NO. 5 STABILITY OF AEROPLANES— IIUXSAKEK AND OTHERS 73 



In a similar manner, the rolling moment, due to side slip, or restor- 

 ing moment, such as is given by high fins or raised wing tips, should 

 be large to avoid " spiral " instability. In the present case, however, 

 we wish to make Lv small. 



Likewise the natural banking due to spin in yaw we wish small 

 for " spiral '' stability, but we now wish to have this coefficient large. 

 The conflicting nature of the requirements for stability is here 

 shown by the use of rather drastic simplifications in the more exact 

 formulze. For the analysis of stability the exact formulae are easily 

 applied, and the present approximate forms are deduced only in order 

 to trace the efifect on the motion of such changes as the designer may 

 be tempted to make on a machine. 



It is believed that an excessive dihedral angle upwards is not a 

 cure-all for stability problems. Indeed, in practice, aeroplanes with 

 a large dihedral angle for the wings have been found so violent in 

 their motion under certain circumstances that the average pilot has a 

 firm prejudice against the use of such a wing arrangement. That 

 this prejudice has some physical basis has been shown here. A 

 dihedral angle machine is not likely to run into a " spiral dive,'' but 

 it is very likely to be unstable on what we may term a " Dutch roll," 

 from analogy to a well-known figure of fancy skating. 



We may imagine an aeroplane to yaw to the right accidentally. 

 Due to Lr and Lv the aeroplane banks in a manner proper for the 

 turn, but the roll is retarded by the large damping due to Ly. The 

 turn is assisted by the increased drift on the lower wing due to A';,, 

 and were it not for the much discussed " weather helm " given by Nv, 

 the aeroplane would run off on a right turn. However, Nv tends to 

 turn the aeroplane back to her course. If Nv be sufficient, the machine 

 will swing back to her course and the bank will flatten out. But since 

 the moment of inertia in yaw is considerable, the machine will swing 

 past her course and start on a turn to the left. This swinging to right 

 and left of her course is accompanied by rolling outward and some 

 side slipping. 



The analogy to a " Dutch roll " on skates is obvious. If the skater 

 lean too far out he may fall, and if the aeroplane roll too far on the 

 side swings it may happen that the motion will become unstable. If 

 the air be gusty it is very likely that such an aeroplane may be caught 

 on the roll by a side gust and capsized. 



The " Dutch roll " in ordinary aeroplanes (which are " spirally '' 

 unstable) is not likely to be present, since there is no dihedral and a 

 large rudder. The average pilot would much prefer to deal with a 



