NO. 5 STABILITY OF AEROPLANES IIUNSAKER AND OTHERS 69 



In our case p=i°6, then for i=i2° and i/'=io°, i'=i2°3, while 

 for i = 6°, i' = 6°3. This is an increase of incidence with io° yaw of 

 but 2.5 per cent at low speed, and 5 per cent at intermediate speed. 



Since a side slip is equivalent to a yaw, and since the rolling moment 

 due to side slip is largely caused by greater lift on the wing which is 

 toward the wind, it appears reasonable to conclude that this greater 

 lift is a consequence of the greater angle of incidence. But we see 

 above, by a rough calculation, that the relative increase in incidence 

 on a dihedral wing for given angle of yaw is much greater for the 

 6° attitude than for the 12° attitude. The falling off of Lv observed 

 experimentally is, therefore, to be expected for an aeroplane with 

 raised wing tips. 



A discussion might be opened here as to whether it would not be 

 preferable to use vertical fin surfaces above the center of gravity or 

 a swept back wing (" retreat ") to obtain the desired righting moment 

 Lv on side slip, rather than the dihedral arrangement. Until further 

 experiments have been made, it is not profitable to speculate on this 

 question, but one would see no reason a priori to expect the coeffi- 

 cient Lr, given by vertical fins, to depend in any way upon the angle 

 of incidence of the normal flight attitude. 



To preserve stability, we must make A^- large also. This coeffi- 

 cient is a measure of the damping of angular velocity in yaw, and 

 can be made great by vertical surface forward and aft of the center 

 of gravity. A rectangular body with flat sides, vertical fin surface at 

 the tail (rudder), and the increased drift on the forward moving 

 wing all combine to resist or damp the spin in yaw. The designer can, 

 at his pleasure, increase both L,. and Nr by proper fin disposition. 

 Note that Nr is not different at different speeds. 



On the other hand, it is necessary to make Nv or the yaw due to 

 side slip small. A preponderance of fin surface aft will make Nv 

 large and is, therefore, dangerous. A machine that shows strong 

 " weather helm " or has great so-called directional stability is likely 

 to be unstable because the large Nv may make £, negative. The 

 vertical fin surface should be fairly well balanced fore and aft, and 

 directional restoring moments should not be great. Note that Nv 

 does not vary much with different speeds. 



The derivative Lr is characteristic of the rolling moment due to 

 velocity of yaw or spin and was shown to be caused by the greater 

 air speed on the outer wing in turning. It is not generally possible 

 for a designer to make Lr small, though a short span will help matters. 



