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ENGINEERING: J. C. HUNSAKER 
expression representing the motion shows that the aeroplane starts off on 
a spiral dive. 
A simple relation may be obtained involving four of the aerodynamical 
coefficients which, if positive, insures that spiral instability of this kind 
is not present. It appears that spiral instability is caused by too much 
fin surface to the rear or to too large a rudder, and by not enough fin sur- 
face above the center of gravity. A proper adjustment is easily obtained 
without sacrifice of desirable flying properties. Aeroplane S has a small 
rudder and wing- tips raised about 1?6; aeroplane U has no rise to wing- 
tips nor vertical surface above the center of gravity and has a very deep 
body giving the effect of a rear vertical fin. These differences in design 
account for the respective stability and instabiHty of the two machines. 
Rolling. — The second factor in the equation of motion represents a 
rolling of the aeroplane which is so heavily damped by the wide spread- 
ing wings as to be ordinarily of no consequence. In the extreme case of 
a 'stalled' aeroplane, the damping of the roll vanishes because the down- 
ward moving wing has no more lift than the other. Here we may ex- 
pect trouble, and frequent accidents to stalled aeroplanes indicate that 
the pilot's lateral control by ailerons also becomes operative. 
Dutch Roll. — The third element in the motion is a yawing to right and 
left, combined with rolling. The motion is oscillatory of period from 5 
to 12 seconds, which may or may not be damped. The analogy to the 
'Dutch Roir or 'Outer Edge' in ice-skating is obvious. If the skater 
lean too far out on his swings he may fall, and in the same manner if the 
aeroplane bank too much a slight puff of wind may capsize it. 
The motion of the Dutch Roll is stable provided there be sufficient 
vertical fin surface on the tail and not too much fin surface above the 
center of gravity. These requirements conffict with those previously 
stated for spiral stability and a compromise must be made. Over-cor- 
rection of spiral instability may produce instabiHty in the Dutch Roll 
and vice versa. Fortunately, the damping of rolling by the wings is 
helpful in both cases, and it appears possible to obtain that nice adjust- 
ment of surfaces which will render both motions stable. 
Model S was stable in the Dutch Roll at all speeds, having a period 
from 6 to 12 seconds, and the initial amplitude damped 50 per cent in 
from 1.5 to 6 seconds. Model U was stable in this respect except at low 
speed when it showed a period of 6 seconds and the initial amplitude was 
doubled in 8 seconds. 
The following table summarizes the results obtained for the lateral 
motion. 
