NAVWEPS OO-BOT-BO  BASIC AERODYNAMICS  root chord but an MAC equal to two-thirds  ~ ‘ of the root chord.  If the planform has curvature and the aver-  age chord is not easily determined, an  alternate expression is:  The aspect ratio, taper ratio, and sweepback  of a planform are the principal factors which  determine the aerodynamic characteristics  of a  .wing.  These same quantities also have a defi-  nite influence on the structural weight and stiff-  ness of a wing.  The aspect ratio is a fineness ratio of the  wing and this quantity is very powerful in  determing the aerodynamic characteristics  and structural weight.  Typical aspect  ratios  vary from 33 for a high performance sail-  plane to 3.5 for a jet fighter to 1.28 for a  flying saucer.  (5) The raat chord, c,, is the chord at the  wing centerline and the rip chord, c,, is  measured at the tip.  DEVELOPMENT OF LIFT BY A WING.  In order to appreciate the effect of the planform  on the aerodynamic characteristics, it is neces-  sary to study the manner in which a wing  produces  lift.’  Figure 1.29 illustrates the three-  dimensional flow pattern which results when  the rectangular wing creates  lift.  (6) Considering the wing planform to  have straight lines for the leading and trail-  ing edges, the taper ratio, A (lambda), is the  ratio of the tip chord to the root chord.  J.f a wing is producing lift, a pressure  differ-  ential will exist between the upper and lower  surfaces,  i.e., for positive lift, the static pres-  sure on the upper surface will be less than on  the lower surface. At the tips of the wing,  the existence  of this pressure  differential creates  the spanwise flow components shown in figure  1.29: For the rectangular wing, the lateral  flow developed at the tip is quite strong and a  strong vortex is created at the tip.  The lateral  ‘ flow-and  consequent  vortex strength-reduces  inboard from the tip until it is zero at the  centerline.  The taper ratio affects the lift distribution  and the structural weight of the wing.  A  rectangular wing has a taper ratio of 1.0  while the pointed tip delta wing has a taper  ratio of 0.0.  (7) The sweep  angle, A (cap lambda), is  usually measured as the angle between the  line of 25 percent chords and a perpendicular  to the root chord. The sweep of a wing  causes definite changes in compressibility,  maximum lift, and stall characteristics.  The existence of the tip vortex is described  by the drawings of figure 1.29. The rotational  pressure  flow combines with the local airstream  flow to produce the resultant flow of the  trailing  vortex. Also, the downwash flow  field behind a delta wing is illustrated by the  photographs of figure 1.29. A tuft-grid is  mounted aft of the wing to visualize the local  flow direction by deflection of th,e tuft ele-  ments. This tuft-grid illustrates the existence  of the tip vortices and the deflected airstream  aft of the wing.  Note that an increase in  angle of attack increases  lift and increases  the  flow deflection and strength of the tip vortices.  (8) The mean aerodynamic  chord, MAC,  is the chord drawn through the centroid  (geographical center) of plan area. A rec-  tangular wing of this chord and the same  span would have identical pitching moment  characteristics. The MAC is located on the  reference  axis of the airplane and is a primary  reference  for longitudinal stability considera-  tions.  Note that the MAC is not the average  chord but is the chord through the centroid  of area. As an example, the pointed-tip  delta wing with a taper ratio of zero would  have an average chord equal to one-half the  Figure 1.30 illustrates the principal effect  of the wing vortex system. The wing pro-  ducing lift can be represented by a series of  AR = b2/.S  A=& 