NAVWE,PS OO-ROT-80  STABILITY AND CONTROL  moment about the lateral axis is studied in  the coefficient form.  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.  The degree of static longitudinal stability is  indicated by the slope of the curve of pitching  moment coefficient with lift coefficient. Graph  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 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.  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  where  or  M = C,qS(MAC)  M  &= qS(MAC)  251 