NO. 5 STABILITY OF AEROPLANES HUNSAKER AND OTHERS 59 



INCIDENCE OF WINGS 12° 



V 35 30 24 18 o 



t 6.5 8 II 14.5 175 



A 027 .022 .016 .0121 .001 



Ao 001 .001 .001 .001 .001 



Atu 001 .001 .001 .001 o 



A„, 025 .020 .014 .010 o 



The values of \w due to wind on apparatus are taken from the curve 

 of Xio on figure i6 and apphed in the calculation to find A,„ net. Figure 

 16 shows the values of Am. It is obvious that the values of Am for i = o'' 

 at 35 miles per hour is grossly in error. This point is, therefore, 

 rejected. 



The curves of A,,, appear to increase more rapidly than the velocity : 

 in fact, a plot on logarithmic paper shows that over the range of wind 

 tunnel speeds Am varies approximately as l'^-^-'. 



Since this damping- helps to stop violent rolling, we shall be on the 

 safe side in our stability calculation if we assume that the damping 

 varies directly as the velocity. 



To convert Am to full scale, we have 



J _ -26* V . 



J-'P — • 1 >" * Am- 



m V„, 

 Where Tm is the speed at which Am was measured. Taking the scale 

 factor 26, m=SO slugs, Fm = 30 miles, ^ = 76.9 miles for 1 = 0°, and 

 J/ = 36.9 miles for /= 12°, we have 



Lp= —631 = 5.61 1/, for high speed, 

 Lp= —224 = 4. 1 5 [7, for low speed, 

 and for the intermediate speed, by interpolation, 

 /^.= -319 = 4.88^7. 



§6. DAMPING OF YAW, Nr 



The damping of an oscillation in yaw is probably due to the long- 

 body and vertical surfaces at the tail, as well as to the wings. It is 

 not practicable to compute this, and we have employed the same 

 apparatus as before to determine the damping in yaw by the method 

 of oscillations. The model set for the oscillation in yaw is shown on 

 figure 18 (pi. 3). 



The equation of motion is similar to that for roll and pitch, thus : 



and 



^ t^ +(''0 + ''.. + ''»,) jfl- +iK-cm')^ + Mo-Ms = o, 



il^ = ^,e 2I, or-^. =log, 7 =log, 9. 



