NO. 5 STABILITY OF AEROPLANES HUNSAKER AND OTHERS 5/ 



from a curve corrected to apply to full-speed full-scale, aspect ratio 7, 

 and biplane of gap 1. 1 times chord. 



Note that the positive sign of Np indicates that for a positive roll 

 (to the right) a yaw to the right is assisted. At high speed the aero- 

 plane flies at a small angle of incidence where the drift curve plotted 

 on incidence is about horizontal. Np is, therefore, zero at this attitude. 



§5. DAMPING OF ROLL, Lp 



The wide spreading wings very effectively damp the rolling, and 

 the resisting or damping moment in pounds-feet on the aeroplane is 

 nipLp for an angular velocity p radians per second in roll. 



The method of oscillations previously used to determine the damp- 

 ing of the pitching Mq is applied to determine Lp. Figure 17 (pi. 2) 

 shows the oscillating apparatus set up to impress an oscillation in 

 roll about the center of gravity of the model. 



Using a similar notation, the equation of motion of the complete 

 apparatus with model is 



/^'^f +(Ao + A^-fA„0 '^"^ +{K-Cm')<p + M,-A4s = o. 



Where Aq represents damping due to friction, k^) due to wind on 

 apparatus, and A„, due to wind on model. The moment of inertia of 

 the entire oscillating mass / is found by a simple experiment. 

 The solution for points of maximum amplitude is of the form 



_xt 



or 



f = iog.*;=iog.9. 



since the ratio *^- is arranged to be as 9 to i on the scale for the pencil 



of light. 



The numerical work follows : 



Oscillation in Roll 



/ model and apparatus = .0399, ^ =9 



9 

 I apparatus =-0373 



Test on Bare Apparatus 



V, wind velocity, miles 30 20 O 



t, seconds 78 98 197 



A 0021 .00168 .00083 



Aw (less zero) 0013 .00085 o 



