NAVWEPS O&601-80  BASIC AERODYNAMICS  lower surface lifts act along the same vertical  line.  An increase in.lift  on the symmetrical  airfoil produces  no change in this situation and  the center of pressure  remains fixed at the aero-  dynamic center.  $_{C%C. }$versus lift coefficient for several repre-.  sentative sections. The sign convention ap-  plied to moment coefficients  is that the nose-up  moment is positive.  The NACA Ooog  airfoil is a symmettical sec-  tion of 9 percent maximum thickness. Since  the mean line of this airfoil has no camber,  the coefhcient of moment about the aerody-  namic center is zero, i.e., the c.p. is at the ac.  The departure from zero cno.+  occurs  only as the  airfoil approaches  maximum lift and the stall  produces a moment change in the negative  (nose-down) direction.  The NACA 4412 and  63,-412 sections have noticeable positive cam-  ber which cause  relatively large moments about  the aerodynamic center. Notice that for each  sectionshowninfrgure 1.22, the c,,,....  isconstant  for all lift coefficients  less than cl,-.  The location of the aerodynamic center of an  airfoil is not affected  by camber, thickness, and  angle of attack. In fact, two-dimensional in-  compressible airfoil theory will  predict the  aerodynamic center at the 25 percent chord  point  for any airfoil regardless of camber, thickness,  and angle of attack. Actual airfoils, which  are subject to real fluid flow, may not have the  lift due to angle of .attack concentrated at the  exact 25 percent chord point.  However, the  actual location of the aerodynamic center for  various sections is rarely forward of 23 percent  or aft of 27 percent chord point.  The moment about the aerodynamic center  has its source in the relative pressure distribu-  tion and requires application of the coefficient  form of expression for proper evaluation. The  moment about the aerodynamic center is ex-  pressed  by the following equation :  The NACA 23012 airfoil is a very efficient  conventional section which has been used on  many airplanes. One of the features of the  ~section  is a relatively high c& with only a  small c,,,,,,; The pitching moment coefficients  1  for this section are shown on figure 1.22 along  with the effect of various type flaps added to  the basic section. Large amounts of camber  applied well aft on the chord cause large nega-  tive moment coefficients. This fact is illus-  trated by the large negative moment coefli-  cients produced by the 30” deflection of a 25  percent chord flap.  me  kc.  is a quantity determined by the  shape of the mean-camber line.  Symmetrical  airfoils have zero c,,,,. and the c.p. remains at  the a.~. in unstalled flight.  The airfoil with  positive camber will  which means the c.p. is behind the a.~. Since  the c5.c.  is constant in unstalled flight a certain  relationship between lift coefficient and center  of pressure can be evolved. An example of  this relationship is shown in figure 1.22 for the  NACA 63i-412 airfoil by a plot of c.p. versus  c,. Note that at low lift coefficients  the center  of pressure is well aft-even past the trailing  edge-and an increase in C~  moves the c.p, for-  ward toward the a.~. The c.9. approaches  the  where  The moment coefficient used in this equation is  the dimensionless ratio of the moment pressure  to dynamic pressure  moment and is a function  A&, = moment about the aerodynamic center,  a.c., ft.-lbs.  CMa.c,=coefbcient  of moment about the a.c.  q= dynamic pressure,  psf  S=wing area, sq ft.  c=chord, ft.  c  ML3.C.  %.c. = p-  of. the shape of the airfoil mean camber line.  Figure 1.22 shows the moment coefficient,  49  Revised Jmuoy  1965 