ENGINEERING: J. C. HUNSAKER 
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speed is due, first, to the decrease in damping of the tail surfaces on ac- 
count of the low speed and, secondly, to the decrease in rate of change of 
lifting force with change in attitude for high angles of incidence. The 
latter has a predominating effect on the damping of the long oscillation. 
Consequently, if an aeroplane is to be stable and land at a relatively slow 
speed, it must not operate at too great an angle of incidence. To sus- 
tain its weight it should therefore have a comparatively large wing area. 
The principal difference between aeroplanes S and U is that the former 
supports a weight of 3.55 pounds per square foot of wing area and the 
latter 5.2 pounds per square foot. 
The following recommendations are made for an aeroplane to have 
its longitudinal motion damped at lower speeds than is usual in practice : 
(1) Provided large horizontal surfaces of long arm for damping the 
pitching. (2) Provide wings of such area that the slow speed does not 
require a great angle of incidence. Roughly the safe slow speed should 
not require more than 80 per cent of the maximum lift of the wings. 
(3) Keep the longitudinal radius of gyration small by concentrating the 
principal weights. 
Slowness in pitching. — It may be imagined that a dynamically stable 
aeroplane of rapid period might be so violent in its motion that the pilot 
would be shaken about to such an extent as to be hindered in the per- 
formance of his military duties of observation, gun-fire, or bomb drop- 
ping. It appears that the expression representing the period of the long 
oscillation contains certain predominating coefficients, and a considera- 
tion of their magnitude leads to the following conclusions: The natural 
period of pitching is increased by: (1) High speed of flight, (2) Large 
damping surfaces on the tail, (3) Small angle of incidence, (4) Small 
righting moments. 
Lateral motion. — ^After measuring the aerodynamical coefficients, and 
the radii of gyration in roll and yaw, the dynamical equations for the 
asymmetrical or lateral motion may be set down. For small oscilla- 
tions these reduce, as in the longitudinal case, to three linear differential 
equations with constant coefficients. The determinant formed from the 
coefficients may be factored by use of approximate methods and the mo- 
tion may be compounded from that represented by each of three factors. 
Spiral Dive. — The first factor may correspond either to a damped or 
to an amplified motion. At high speeds model S shows a subsidence 
damped to half amplitude in 10.4 seconds. At lower speeds this damping 
diminishes and at 37 miles per hour the motion becomes a divergence 
which doubles in amplitude in 7.2 seconds. Aeroplane U is spirally un- 
stable at high speeds. Examination of the preponderating terms in the 
