54 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62 



The derivative Lr is the rate of change of rolhng moment with an 

 angular velocity in yaw of r radians per second, or 



dL _j 

 or 



Let [/ = the velocity of advance of the center of gravity of the aero- 

 plane in feet per second. U is a negative number. 

 5" = span of the aeroplane (one plane) in feet. 

 & = chord of one plane in feet. 

 lV/g = m = mass of aeroplane in slugs. 



r= angular velocity of yaw in radians per second, positive for a 



right-hand turn. 



Consider an element of wing area on the left wing of width dy in 



the y axis and depth b in x axis. The distance from the center of 



gravity of the aeroplane to the center of this element is 3; feet, positive 



for the left wing. 



The velocity through the air of this element is U — yr, since the 

 increase of air speed due to spin is yr. 



If we assume that the lift of the wings is equal to the weight of the 



aeroplane, we neglect the small vertical forces on body and tail only. 



The lift in pounds per square foot per foot-second velocity is the 



usual " lift coefficient " for the wing, which can be computed from 



the model tests for Z. Thus : 



Where : 



.^ = 265, the total area of both wings. 



Then the lift in pounds on the elementary strip of wing of area 



bdy is 



Kbdy{U — yr)-. 



The rolling moment on the aeroplane of this elementary lift force is 



Kbydy (U^ — 2 Uyr -f- y'r- ) , 



and the total rolling moment on one whole plane is, 



f+l 

 Kb (U~ — 2Uyr + y-r-)ydy. 



But I by-dy = I, the moment of inertia of the area of one plane, 



and 



V U'-ydy-O- V y^dy. 



