= +132.5, intermediate speed, i=6°, 



= + 160.0, slow speed, j= 12°. 



Note that /.,• (which is unfavorable to " spiral " stability) becomes 

 larger at low speed. 



§4. YAWING MOMENT DUE TO ROLLING, Np 



When an aeroplane rolls with an angular velocity p radians per 

 second (positive when right wing goes down), an elementary area of 

 the right wing has its angle of incidence increased and a correspond- 

 ing element of the left wing has its angle of incidence diminished by 

 the same amount. 



If p is small, the resultant air velocity at a point y feet from the 

 center line is 



VU^ + p^y"=U, neglecting p-. . 

 On the right wing, the angle of incidence at any point is increased by 

 a small angle a, given by ta.n u = py/U. Due to the greater angle of 

 incidence, the head resistance of the element is increased. 



On a curve of the "drift coefficient" for the wing shape (see 

 fig. 3, Part I) we may draw a tangent line at the point on the curve 

 corresponding to the angle of incidence for normal flight. For small 

 changes in incidence from normal incidence, we may substitute this 

 tangent line for the actual curve without material error. The value 



