moment about the lateral axis is studied in 
the coefficient form. 
or 
M = C,qS(MAC) 
M 
&= qS(MAC) 
where 
M=pitching moment about the c.g., ft.- 
lbs., positive if in a nose-up direction 
q= dynamic pressure, psf 
S= wing area, sq. ft. 
MAC=mean aerodynamic chord, ft. 
C,= pitching moment coefficient 
The pitching moment coefficients contributed 
by all the various components of the aircraft 
are summed up and plotted versus lift coeffi- 
cient. Study of this plot of C, versus C, 
will relate the static longitudinal stability 
of the airplane. 
Graph A of figure 4.5 illustrates the variation 
of pitching moment coefficient, C,, with lift 
coefficient, C,, for an airplane with positive 
static longitudinal stability. Evidence of 
static stability is shown by the tendency to re- 
,t,urn to equilibrium-or “trim”- upon dis- 
.,placement. The airplane described by graph A 
is in trim or equilibrium when C,=O and, if the 
‘airplane is disturbed to some different C,, the 
pitching moment change tends to return the 
aircraft to the.point of trim. If the airplane 
‘were disturbed to some higher C, (point Y), a 
negative or nose-down pitching moment is de- 
veloped which tends to decrease angle of attack 
back to the trim point. If the airplane were 
disturbed to some lower C,, (point X), a posi- 
tive, or nose-up pitching moment is developed 
which tends to increase the angle of attack 
back to the trim point. Thus, positive static 
longitudinal stability is indicated by a negative 
slope of C, versus C,, i.e., positive stability is 
evidenced by a decrease in CM with an increase 
in C,. 
The degree of static longitudinal stability is 
indicated by the slope of the curve of pitching 
moment coefficient with lift coefficient. Graph 
NAVWE,PS OO-ROT-80 
STABILITY AND CONTROL 
B of figure 4.5 provides comparison of the 
stable and unstable conditions. Positive sta- 
bility is indicated by the curve with negative 
slope. Neutral static stability would be the 
result if the curve had zero slope. If neutral 
stability exists, the airplane could be dis- 
turbed to some higher or lower lift coefficient 
without change in pitching moment coefficient. 
Such a condition would indicate that the air- 
plane would have no tendency to return to 
some original equilibrium and would not hold 
trim. An airplane which demonstrates a posi- 
tive slope of the C, versus C, curve would be 
unstable. If the unstable airplane were subject 
to any disturbance from equilibrium at the 
trim point, the changes in pitching moment 
would only magnify the disturbance. When 
the unstable airplane is disturbed to some 
higher CL, a positive change in C, occurs which 
would illustrate a tendency for continued, 
greater displacement. When the unstable air- 
plane is disturbed to some lower C,,, a negative 
change in C, takes place which tends to create 
continued displacement. 
Ordinarily, the static longitudinal stability 
of a conventional airplane configuration does 
not vary with lift coefficient. In other words, 
the slope of C, versus CL does not change with 
CL. However, if the airplane has sweepback, 
large contribution of power effects to stability, 
or significant changes in downwash at the 
horizontal tail, noticeable changes in static 
stability can occur at high lift coefficients. 
This condition is illustrated by graph C of 
figure 4.5. The curve of C, versus CL of this 
illustration shows a good stable slope at low 
values of CL. Increasing CL effects a slight 
decrease in the negative slope hence a decrease 
in stability occurs. With continued increase 
in C,, the slope becomes zero and neutral 
stability exists. Eventually, the slope be- 
comes positive and the airplane becomes un- 
stable or “pitch-up” results. Thus, at any 
lift coefficient, the static stability of the air- 
pl.ane is depicted by the slope of the curve of 
CM versus CL. 
251