280 
ENGINEERING: J, C. HUNSAKER 
the aeroplane is never unstable and to make the oscillation dynamically 
stable by the use of generous damping surfaces and large wings. 
The investigation is most conveniently discussed in two parts, the 
first dealing with the longitudinal' motion involving pitching of the 
aeroplane and rising and sinking of its center of gravity combined with 
change of forward speed, and the second with the 'lateral' motion, which 
involves side-slipping, or skidding, combined with rolling and yawing to 
the right and left. 
Longitudinal motion. — From the dynamical equations of motion for 
the full scale aeroplane written down with the aerodynamical coefficients 
determined by tests on the models, the small oscillations about the equi- 
librium position are determined by three simultaneous linear differential 
equations with constant coefficients, of which the solution shows that 
the motion may be considered as composed of two oscillations one of a 
period of the order of 2 seconds damped to half amplitude in 0.1 seconds, 
the other of period from 10 to 30 seconds not very strongly damped. 
The short oscillation appears never to be of importance in ordinary 
aeroplanes, but the long oscillation, being only moderately damped, may 
cause trouble, especially for an aeroplane that flies with a large angle of 
incidence for the wings. 
The calculation of the period and damping of the long oscillation was 
repeated for several speeds from highest to lowest corresponding to small 
and large angles of incidence with the results shown in the following 
table: 
Aeroplane* SSSS UU UU 
Velocity, miles-hour 76.9 53.4 44.6 36.9 79 51.8 47 44.2 
Incidence of wings 0? 30? 6? 12? 1? 7? 10? 14? 
Period, seconds 34.7 17.6 15.8 10.56 34.0 16.7 13.7 11.5 
Damp 50 per cent, seconds 8.1 11.0 13.1 — 11.0 17.7 63.0 — 
Double amplitude, seconds — — — 24.7 — — — 24.7 
* The letters S and U represent respectively the machine designed for inherent stability 
and a standard military tractor. 
InstabiHty at low speed. — It appears that the period becomes much 
more rapid at low speed, that at some critical speed the damping van- 
ishes, and below this speed both aeroplanes become frankly unstable. 
This instability at extreme low speed is common to all aeroplanes and 
the only advantage of our 'stable' aeroplane S is that its longitudinal 
motion is stable down to about 40 miles per hour while aeroplane U is 
stable only down to about 47 miles per hour. 
A study of the relative magnitudes of the coefficients for these typi- 
cal aeroplanes leads to the conclusion that longitudinal instability at low 
